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Fundamentals of Modern Audio Measurement

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					Fundamentals of Modern
  Audio Measurement
       Richard C. Cabot, AES Fellow
 Audio Precision, Inc. Beaverton, Oregon 97075, USA




                           Reprinted by permission from
                           the Journal of the Audio Engineering Society
                                                       Richard C. Cabot, AES Fellow
                                             Audio Precision, Inc., Beaverton, Oregon 97075 USA

                     Fundamental concepts in testing audio equipment are reviewed, beginning with an ex-
                     amination of the various equipment architectures in common use. Several basic ana-
                     log and digital audio measurements are described. Tradeoffs inherent in the various
                     approaches, the technologies used, and their limitations are discussed. Novel tech-
                     niques employing multitone signals for fast audio measurements are examined and ap-
                     plications of sampling frequency correction technology to this and conventional FFT
                     measurements are covered. Synchronous averaging of FFTs and the subsequent noise
                     reduction are demonstrated. The need for simultaneity of digital and analog generation
                     is presented using converter measurements as an example.




Introduction                                             Other times it is due to the peculiarities                               ments and their use in practical engi-
Characterizing professional and con-                     of the audio industry. Other fields deal                                 neering and production applications.
sumer audio equipment requires tech-                     with some of the same measurements as                                       Audio has been an analog world for
niques which often differ from those                     those in audio. From level and THD to                                    most of its life. The last 15 years have
used to characterize other types of                      jitter and noise modulation, no other                                    seen a steady increase in the use of
equipment. Sometimes this is due to the                  field has the breadth of requirements                                    digital technology, including the digital
higher performance requirements.                         found in high performance audio.                                         recorder, digital effects units, the com-
                                                             Performing these measurements re-                                    pact disc, digital mixing consoles and
                                                         quires a knowledge of the tradeoffs in-                                  lossy data compression systems. Each
*Presented at the 103rd Convention of the Audio          herent in the various approaches, the                                    has necessitated its own collection of
Engineering Society, New York, NY, USA, 1997
September 26–29, revised 1999 August 8.
                                                         technologies used, and their limita-                                     new measurements for the new prob-
                                                         tions. We will examine these measure-                                    lems introduced.

                                                                      ANALOG    ANALOG
                                                                                                  BAL/UNBAL
                                                                      OUTPUT     INPUT            AMPLIFIER



                                         VAR           BALANCING OUTPUT                      ATTEN
                                         GAIN AMPLIFIER CIRCUITS ATTENUATOR                                            12.345 kHz
                                                                                      TERM        BAL/UNBAL
                                                                                                  AMPLIFIER             FREQUENCY
                                                                                                              LEVEL      COUNTER
                                                                                                                                             NOTCH/     WEIGHTING         LEVEL
                                                                                                                                            BANDPASS     FILTER           METER
                                         VAR           BALANCING OUTPUT                      ATTEN
                                         GAIN AMPLIFIER CIRCUITS ATTENUATOR                                            12.345 kHz
                                                                                      TERM
                                                                                                                        FREQUENCY
                                                                                                              LEVEL      COUNTER                        A/D

                                                                                                                                            MUX
                                                                                                                                                        A/D
              RAM         DSP          D/A
                                                   NORMAL    COMMON
                                                    MODE      MODE
                                                                                                                                                               STATUS BIT
                                                                                                      A/D                RAM
                                                                                                                                                                DISPLAY
                                                                      DIGITAL   DIGITAL
                                                                      OUTPUT     INPUT
                          DIGITAL                    IMPAIRMENT                                                         DIGITAL
                        INTERFACE                                                                                     INTERFACE     AUDIO         DSP
                                                       CIRCUITS                                                                     DATA

                                                                                                     12,345 kHz                                                 DISPLAY

           REF OUT                                                                                     SAMPLE                                     RAM
                         CLOCK                                                        AMPLITUDE         FREQ
                       GENERATOR                                                                                        JITTER
                                      JITTER
            REF IN                  GENERATOR
                         CLOCK
                        EXTRACT




Fig. 1. Dual-domain audio measurement system.
Fundamentals of Modern Audio Measurement

Dual Domain Measurement                                systems. By using internal A/D and D/A                               done this way, such as active bits mea-
Characterizing modern audio equip-                     converters it also added the ability to                              surements and bit error rate
ment requires operating in both analog                 perform many analog measurements                                     measurements.
and digital domains. Measurement                       which were previously not included in                                   Another approach, used in several
equipment and techniques for analog                    the system (such as FFT-based spectrum                               commercial instruments, is shown in
systems are well established (Metzler                  analysis and fast multitone measure-                                 Fig. 3. All signals are generated in the
1993). Signal generation was usually                   ments). This also allowed measure-                                   digital domain through dsp algo-
done with analog hardware signal gen-                  ments which were previously impossi-                                 rithms. If analog signals are needed,
erators. Signal measurement was usu-                   ble, such as bit error measurements on                               they are created by passing the digital
ally done with analog filters and ac to dc             digital processing equipment which                                   signal through a D/A converter. Con-
conversion circuits. In recent years these             only have analog ports available. This                               versely, all signals are analyzed in the
were connected to microprocessors or                   was followed in 1995 by the next gener-                              digital domain, and analog signals to
external computers for control and dis-                ation Dual Domain System Two (see                                    be measured are converted by an in-
play. In 1989, with the increasing preva-              Fig. 1).                                                             ternal A/D converter. This approach
lence of digital audio equipment, Audio                   Other manufacturers have intro-                                   has the advantage of simplicity, since
Precision introduced the first Dual                    duced test equipment for measuring                                   much of the measurement and genera-
Domain1 audio measurement system. It                   combined analog and digital audio                                    tion hardware is re-used for all opera-
maintained the traditional use of analog               equipment. One approach uses an                                      tions.
hardware for analog signal generation                  AES-3 digital interface receiver circuit                                However, hardware simplicity co-
and measurement, and added the abil-                   and a D/A converter in front of a con-                               mes at a price. The signal generation
ity to generate and measure digital au-                ventional analog instrument to allow                                 performance of current technology
dio signals directly in the digital domain.            measuring digital signals. All measure-                              D/A converters is not equivalent to
This allowed all combinations of simul-                ments must go through the digital to                                 what can be achieved with high per-
taneous analog and digital generation                  analog reconstruction process and suf-                               formance analog electronics. The
and measurement, enabling the mea-                     fer the limitations of the converter and                             measurement performance of A/D
surement of A/D converters, D/A con-                   reconstruction filter used. This tech-                               converters is similarly limited by avail-
verters, digital processing equipment,                 nique, illustrated in Fig. 2, allows an                              able devices. Indeed, it is difficult to
etc. in addition to the usual all-analog               inexpensive, albeit less accurate,                                   characterize state-of-the-art convert-
                                                       method of making measurements on                                     ers when the equipment performing
1
  Dual Domain and System Two are trademarks of         digital domain signals. Some inher-                                  the measurements uses commercially
Audio Precision, Inc.                                  ently digital measurements cannot be                                 available converter technology. These



                                                                    ANALOG    ANALOG
                                                                                                BAL/UNBAL
                                                                    OUTPUT     INPUT            AMPLIFIER

                                                    BALANCING
                                                    AMPLIFIER
                                                                                           ATTEN
                                                                  OUTPUT
                                                                ATTENUATOR          TERM        BAL/UNBAL
                D/A                                                                             AMPLIFIER
                                    VAR
                                    GAIN

                                                                                           ATTEN
                                                                                                                                         NOTCH/    WEIGHTING     LEVEL
                                                                                    TERM                                                BANDPASS    FILTER       METER




                                                                                                                                                   12.345 kHz
                  RAM         DSP                                                                                                                                LEVEL
                                                                                                                                                   FREQUENCY     METER
                                                                                                                                                    COUNTER



                                                                    DIGITAL   DIGITAL
                                                                    OUTPUT     INPUT
                             DIGITAL                                                                              DIGITAL         D/A
                                                IMPAIRMENT
                           INTERFACE                                                                            INTERFACE                               STATUS BIT
                                                  CIRCUITS
                                                                                                                                                         DISPLAY
                                                                                                   12.345 kHz
                                                                                                     SAMPLE
                            CLOCK                                                   AMPLITUDE         FREQ
                          GENERATOR                                                                               JITTER

                                       JITTER
                                       SIGNAL

                REF IN
                            CLOCK
                           EXTRACT




Fig. 2. Simple Mixed Signal Audio Measurement System.
                                                                  ANALOG    ANALOG
                                                                                             BAL/UNBAL
                                                                  OUTPUT     INPUT           AMPLIFIER

                                                  BALANCING
                                                  AMPLIFIER                                                                                       RAM
                                                                                         ATTEN                NOTCH
                                                                OUTPUT
                                                              ATTENUATOR                                      FILTER
       D/A                                                                        TERM      BAL/UNBAL
                                                                                            AMPLIFIER
                                       VAR                                                                                                         DSP
                                       GAIN                                                                                     A/D

                  LOWPASS                                                                ATTEN                NOTCH
                                                                                                              FILTER
                                                                                  TERM




                                                                                                                                                 DISPLAY
         RAM          DSP                           COMMON MODE
                                                       SIGNAL


                                                                                          AMPLITUDE                JITTER
                                                                  DIGITAL   DIGITAL        MEASURE                MEASURE
                                                                  DIGITAL
                                                                  OUTPUT     INPUT
                                                                   OUTPUT
                    DIGITAL                   IMPAIRMENT                                                            DIGITAL   AUDIO DATA
                  INTERFACE                     CIRCUITS                                                          INTERFACE
                                                                                                                              STATUS BITS
                                                                                                 12.345 kHz
      REF OUT                                                                                      SAMPLE
                    CLOCK                                                                           FREQ
                  GENERATOR

                              JITTER
                              SIGNAL
      REF IN
                    CLOCK
                   EXTRACT




Fig. 3. Typical Mixed Signal Audio Measurement system.

limitations include frequency response                capable of making interface jitter                          easily accomplished by analog means.
irregularities which exceed 0.01 dB                   susceptibility measurements on A/D                          The D/A converters are used for
and distortion residuals which rarely                 converters or D/A converters. It cannot                     multitone waveforms, shaped bursts,
reach 100 dB THD+N. Consequently,                     generate digital and analog signals si-                     sines with interchannel phase shift (use-
several of the available instruments                  multaneously, nor can it generate a                         ful for testing surround sound decod-
which use this approach add a true an-                digital signal simultaneous with the jit-                   ers), etc. With the exception of multitone
alog signal generator for high perfor-                ter embedded on its clock or simulta-                       signals, these waveforms tend to have
mance applications. They also add an                  neous with the common mode inter-                           lower nonlinearity requirements than
analog notch filter in front of the A/D               face signal. This prevents testing                          the other waveforms.
converter for high performance analy-                 AES/EBU interface receiver operation                           Testing state-of-the-art A/D con-
sis. As we will see later, this negates               under worst case conditions. The Dual                       verters to their performance limit re-
much of the cost and complexity ad-                   Domain approach does allow any                              quires a dedicated analog oscillator to
vantages of the all-digital approach,                 cross domain testing without compro-                        achieve adequate THD+N. Several
while retaining most of its problems.                 mise since all signals are simulta-                         manufacturers have added tunable or
   These evolved mixed signal archi-                  neously available, enabling complete                        switchable lowpass filters to d/a based
tectures do not qualify as Dual                       characterization of mixedsignal de-                         generators in an attempt to achieve
Domain because neither signal gener-                  vices under test.                                           analog oscillator harmonic distortion
ation nor analysis can be done simul-                                                                             performance. These have met with
taneously in both domains. Simulta-                   Signal Generation                                           varying degrees of success. The trade-
neity of signal generation in the analog              Audio testing generally uses sinewaves,                     off between sharpness of filtering (and
and digital domains is a critical issue               squarewaves, random noise, and com-                         the corresponding distortion reduc-
for many types of testing, especially in-             binations of those signals. The dual do-                    tion) and flatness is difficult to balance.
volving converter and interface per-                  main approach described earlier uses                        Sharper filters need a finer degree of
formance. In many ways the need to                    multiple oscillators or waveform gener-                     tunability and have more response rip-
simultaneously jitter the active digital              ators in the analog domain to optimize                      ples, making the signal amplitude fluc-
audio signal, as well as drive an analog              performance. Digital to analog con-                         tuate with frequency. These filters also
signal, creates a third domain. The                   verter based generation is used when                        require more switchable elements,
mixed signal architecture shown is in-                particular waveform generation is not                       which introduce more noise and dis-
Fundamentals of Modern Audio Measurement

tortion. Therefore most high                                                                                      A smaller amplitude ver-
quality audio measurement                     +0
                                                                                                               sion of this same signal is
equipment includes a provi-                  -20
                                                                                                               shown in the time domain in
sion for a dedicated analog                  -40
                                                                                                               Fig. 5. The upper trace shows
oscillator which is used for                 -60
                                                                                                               the sinewave with no dither.
THD+N testing.                         d
                                       B
                                       F
                                           -80
                                                                                                               The samples are limited to 16
   Digital sinewaves may be            S -100
                                                                                                               bit resolution, which results
generated in several different           -120
                                                                                                               in the familiar digital stair
ways. The most common are                -140
                                                                                                               step waveshape. Note that
table look-up and polynomial             -160
                                                                                                               each cycle repeats the same
approximation. The table                 -180
                                                         0    2.5k        5k          7.5k        10k          sample values. The lower
                                                                                                            12.5k   15k       17.5k              20k


look-up method is fast but                                                                                     trace shows the same
                                                                                                  Hz



suffers from time resolution                                                                                   sinewave with triangular
limitations driven by the lim- Fig. 4. Illustration of distortion reduction in return for higher noise         dither. The sample values are
ited length of the table. Com- floor with the addition of dither.                                              different on each cycle,
mercial direct digital synthesis                                                                               though they still are re-
chips are implemented this                      Audio Precision
                                              0.05                                                             stricted to the 16 bit system
                                                                                                                                          04/17/97 14:16:46



way. Theoretical analyses (for                0.04                                                UNDITHERED   resolution. The middle trace
example Tierney et al, 1971)                  0.03
                                                                                                               shows the average of 64 of
have shown that the sine rom                  0.02
                                                                                                               the dithered sinewaves. The
length should be at least 4                   0.01
                                                                                                               same sample values now av-
                                                                                                                     TRIANGULAR DITHER,
                                                                                                                         64 AVERAGES


times the data width output                                                                                    erage out to values between
                                         %
                                         F       0

                                         S


from the rom. This makes the                 -0.01

                                                                                                               that limited by the 16 bit sys-
distortion introduced by                     -0.02

                                                                                                               tem. Dither randomizes the
                                                                                                                    TRIANGULAR DITHER




quantization in the sample                                                                                     limited resolution of the 16
                                             -0.03




timing equal to the distortion                                                                                 bit system into a smooth
                                             -0.04




introduced by quantization in                                                                                  waveform with resolution
                                             -0.05
                                                     0       500u    1m        1.5m          2m      2.5m      3m   3.5m        4m        4.5m         5m

                                                                                                     sec

the data word. Both of these                                                                                   much better than the sample
errors may be converted to                                                                                     resolution permits.
                                   Fig. 5. Effectiveness of dither illustrated with 16 bit quantized signal.
white noise through proper
use of dither or error feedback                                                                                Complex Signal
techniques. The polynomial                     also prime to the 44.1 kHz consumer                             Generation
approximation technique yields sine            standard sampling frequency.                         The multitone techniques discussed
accuracies dependent on the number                 Dither is one of the most misunder-              later require a means of generating mul-
of terms in the power series expansion         stood aspects of digital signal genera-              tiple sinewaves simultaneously. For
used. Arbitrarily accurate signals may         tion. When a signal is created in a finite           small numbers of sines this may be done
be obtained at the expense of compu-           word length system, quantization                     with real-time computation of each sine
tation time.                                   distortion      will      be     introduced.         in a dsp and subsequent summation.
   Finger (1986) has shown that                Vanderkooy and Lipshitz (1987) have                  For larger numbers of tones rom or ram
proper signal generation in digital sys-       shown that the proper addition of                    based waveform generation is normally
tems requires that the generated fre-          dither to the signal before truncation to            used. For analog applications this is
quencies be relatively prime to the            the final word width will randomize the              passed through a D/A converter. The
sample rate. If frequencies are used           distortion into noise. This comes at a               rom size sets the waveform length be-
which are submultiples of the sample           3dB (overall) increase in the back-                  fore repeating, and therefore sets the
rate, the waveform will exercise only a        ground noise level. However, it allows               minimum spacing of tones. The typical
few codes of the digital word. For ex-         the generation of signals below the                  size in commercial equipment is 8192 or
ample, generating 1 kHz in a 48 kHz            system noise floor, and it frees large               16384 points which gives an approxi-
sample rate system will require only 48        amplitude signals of any distortion                  mately 6 or 3Hz spacing respectively at
different data values. This may leave          products far below the system noise                  a 48 kHz sample rate.
large portions of a converter untested.        floor. This is illustrated in Fig. 4 which              Other waveforms such as those
If frequencies are used which are              shows two FFTs of a 750 Hz tone over-                used for monotonicity testing of A/D
prime to the sample rate then eventu-          laid on the same axes. The first is with             converters may be created using table
ally every code in the data word will be       16 bit resolution, but no dither. The                look-up techniques, or they may be
used. Using 997 Hz instead of 1 kHz            second is with correct amplitude trian-              computed in real time. For signals
will result in all codes of a digital sys-     gular dither. Dither randomizes the                  which do not need control of their pa-
tem (operating at standard sample              distortion products into a smooth                    rameters such as repetition rate or fre-
rates) being exercised. This frequency         noise floor below the peak level of the              quency, the look-up table approach
makes a good “digital 1 kHz” since it is       distortion.                                          has a speed advantage. It does how-
ever consume more memory or re-                Exponential averaging uses a first    been used in dsp based measurement
quires downloading from disk. The al-       order running average (single pole in    systems for many years (Mahoney
gorithmic approach offers complete          analog filter terms) which weights the   1987) and has even been included in
control of waveform parameters, al-         most recent portion of the waveform      an analog based audio measurement
lowing signals such as shaped bursts or     more heavily than the earlier portion.   system (Amber 1986). When measur-
walking bit patterns to be adjusted to      This is the most commonly used tech-     ing simple periodic signals which con-
the use’rs needs. The available mem-        nique for analog based implementa-       tain little noise this technique can yield
ory size and instrument architecture        tions and has the benefit of making no   repeatable        measurements         very
usually impacts this greatly. At least      assumptions about the waveform peri-     quickly. Arbitrarily short measurement
one commercial piece of audio test          odicity. It is merely necessary that the intervals may be used with no loss in
equipment derives all waveforms from        signal being measured have a period      accuracy, as long as the integer num-
disk files, though most use the algorith-   shorter than a fraction of the averaging ber of cycles constraint is obeyed.
mic approach.                               time. The fraction sets the accuracy of  However most implementations will
    Most audio devices are multichan-       the measurement, creating a mini-        yield unstable or inaccurate results for
nel. The usual approach to multichan-       mum measurement frequency for a          noisy signals or inharmonic signals
nel testing is to use a single generator    given accuracy. For complex signals,     such as imd waveforms, since the inte-
with a single variable gain stage which     not only must each component meet        ger averaging constraint is inherently
is switched between two or more out-        the minimum frequency value, but         violated. Hence, it must be used with
put channels. This can cope with sim-       their spacing in the frequency domain    care when measuring complex signals
ple crosstalk or separation measure-        must also meet the minimum fre-          or when used for distortion or sig-
ments, but cannot handle more               quency requirement. The accuracy of      nal-to-noise ratio measurements.
complex versions of these. For exam-        exponential rms converters is better     When this approach is applied to
ple: crosstalk measurements with            than the measurement repeatability or    sinewave frequency response sweeps,
multitone signals require different fre-    fluctuation due to ripple in the com-    the resulting speed can be quite im-
quency tones in the two channels;           puted value. This fluctuation may be     pressive. However, because of errors
measuring                  cross-channel    reduced without increasing the aver-     in finding the zero crossings on digi-
intermodulation requires different fre-     aging time by post filtering the rms     tized signals, the repeatability can
quency sinewaves in the two channels;       value. The optimum combination of        leave something to be desired. Fig. 6
record/reproduce measurements of            averaging time and post filtering char-  shows the results of 10 frequency re-
tape recorder saturation characteris-       acteristics is well known (Analog De-    sponse sweeps of a commercial system
tics requires the ability to make one       vices 1992).                             which uses this technique. Note that
channel sweep frequency while the              Uniform averaging computes the        the error is approximately ±0.02 dB
other sweeps level so the frequency         rms average of the signal over a fixed   over most of the frequency range, ris-
sweep may be used to identify the           time period where all portions of the    ing to ±0.05 dB at high frequencies.
original channel’s amplitude at each        signal have equal weight. Theoretical       This error can be compensated for if
step. The common output amplifier           analyses of rms amplitude typically      corrections for the fractional portion of
splitting to multiple output connectors     make the averaging time a fixed inter-   the sinewave cycle are computed.
also means that there will be a com-        val, which is then shown to directly af- These corrections are dynamic,
mon connection between channels             fect the error in the measurement.       changing from cycle to cycle with the
that may affect measured separation.        Longer time intervals yield more accu-   phase of the waveform relative to the
It also prevents adjusting the two chan-    rate and repeatable measurements at      sampling instants at both the begin-
nels of a stereo device for maximum         the expense of
output if the gains differ slightly.        measurement time.
                                               This error may
Amplitude (Level) Measurement               be eliminated for
The most basic measurement in audio is      periodic signals if
amplitude, or “level”. There are many       the averaging in-
techniques for doing this, but the math-    terval is made an
ematically purest way is the root mean      integer multiple of
square value. This is representative of     the signal period.
the energy in the signal and is computed    This technique is
by squaring the signal, averaging over      normally referred
some time period and taking the square      to as “synchronous
root. The time period used is a parame-     rms conversion”
ter of the measurement, as is the type of   since the averag-
averaging employed. The two ap-             ing interval is syn-
proaches to averaging in common use         chronous to the Fig. 6. Frequency response flatness variation due to errors in period
are exponential and uniform.                signal. This has computation.
Fundamentals of Modern Audio Measurement

ning and end of the zero crossing. The                  proportional to the frequency of the           limitations. The FFT is merely a faster
graph in Fig. 7 illustrates the flatness of             highest frequency component in the             method of computing the discrete Fou-
a cycle based rms converter using                       spectrum, and to its proportion of the         rier transform. The discrete Fourier
these enhancements. Note the tenfold                    total signal energy. This problem may          transform determines the amplitude of a
difference in graph scale compared to                   be reduced to any desired significance         particular frequency sinewave or
Fig. 6.                                                 by interpolation of the waveform and           cosinewave in a signal. The algorithm
    The simplest technique for ampli-                   peak determination on the higher               multiplies the signal, point by point, with
tude measurement of analog signals,                     sample rate version.                           a unit amplitude sinewave. The result is
rectification and averaging, is ex-                         Quasi-peak amplitude measure-              averaged over an integer number of
tremely difficult for digital signals. The              ments are a variant of the peak value          sinewave cycles. If the sinewave is not
rectification process is nonlinear and                  measurement where the effect of an             present in the signal being analyzed, the
creates harmonics of the signal which                   isolated peak is reduced. This tech-           average will tend to zero. This process is
will alias based on the finite sample                   nique was developed to assess the au-          repeated for a unit amplitude
rate. For very low frequency signals                    dibility of telephone switch gear noise        cosinewave, since the sine and cosine
this is not a problem, since the har-                   in the days when telephone systems             are orthogonal. Again, if the
monic amplitudes decrease with in-                      used relays and electromagnetically            cosinewave is not present, the average
creasing order and are adequately                       operated rotary switch devices. The            will tend to zero. If there is some of the
small by the time the folding frequency                 clicks that these devices could intro-         sine or cosine wave present, the average
is reached. However, high frequency                     duce into an audio signal were more            will be proportional to the amplitude of
signals have enough energy in the har-                  objectionable than their rms or aver-          the component in the signal. The rela-
monics that the average value ob-                       age amplitude would imply. This tech-          tive proportion of sine and cosine com-
tained will depend on the phase align-                  nique spread from its origins in the           ponents at a given frequency, along with
ment of the aliased components and                      telecom world to the professional au-          their polarities, represents the phase.
the original signal. The result is beat                 dio world, at least in Europe, and has             If this process is repeated for each
products between these components                       lasted long after the problem it was de-       hypothetical          sinewave         and
which yield fluctuating readings.                       vised to characterize disappeared.             cosinewave whose period is an integer
    Peak measurements have a similar                    This measurement is implemented                submultiple of the waveform length,
problem with limited bandwidth. The                     with a full wave rectification and lim-        several redundancies will occur in the
peak value of the signal values is easy                 ited attack and decay time averaging,          computation. By eliminating these re-
to determine in software, and several                   similar audio compressor implementa-           dundancies the number of operations
instruments supply this as an indicator                 tions. The implementation techniques           may be reduced. The resulting simpli-
of potential signal clipping. However,                  in the digital domain are similar.             fied process is called the FFT.
the peak value of the analog signal that                    Any measurement system which                   Since all hypothetical sine and co-
the samples represent may well be dif-                  implements analog amplitude mea-               sine frequencies in the FFT are multi-
ferent. This difference increases with                  surements with dsp techniques by digi-         ples of the reciprocal of the waveform
signal frequency. When a digital signal                 tizing the original analog signal must         length, the analysis is inherently equal
is converted to analog (or when an an-                  consider the effects of converter re-          resolution in the frequency domain.
alog signal is sampled) the sample val-                 sponse ripple. This can be substantial,        This analysis also presupposes that the
ues may not fall on the signal peaks. If                exceeding 0.01 dB for some commer-             signal components are at exact multi-
the samples straddle a peak, the peak                   cial devices. The effect of these ripples      ples of the reciprocal of the waveform
value will be higher, unless the signal is              adds directly to the response error in         length; serious problems occur when
a square wave. This error is directly                   the rms algorithm itself and may be a          this is violated. Stated differently, the
                                                                         significant portion of        FFT assumes that the waveform being
                                                                         the instrument flatness       analyzed is periodic with a period
   +0.009
   +0.008
                                                                         specification.                equal to the length of the data record
   +0.007
   +0.006
                                                                                                       being analyzed (Fig. 8). Consequently,
   +0.005
   +0.004
                                                                          FFT                          if the beginning and end of the record
   +0.003
   +0.002
                                                                          Measurements                 do not meet with the same value and
  d
  B
   +0.001
         +0
                                                                          With the advent of inex-     slope when looped back on them-
                                                                          pensive digital signal       selves the discontinuity will result in ar-
  F
  S -0.001
    -0.002
    -0.003
    -0.004
                                                                          processing devices, the      tifacts in the spectrum. The usual way
    -0.005
    -0.006
                                                                          FFT has become a             to deal with this is to “window” the
    -0.007
    -0.008                                                                commonplace audio            data and drive its value to zero at the
    -0.009

     -0.01
                                                                          measurement tool. To         end points. This turns the waveform
                                                                          obtain accurate mea-         into a “shaped burst”, whose spectrum
             10   20   50   100   200   500   1k   2k    5k   10k   20k
                                        Hz



                                                                          surements, it is essential   is the convolution of the window spec-
Fig. 7. Period-based rms measurement flatness variation with a            to understand its opera-     trum and the signal spectrum.
fractional sample compensation.                                           tion, capabilities and           There are approximately as many
different window functions as there are                            chronous to the sample rate. The high-                        asynchronous signals and so allows
papers about windowing. Everyone                                   est sidelobe amplitude is indicative of                       accurate measurements of discrete
has designed their own, probably so                                the ability to resolve a small amplitude                      tones. The Dolph-Chebyshev win-
they can put their name on it and get a                            tone close to a large amplitude tone.                         dows keep all sidelobes an equal dis-
piece of fame. From a practical view-                              The sidelobe roll-off indicates the effi-                     tance down from the peak and so offer
point, very few windows are necessary                              ciency of the window at large distances                       the optimum resolution of small ampli-
for audio measurements. To under-                                  from the main tone.                                           tude tones, but at the expense of
stand the advantages, or lack thereof,                                The simplest window in common                              somewhat larger -3 dB bandwidth.
of the various windows we will start                               use is the Hann window, named after                           The Dolph-Chebyshev windows are a
with the performance metrics of win-                               its inventor, Austrian astronomer Jul-                        family of windows allowing specifica-
dows. Most important are the -3 dB                                 ius von Hann (often incorrectly called                        tion of the desired sidelobe level and
                                                                                                                                 consequently the worst-case spurious
     Signal to be analyzed
                                                   Signal acquisition block            Fig. 8. Discontinuity                     peak in the spectrum (neglecting FFT
                                                                                       in analysis record                        distortion products, which are dis-
                                                                                       resulting from                            cussed below). The Audio Precision
                                                                                       asynchronous signal                       170 dB version specified here as
                                                                                       acquisition.
                                                                                                                                 “Equiripple” was chosen to produce
                                                                                                                                 spurs comparable in magnitude to the
                                                                                                                                 noise floor of 24-bit digital systems.
      Signal as it appears
       in analysis buffer                                                                                                           An approach developed by this au-
                                                                                                                                 thor called frequency shifting results in
                                                                                                                                 large improvements over the window-
                                                                                                                                 ing approaches. The FFT assumes that
                                                                                                                                 any signal it analyzes has a period that
                                     Signal analysis block
                                                                                                                                 is an integer fraction of the acquisition
                                                                                                                                 time. If the record does not contain an
                                                                                                                                 integer number of periods, a window
bandwidth (in bins), the worst case                                the Hanning window because of con-                            must be used to taper the ends of the
amplitude accuracy or scalloping loss,                             fusion with the Hamming window,                               acquired waveform to zero. The win-
the highest sidelobe amplitude and the                             named after Richard Hamming). The                             dow will smear the sine in the fre-
sidelobe roll-off. Fig. 9 illustrates these                        Hann window does allow good differ-                           quency domain, reducing the ability to
parameters for several representative                              entiation of closely spaced equal am-                         resolve sidebands on the signal and
windows. The -3 dB bandwidth is an                                 plitude tones and, because it is a raised                     consequently the ability to resolve low
indicator of the ability to resolve two                            cosine wave, is very easy to compute.                         frequency jitter sidebands, noise side-
closely spaced tones which are nearly                              The Blackman-Harris 4-term 94 dB                              bands or the ability to measure har-
equal in amplitude. The scalloping loss                            window      (one     of   the      many                       monics of low frequency tones. If, after
is the maximum variation in measured                               Blackman-Harris windows) offers a                             acquisition, the sample rate of the
amplitude for a signal of unknown fre-                             good balance of attenuation (94 dB to                         waveform is changed to make an inte-
quency. This indicates the worst case                              the highest sidelobe) and moderate -3                         ger number of signal periods fit in the
measurement error when displaying                                  dB bandwidth. The flat-top window                             acquired record, there will not be any
isolated tones which may be asyn-                                  offers negligible amplitude error for                         need for a window. This allows the am-

                                                                                                     +0
                                       Rectangular Window
                                                                                                                         NO WINDOW
        0                                                                                            -20

                                 Main Lobe
                                                              Highest                                -40
        -5
                Side Lobes                       Width       Sidelobe
                                                             Amplitude                               -60                                            FLAT TOP
       -10                                                                                                                HANN                                 BLACKMAN-HARRIS
                                                                                                                                                                    (BH-4)
                                                                                                     -80
       -15                                                                                      d          EQUI-RIPPLE
                                                                                                B   -100
  Mag                                                                                           F
  (dB) -20                                                                                      S
                                                                                                    -120

       -25                                                                                          -140


       -30                                                                                          -160


       -35                                                                                          -180


       -40                                                                                          -200
                                                                                                           11.96k                11.98k    12k      12.02k            12.04k
         -0.5                -0.25                 0                  0.25      0.5                                                        Hz




Fig. 9. Illustration of Window Parameters.                                               Fig. 10. Effective response of various windows.
Fundamentals of Modern Audio Measurement

plitude of neighboring bins to be re-                    transformed into the frequency do-           rate and corresponding data averaging
solved to the full dynamic range of the                  main.     An     example     of    this      are used to determine this time interval.
FFT and component amplitudes to be                       measurement is the distortion intro-         At low frequencies, the measurement is
correctly measured without scalloping                    duced by a compressor on a tone burst        typically made over one cycle of signal
loss. This allows devices such as A/D                    during its attack, sustain and release       while at high frequencies, many cycles
converters to be tested with signals                     operations. By performing a short FFT        are used.
which are not a submultiple of the                       every few milliseconds through the ac-          Spectrum peak based techniques
sample rate. This maximizes the num-                     quired record the distortion products        have been around since spectrum an-
ber of codes tested and maximizes the                    may be studied.                              alyzers were invented. The concept is
creation of spurious tones.                                                                           simple enough: if you know the shape
    Fig. 11 illustrates the operation of                 Frequency Measurement                        of the filter used to make the spectrum
this sample rate adjustment for an 18                    There are two basic approaches to mea-       measurement, you can interpolate the
Hz sinewave. The three traces are the                    suring frequency: zero crossing based        exact location of the spectrum peak
unwindowed version, the equiripple                       schemes and spectrum peak localiza-          and therefore determine the fre-
windowed version and the frequency                       tion based schemes. Zero crossing            quency. This assumes two things: that
shifted version. Each has been aver-                     counting has been used for decades on        there is only one frequency compo-
aged 64 times. Note the complete ab-                     analog signals in stand-alone frequency      nent within the filter bandwidth, and
sence of window-induced spreading                        counters. In a simple sense, the number      that the filter shape does not change as
and the 150 dB dynamic range ob-                         of zero crossings occurring during a         a function of frequency or signal
                                                                                                      phase. These limitations are not se-
     +0                                                                      Fig. 11. Selectivity     vere, and this technique offers a signif-
     -20                               NO WINDOW
                                                                             improvement with         icant noise bandwidth advantage over
                                                                             frequency shifting
                                                                                                      the zero crossing based approaches. If
     -40                                                                     over windowing.
     -60
                     EQUIRIPPLE
                      WINDOW
                                                                                                      a sinewave is measured in the pres-
                                                                                                      ence of wideband interfering noise,
     -80
                                                                                                      only the noise which falls within the fil-
 d -100
 B
                           FREQUENCY
                            SHIFTING                                                                  ter bandwidth will affect the measure-
                                                                                                      ment. This technique is especially well
 F
 S -120

    -140                                                                                              suited to FFT based implementation
    -160
                                                                                                      since the window functions normally
                                                                                                      used provide a predictable window
    -180
           0   25    50           75    100        125    150    175   200                            shape. Rosenfeld (1986) describes a
                                         Hz
                                                                                                      window optimized for the task of fre-
                                                                                                      quency measurement, though any
tained. This reduction in window                         fixed amount of time may be counted          window shape may be used if appro-
spreading also results in a substantial                  and reported as the signal frequency. In     priate modifications to the software
improvement in frequency resolution.                     practice, this approach is never used at     are made. The proprietary scheme de-
The typical window width of between                      audio frequencies because a low fre-         veloped by Audio Precision for its
5 and 11 bins has been reduced to one                    quency signal, such as 20 Hz, would          FASTTEST2 multitone measurement
bin, giving a corresponding 5 to 11                      only be counted to a 1Hz (or 5%) reso-       software allows the use of any window
times improvement in resolution. This                    lution with a 1 second measurement           the customer chooses. The perfor-
is achieved with no increase in acquisi-                 time. Instead, the time interval between     mance tradeoff simply becomes one of
tion time or, more importantly, ac-                      zero crossings is measured which yields      noise bandwidth and selectivity be-
quired record length. Since the record                   the period. This is reciprocated to get      tween adjacent tones.
length is not increased, the ability to re-              frequency. If the time between succes-
solve semi-stationary signals such as                    sive zero crossings is measured, the         Measurement Dynamic Range
tone bursts is maintained.                               measurement rate will be directly pro-       Dynamic range is in itself an interesting
   When making measurements on                           portional to the signal frequency. This      issue for both audio measurement
semi-stationary signals such as tone                     leads to excessively fast readings at high   equipment and audio processing equip-
bursts or transients it is essential to cor-             frequencies which tend to be sensitive to    ment. The bottom line is usually bits,
relate the time and frequency do-                        interfering noise. By measuring the time     how many are used and how are they
mains. The exact segment in the time                     between zero crossings several cycles        used. The issue of how is not usually so
domain which will be transformed                         apart, this noise may be reduced by av-      obvious. Data word widths in profes-
must be selectable to allow windowing                    eraging. Hence, practical equipment          sional audio range from 16 to 24 bits.
out unwanted features while retaining                    measures the number of zero crossings        However, processing algorithms con-
wanted features of the waveform.                         which occur in a time interval which is      sume bits by virtue of the truncation or
Once the segment boundaries are es-                      approximately constant, independent
tablished, the time domain segment is                    of signal frequency. The desired reading     2
                                                                                                          FASTTEST is a trademark of Audio Precision, Inc.
rounding error introduced                                                                                                   ing-point processing, while
with each multiply operation.                -160                                                                           the other was generated with
Consider the effect of multi-                -162
                                                                                                                            48-bit fixed point computa-
plying two 24-bit signed                     -164
                                                                32-bit Floating Point Sine                                  tions in a System Two Cas-
words. The result is 47 bits                                                                                                cade.
                                             -166

                                             -168


wide (one of the sign bits is re-            -170


dundant). When this is con-
                                         d
                                         B
                                         F
                                             -172
                                                                                                                            Measurement Averaging
verted to 24 bits again error is                                                                                            Many audio measurements are
                                         S   -174

                                             -176

introduced in the lsb of the re-             -178                                                                           made on noisy signals. It helps
sulting data. When several                   -180                                                                           to be able to average several
operations are cascaded this                 -182

                                                                                       48-bit Floating Point Sine           measurements together to re-
error can grow to unaccept-                                                                                                 duce the effects of noise. The
                                             -184

                                                0   2k   4k   6k    8k   10k   12k   14k     16k        18k     20k   22k        24k


able levels (Cabot 1990). In-                                                                                               mathematically correct way to
                                                                               Hz




deed, for measurement equip-                                                                                                do this is either with power law
ment which is intended to test                                                                                              or with vector operations. Each
24-bit systems, any introduc- Fig. 12. Comparision of harmonic distortion of 32-bit floating point                          has its place. Power law averag-
tion of error in the 24th bit is and 48-bit fixed point sinewaves, quantized to 24-bits.                                    ing takes successive data
unacceptable.                                                                                                               points, squares them, and
    The two most common operations              this Fig. by a few bits at most. Fixed                                      accumulatess them into a run-
in audio measurement are filtering and          point 48-bit processing allows a theo-                            ning sum. This reduces the measure-
FFTs. It can be shown that conven-              retical 288 dB dynamic range and res-                             ment variability, since the variance of
tional digital filters introduce a              olution, providing considerable mar-                              the final measurement result is the vari-
noise-like error due to truncation op-          gin for loss in the algorithms. Noise                             ance of the original measurements di-
erations which is proportional to the           problems become even more pro-                                    vided by the square root of the number
ratio of the sample rate and the filter         nounced in the new 192 kHz sample                                 of data points averaged. Fig. 14 illus-
cutoff or center frequency. For a 20 Hz         rate systems.                                                     trates this improvement for a typical dis-
filter operating at a 48 kHz rate this             Floating-point processing is usually                           tortion and noise spectrum of an A/D
gives a noise gain of 2400, approxi-            touted as being a panacea since the                               converter. The upper trace is a single
mately 67 dB or 11 bits. For a 24-bit           dynamic range of 32-bit floating-point                            FFT of the A/D converter under test.
processor this filter would give 13 bit         numbers is many hundreds of dB.                                   The trace immediately below it is a
noise and distortion performance.               Most floating point formats consist of a                          power law average of 64 FFTs. Note
There are alternative filter structures         24-bit mantissa and an 8-bit exponent.                            that the variability is drastically reduced.
which reduce this error, but none can           For major portions of a waveform,                                 The trace is smooth and general trends
eliminate it. Similarly, it can be shown        even those as simple as a sine, the                               are clearer.
that the FFT algorithm introduces ap-           mantissa resolution actually sets the                                Power law averaging is inherently
proximately 3 dB (or one half bit) of           performance of the processing. This is                            phase insensitive. Vector averaging
noise increase for each pass of the             because the exponent is zero for 240                              considers both a magnitude and phase
transform. A 16 k transform requires            degrees of the cycle. The FFT in Fig.                             of each data point. Instead of operat-
14 passes (16k = 214), giving a 42 dB           12 shows two 187.5 Hz sinewaves (at                               ing on the FFT results, successive ac-
noise increase. The result is that a            48 kHz sample rate). One was gener-                               quisitions are averaged before trans-
24-bit 16 k transform gives a 17-bit re-        ated by a commercial audio measure-                               forming. This is equivalent to
sult. Special techniques can improve            ment system which uses 32-bit float-                              vectorially averaging the FFT results


                                                                                             -100
                                                                                             -105

                                                                                             -110

                                                                                             -115                                      SINGLE FFT

                                                                                             -120

                                                                                             -125                                                            POWER
                                                                                           d                                                               AVERAGING
                                                                                           B -130
                                                                                           V
                                                                                             -135

                                                                                             -140
                                                                                                                                                                   SYNCHRONOUS
                                                                                             -145                                                                    AVERAGING
                                                                                             -150

                                                                                             -155

                                                                                             -160
                                                                                                    0         2.5k          5k          7.5k        10k   12.5k        15k   17.5k   20k
                                                                                                                                                     Hz




Fig. 13. Residual distortion of a 32-bit floating                                     Fig . 14. A/D converter noise and distortion improvement with
point FFT.                                                                            averaging.
Fundamentals of Modern Audio Measurement



                                                                                            DUT
                 Multitone Test Signal sourced from                                      Device Under Test                                     Spectrum of Test Signal
                 System Two generator. User can                                     Any audio or communications                                 after passing through
                  choose quantity, frequency, and                                 device such as amplifiers, mixing                               device under test.
                       level of individual tones.                                consoles, signal processing devices.




            Fundamental components                        Total Distortion Components                  Noise versus Frequency             Multitone Test Signal has slightly
             extracted from Multitone                      (THD, IMD etc.) extracted                   extracted by examining             different high frequency tones on
                    Test Signal                            from Multitone Test Signal                   analyzer alternate bins          each channel to allow interchannel
                                                                                                                                               crosstalk to be extracted.




            20     100    1k     10k   20k   20     100      1k      10k   20k                                                                           20   100   1k    10k   20k
                                                                                     20    100    1k     10k   20k   20     100   1k     10k   20k




                2-channel                           Interchannel                           Total Distortion               Noise vs Frequency          Interchannel Separation vs
           Frequency Response                     Phase Response                          versus Frequency                (in the presence of        Frequency (L to R & R to L)
                                                                                             (2-channel)                         signal)
Fig. 15. FASTTEST multitone measurement concept.

(considering both magnitude and                                   quency, interchannel crosstalk and                                    easily be obtained from the measure-
phase of the data values). If two values                          noise, as well as nonlinear effects. Ori-                             ment by appropriate choice of signal
are equal magnitude but opposite in                               ginally developed to allow very fast                                  and analysis frequencies.
phase they average to zero. Power law                             measurements of broadcast links, the                                     The      number       of    individual
averaging would give the same magni-                              technique has also found wide applica-                                sinewaves in the FASTTEST signal,
tude as each of the two original magni-                           tion in production test, because of its                               their frequencies and the individual
tudes. The result is that vector or “syn-                         high speed, and in tape recorder testing,                             amplitudes may be set by the user. The
chronous”       averaging      reinforces                         since it does not need synchronization                                only restriction is that they be a multi-
coherent signals and reduces the vari-                            between      source     and     receiver.                             ple of the basic FFT analysis length. In
ability of their amplitude and phase,                             FASTTEST is the trade name for the im-                                the typical configuration with an 8192
just as power law averaging reduces                               plementation and enhancements of the                                  point waveform at a 48 kHz sample
variability of their magnitude. How-                              basic multitone concept developed and                                 rate this results in 4096 bins of 5.96Hz
ever, synchronous averaging reduces                               described by Cabot (1991). Classic                                    frequency resolution spanning the dc
the amplitude of noncoherent signals                              multitone measurements are detailed                                   to 24 kHz range. This flexibility may be
but not their variability. Consequently                           by Mahoney (1987).                                                    used to adjust the test signal spectrum
the fundamental and its harmonics are                                The operation of the FASTTEST                                      to simulate the typical frequency distri-
more easily visible because the noise                             measurement technique is illustrated                                  bution of program material. The
floor moves down. This is shown in                                in Fig. 15. The excitation is the sum of                              phases of the sinewaves comprising
Fig. 14 as the lowest trace. Note that                            several sinewaves whose frequencies                                   the test signal may also be adjusted to
the variability of the background noise                           are     typically   distributed     loga-                             control the crest factor. For instance, if
is the same as the unaveraged case but                            rithmically across the audio range. The                               all tones are set to a cosine phase rela-
its amplitude is 18 dB lower (8 times or                          device under test output spectrum is                                  tionship the peaks will add coherently,
the square root of 64).                                           measured and the amplitudes and                                       producing a maximum amplitude
                                                                  phases of the components at the origi-                                equal to the sum of the individual
Multitone Measurements                                            nal stimulus frequencies provide the                                  sinewave peak amplitudes. The test
Multitone measurements allow very fast                            linear amplitude and phase vs. fre-                                   signal rms amplitude will be the power
measurement of linear errors such as                              quency response. Additional measure-                                  sum of each sinewave rms amplitude,
amplitude and phase response vs.. fre-                            ments such as crosstalk and noise may                                 and the resulting crest factor will be
                                                                                                  the distortion components in real time
                                          DUT                                                     on an oscilloscope will immediately re-
                                                                                                  veal such things as oscillation on the
             LOW FREQUENCY                DEVICE             NOTCH
                SINEWAVE   ATTENUATOR     UNDER           (BANDREJECT)
                                                                         LEVEL
                                                                         METER
                                                                                                  peaks of a signal, crossover distortion,
               GENERATOR                   TEST              FILTER
                                                                                                  clipping, etc. This is an extremely valu-
                                                                                                  able tool in design and development of
              A
                                                                                                  audio circuits, and one which no other
                                                                                                  distortion test can fully match. Viewing
                                                                                                  the residual components in the fre-
                                                                                                  quency domain also gives much infor-
                                                                                                  mation about the distortion mecha-
                                                                                                  nism inside the device under test. This
                                                                                                  usually requires experience with the
                                                                                                  test on many circuits of known behav-
                                                                                 F                ior before the insight can be obtained.
                         fo        2 fo     3 fo   4 fo         5 fo
                                                                                                     Another advantage of the classic fil-
                                                                                                  ter based approach to harmonic dis-
Fig. 16. Total Harmonic Distortion (THD).
                                                                                                  tortion measurement is the opportu-
proportional to the square root of the               contain both harmonics and random            nity for listening to the distortion
number of tones. This is the maximum                 noise. At low levels of harmonic distor-     products. This will often yield signifi-
possible for a given signal spectrum.                tion, this noise will begin to make a con-   cant insights into the source of the dis-
Alternatively, the phases may be ad-                 tribution to the measured distortion.        tortion or its relative audible quality.
justed to minimize the crest factor. This            Therefore measurements with this sys-           The frequency of the fundamental
will typically result in a crest factor              tem are called THD+N to emphasize            component is a variable in harmonic
which increases as the fourth root of                the noise contribution.                      distortion testing. This often proves to
the number of tones. Typical crest fac-                 Low frequency harmonic distortion         be of great value in investigating the
tors for 1/3rd octave-spaced tone sig-               measurements suffer a serious resolu-        nature of a distortion mechanism. In-
nals are around 3.5, approximately                   tion limitation when measured with           creases in distortion at lower frequen-
2.5 times that of a single sinewave.                 FFT techniques. Measuring a 20Hz             cies are indicative of fuse distortion or
                                                     fundamental requires the ability to          thermal effects in the semiconductors.
Harmonic Distortion                                  separate a 40 Hz second harmonic             Beating of the distortion reading with
Harmonic distortion, illustrated in Fig.             with a dynamic range equal to the de-        multiples of the line frequency is a sign
16 is probably the oldest and most uni-              sired residual THD. Since the FFT            of power supply ripple problems,
versally accepted method of measuring                yields a linear frequency scale with         while beating with 15.625 kHz, 19kHz
linearity (Cabot 1992). This technique               equal bin sizes, an 8192 point FFT           or 38kHz is related to subcarrier prob-
excites the device under test with a sin-            gives approximately 6 Hz bins at a 48        lems in television or FM receivers.
gle high purity sine wave. The output                kHz sample rate. To resolve a 100 dB            The subject of high frequency har-
signal from the device will have its                 residual 2nd harmonic requires a win-        monic distortion measurements brings
waveshape changed if the input en-                   dow attenuation of 100 dB only 3 bins        up the main problem with the har-
counters any nonlinearities. A spectral              away from the fundamental. This is           monic       distortion     measurement
analysis of the signal will show that in             not achievable. The FFT length may           method. Since the components being
addition to the original input sinewave,             be increased to reduce the bin width,        measured are harmonics of the input
there will be components at harmonics                but this will lengthen the measurement       frequency, they may fall outside the
(integer multiples) of the fundamental               time.                                        passband of the device under test. An
(input) frequency. Total harmonic dis-                  A sine wave test signal has the dis-      audio device with a cutoff frequency of
tortion (THD) is then defined as the ra-             tinct advantage of simplicity, both in       22kHz will only allow measurement of
tio of the RMS voltage of the harmonics              instrumentation and in use. This sim-        the third harmonic of a 7kHz input.
to that of the fundamental. This may be              plicity has an additional benefit in ease    THD measurements on a 20kHz input
accomplished by using a spectrum ana-                of interpretation. If a notch type distor-   can be misleading because some of
lyzer to obtain the level of each har-               tion analyzer (with an adequately nar-       the distortion components are filtered
monic and performing an RMS summa-                   row notch) is used, the shape of the re-     out by the recorder. Intermodulation
tion. This level is then divided by the              sidual signal is indicative of the shape     measurements do not have this prob-
fundamental level, and cited as the total            of the nonlinearity. Displaying the re-      lem and this is the most often cited rea-
harmonic distortion (usually expressed               sidual components on the vertical axis       son for their use. THD measurements
in percent). Alternatively a distortion              of an oscilloscope and the input signal      may also be disturbed by wow and
analyzer may be used which removes                   on the horizontal gives a plot of the        flutter in the device under test, de-
the fundamental component and mea-                   transfer characteristic deviation from a     pending upon the type of analysis
sures the remainder. The remainder will              best fit straight line. Examination of       used.
Fundamentals of Modern Audio Measurem ent

SMPTE Intermodulation
Intermodulation measurements using
the SMPTE method (originally stan-
dardized by the Society of Motion Pic-                  LOW FREQUENCY
                                                           SINEWAVE                   DUT
ture and Television Engineers, hence its                  GENERATOR

                                                                         ATTENUATOR
name) have been around since the                                                      DEVICE
                                                                                               HIGHPASS     AM     LOWPASS            LEVEL
                                                                                      UNDER
1930s. The test signal consists of a low                                               TEST
                                                                                                 FILTER DEMODULATOR FILTER            METER

frequency (usually 60Hz) and a high fre-                HIGH FREQUENCY
                                                            SINEWAVE
quency (usually 7kHz) tone, summed                         GENERATOR

together in a 4 to 1 amplitude ratio as
shown in Fig. 17. Other amplitude ratios
                                                         A
and frequencies are used occasionally.
This signal is applied to the device under
test, and the output signal is examined
for modulation of the upper frequency
by the low frequency tone. As with har-
monic distortion measurement, this
may be done with a spectrum analyzer
                                                                                                                                              F
or with a dedicated distortion analyzer.                            fL                                fH-2fL          fH     fH+2fL
                                                                                                               fH - fL fH+fL
The modulation components of the up-
per signal appear as sidebands spaced
                                             Fig. 17. SMPTE Intermodulation Distortion.
at multiples of the lower frequency tone.
The amplitudes of the sidebands are
added in pairs, root square summed,          tone, since the analyzer will view these            gain of the device and introducing
and expressed as a percentage of the         as distortion. After the first stage of             modulation distortion. Another excel-
upper frequency level. Care must be          high pass filtering in the analyzer there           lent application is the testing of output
taken to prevent sidebands introduced        is little low frequency information left            LC stabilization networks in power
by frequency modulation of the upper         to create intermodulation in the ana-               amplifiers. Low frequency signals may
tone from affecting the measurement.         lyzer itself. This simplifies design of the         saturate the output inductor, causing it
For example, loudspeakers may intro-         remaining circuitry.                                to become nonlinear. Since the fre-
duce Doppler distortion if both tones are       A major advantage of the demodu-                 quency is low, very little voltage is
reproduced by the same driver. This          lator approach to SMPTE distortion                  dropped across the inductor, and there
would be indistinguishable from              measurement is the opportunity for lis-             would be little low frequency har-
intermodulation if only the sideband         tening to the distortion products. As               monic distortion. The high frequency
powers were considered. If the mea-          with listening to harmonic distortion, it           tone current creates a larger voltage
surements are made with a spectrum           often yields insights into the source of            drop across the inductor (because of
analyzer which is phase sensitive, the       the distortion or its relative audible              the rising impedance with frequency).
AM and FM components may be sepa-            quality.                                            When the low frequency tone creates a
rated by combining components sym-              Considering the SMPTE test in the                nonlinear inductance, the high fre-
metrically disposed about the high fre-      time domain helps understand its op-                quency tone becomes distorted. A
quency tone.                                 eration. The small amplitude high fre-              third common use is testing for cold
    A dedicated distortion analyzer for      quency component is moved through                   solder joints or bad switch contacts.
SMPTE testing is quite straightfor-          the input range of the device under test                One advantage in sensitivity that
ward. The signal to be analyzed is high      by the low frequency tone. The ampli-               the SMPTE test has in detecting low
pass filtered to remove the low fre-         tude of the high frequency tone will be             frequency distortion mechanisms is
quency tone. The sidebands are de-           changed by the incremental gain of the              that the distortion components occur
modulated using an amplitude modu-           device at each point, creating an am-               at a high frequency. In most audio cir-
lation detector. The result is low pass      plitude modulation if the gain                      cuits there is less loop gain at high fre-
filtered to remove the residual carrier      changes. This test is therefore particu-            quencies and so the distortion will not
components. Since this low pass filter       larly sensitive to such things as cross-            be reduced as effectively by feedback.
restricts the measurement bandwidth,         over distortion and clipping. High or-              Another advantage of the SMPTE test
noise has little effect on SMPTE mea-        der nonlinearities create bumps in the              is its relatively low noise bandwidth, al-
surements. The analyzer is very toler-       transfer characteristic which produce               lowing low residual measurements.
ant of harmonics of the two input sig-       large amounts of SMPTE IM.                              The inherent insensitivity to wow
nals, allowing fairly simple oscillators        SMPTE testing is also good for excit-            and flutter has fostered the widespread
to be used. It is important that none of     ing low frequency thermal distortion.               use of the SMPTE test in applications
the harmonics of the low frequency os-       The low frequency signal excursions                 which involve recording the signal.
cillator occur near the upper frequency      excite thermal effects, changing the                Much use was made of SMPTE IM in
                                                                                                                  ity. If a signal, for example at -20 dBFS,
                                                                                                                  is applied to an audio device the output
                                                                                                                  will depend on the gain. If for this exam-
                                                     DUT                                                          ple the output is also -20 dBFS the de-
                                  ATTENUATOR
                                                     DEVICE
                                                                             LOWPASS         LEVEL
                                                                                                                  vice gain is 0 dB. If the input is changed
                                                     UNDER
                                                      TEST
                                                                              FILTER         METER
                                                                                                                  to -40 dBFS the output should follow. In
                 SINEWAVE
                GENERATORS                                                                                        other words, the gain should be con-
                                                                                                                  stant with signal level. For typical analog
                                                                                                                  equipment except compressor/limiters
                                                                                                                  and expanders this will be true. At low
                   A
                                                                                                                  levels crossover distortion will make this
                                                                                                                  not the case. It is common for A/D and
                                                                                                                  D/A converters to suffer from a form of
                                                                                                                  crossover distortion due to inaccurate
                                                                                                                  bit matching. To measure this, we apply
                                                                                                     F            a sinewave to the input and measure the
                             fH - fL   2 (fH - fL)             2fL - fH   fL fH   2fH - fL
                                                                                                                  amplitude of the output with a meter.
                                                                                                                  The input is changed by known
Fig. 18. CCIF Intermodulation Distortion. (Also called DFD or Difference Frequency
                                                                                                                  amounts and the output level is mea-
Distortion).
                                                                                                                  sured at each step. To enable measure-
the disc recording and film industries.                          This technique has the advantage                 ments below interfering noise in the sys-
When applied to discs, the frequencies                        that signal and distortion components               tem, a bandpass filter tuned to the signal
used are usually 400Hz and 4kHz.                              can almost always be arranged to be in              frequency is placed ahead of the mea-
This form of IM testing is quite sensi-                       the passband of a nonlinear system. At              surement meter. The measurement
tive to excessive polishing of the disc                       low frequencies, the required spacing               block diagram is shown in Fig. 19. Fre-
surface, even though harmonic distor-                         becomes proportionally smaller, re-                 quencies used for this testing are nor-
tion was not. It also has found wide ap-                      quiring a higher resolution in the spec-            mally chosen to avoid integer submulti-
plication in telecom and mobile radio                         trum analysis. At such frequencies a                ples of the sample rate, for example 997
areas because of its ability to test ex-                      THD measurement may be more con-                    Hz in digital systems with standard sam-
tremes of the audio band while keep-                          venient.                                            ple rates. This maximizes the number of
ing the distortion products within the                           Recent versions of IEC standards                 states of the converter exercised in the
band.                                                         for DFD have specified the results in               test.
                                                              spectral terms. Previous versions of the                Graphing the device gain vs. input
CCIF (DFD) Intermodulation                                    IEC standard specified the reference                level gives a level linearity plot. For an
The CCIF or DFD (Difference Fre-                              level computation differently. This in-             ideal converter this would be a hori-
quency Distortion) intermodulation dis-                       troduces a 6 dB difference between the              zontal line whose value is the device
tortion test differs from the SMPTE test                      two versions of the standard for DFD                gain. In practice this gain will vary as
in that a pair of signals close in fre-                       measurements. This re-definition also               the level is reduced. Examples of typi-
quency are applied to the device under                        conflicts with accepted practice for dif-           cal device measurements are shown in
test. The nonlinearity in the device                          ference tone distortion measurements                Fig.s 21 a, c, and e. The level linearity
causes intermodulation products be-                           and with usage of the technique in                  plot is a standard fixture of most con-
tween the two signals which are subse-                        other IEC standards.                                sumer digital audio equipment test re-
quently measured as shown in Fig. 10c.                                                                            ports.
For the typical case of input signals at                      Level Linearity
14kHz and 15kHz, the intermodulation                          One method of measuring the                         Noise Modulation
components will be at 1kHz, 2kHz,                             quantization characteristics of convert-            Fielder developed a technique for char-
3kHz, etc. and 13kHz, 16kHz, 12kHz,                           ers is to measure their amplitude linear-           acterizing digital conversion systems
17kHz, 11kHz, 18kHz, etc. Even-order
or asymmetrical distortions produce the
low “difference frequency” components
while the odd-order or symmetrical                                                                       DUT
nonlinearities produce the components
near the input signals. The most com-                          LOW FREQUENCY                             DEVICE
mon application of this test only mea-                                                                   UNDER    BANDPASS                        LEVEL
                                                                  SINEWAVE ATTENUATOR
                                                                                                          TEST     FILTER                         METER
sures the even order difference fre-                             GENERATOR
quency components, since this may be
achieved with only a multi-pole low
pass filter.                                                  Fig. 19. Level linearity measurement block diagram.
Fundamentals of Modern Audio Measurement

                                                                                            speed error can shift the frequencies
                                                                                            away from the nominal bin centers.
                                  DUT                                                       The traditional approach to this prob-
                                                                                            lem is to synchronize the sampling
 LOW FREQUENCY                     DEVICE       BANDREJECT     TUNABLE
                                                                               LEVEL        clock to a received signal by phase
    SINEWAVE   ATTENUATOR          UNDER        OR HIGHPASS   1/3 OCTAVE
   GENERATOR                        TEST           FILTER   BANDPASS FILTER
                                                                               METER        locking the sampling clock to one com-
                                                                                            ponent of the signal (Mahoney 1987).
                                                                                            This requires a non-trivial amount of
Fig. 20. Noise modulation measurement block diagram.                                        time compared to the total test time of
                                                                                            the measurement. The FASTTEST
called noise modulation which has been         modulation products of these frequen-        multitone software contains a provi-
shown to correlate well with perceived         cies. The FASTTEST total distortion          sion for correcting this frequency error
quality. It measures the variation in the      measure (Cabot 1991) is a summation          after the signal is acquired, not before.
1/3rd octave band noise floor with vari-       over frequency of the powers in the dis-        Sample       rate     correction     in
ations in signal level. If the noise floor     tortion products. If the summation is        FASTTEST relies on the ability to ac-
varies by more than 1 dB in any band,          done in segments, such as those repre-       curately measure the frequencies in
the converter will likely have audible         sented by the space between the origi-       the multitone signal. The measured
modulation of the noise floor with             nal tones, the result may be displayed as    frequencies are compared to the
changes in signal level. This will mani-       a distortion vs. frequency plot. This        known generator frequencies. The ra-
fest itself as an audible shift in the level   graph is not the usual sensitivity of the    tio of the measured frequencies to the
or tonal balance of the background             distortion measure to signal frequency       generator frequencies represents the
noise as music such as piano notes de-         but represents the distribution of distor-   amount of frequency shift which must
cays into the noise floor. Fig. 20 illus-      tion products with frequency. This dis-      be corrected. FASTTEST uses this fre-
trates the test setup for this measure-        tinction is important since it is not an     quency measurement to perform a
ment. The device under test is                 equivalent display. If the summation is      sample rate conversion on the ac-
stimulated with a low frequency                done over the entire frequency band a        quired signal, shifting the frequencies
sinewave. This is removed with either a        single value will be obtained. As with       to their correct values.
notch filter or high pass filter and the       other distortion measures, this value           If the frequency shift is not mea-
spectrum of the remaining signal is mea-       may be graphed as a function of stimu-       sured accurately, then sample rate
sured in 1/3rd octave steps with a 1/3rd       lus amplitude or device output ampli-        conversion will fail to fully “synchro-
octave bandpass filter. The signal level is    tude.                                        nize” the FFT to the acquired data.
changed and the measurement is re-                The average slew rate of a                The result will be skirts around the fun-
peated. The amplitude is typically             FASTTEST signal will be dependent            damental tones in the frequency do-
changed in 5 dB steps beginning 40 dB          on the distribution of energy with fre-      main. These skirts fall between the
below full scale. The deviation in the         quency. Including more tones at high         tones and will produce an elevation in
noise spectrum is the parameter of inter-      frequencies will increase the average        the total noise and distortion plots. If
est, so the peak variation between traces      slew rate, making the test more sensi-       the frequency shifts are significant,
in each band is the noise modulation.          tive to frequency-dependent non-             there will also be an effect on the mea-
Fig.s 21 a-f compare the level linearity       linearities. Including more tones at low     sured amplitudes of the fundamental
and noise modulation for three different       frequencies will make the test more          tones. This is due to scalloping loss in
channels of a digital multitrack tape re-      sensitive to inverse frequency depend-       the FFT as the tones shift substantially
corder. These measurements and the             ent nonlinearities.                          off the bin centers. Cabot (1996)
theory behind them are detailed in                If the sinewave frequencies are cho-      shows that in the presence of interfer-
Cabot (1991).                                  sen to be in the FFT bin centers, the        ing noise, the frequency measurement
    If the amplitude sweep of a noise          transform results contain no spillage        technique used in FASTTEST will re-
modulation measurement is sped up,             into neighboring bins. This maximizes        duce the distortion caused by synchro-
it offers the opportunity for listening to     the dynamic range and frequency res-         nization errors to below the amplitude
the background noise and the result-           olution by avoiding the use of win-          of the interfering noise.
ing shifts of timbre. Being essentially a      dowing. However, if the generator and           FASTTEST is also capable of mak-
test of shifts in noise spectrum balance,      analyzer are not driven by the same          ing rudimentary measurements of dis-
this ability to listen may offer insights      clock, it may be difficult to place the      tortion audibility by computing the
into relative audible quality.                 sinewave frequencies in the bin cen-         masking curve created by a particular
                                               ters because of differences between          multitone test signal. It can then com-
FASTTEST Total Distortion                      the generator and analyzer electron-         pare the total distortion measurement
Most of the distortion products in a           ics. Similarly, there can be a problem if    to the perceptual limit imposed by the
multitone signal will fall between the         the device under test stores and re-         masking curve to assess the audibility
original stimulus frequencies and will in-     plays the signal, as is the case with a      of the distortion. This is detailed in the
clude both harmonics and inter-                tape recorder. The record/playback
Fig. 21a. Deviation form linearity for 1 channel of a digital   Fig. 21b. Corresponding noise modulation. 10dB noise
multitrack. 6dB worst case deviation through -90dB. Poor        modulation at low frequencies. 3dB noise modulation at high
linearity performance.                                          frequencies. Poor noise modulation performance.




Fig. 21c. Deviation from linearity for 1 channel of a digital   Fig. 21d. Corresponding noise modulation. 10dB noise
multitrack. 1dB worst case deviation through -90dB. Good        modulation at low frequencies. 3dB noise modulation at high
linearity performance.                                          frequencies. Poor noise modulation performance.




Fig. 21e. Deviation from linearity for 1 channel of a digital   Fig. 21f. Corresponding noise modulation. 4dB noise
multitrack. 1dB worst case deviation through -90dB. Good        modulation at low frequencies. 1dB noise modulation at high
linearity performance.                                          frequencies. Good noise modulation performance.
Fundamentals of Modern Audio Measurement

low bit rate coder measurements pa-            tude must be checked to see that it is   seen at 6.144 MHz and integer multi-
per by Cabot (1992).                           within the acceptable range for proper   ples of that frequency. If no data is sent
                                               recovery. Readouts of this amplitude     on the interface, discrete products will
Interface Measurements                         are normally measured peak-to-peak       also appear at ½ and ¼ of these fre-
Most audio equipment today is inter-           with a wide bandwidth peak ac-to-dc      quencies. The spectral domain behav-
faced through the AES/EBU serial digi-         converter. Since peak measurements       ior is also driven by the rise times of the
tal interface or its fraternal twin for con-   are used, it is essential that waveform  interface waveform as seen in the time
sumer use standardized by the EIAJ.            fidelity be maintained through the       domain plot shown earlier. Faster rise
When dealing with equipment con-               path leading to the detector. Otherwise  time signals will contain more energy
nected through one of these interfaces,        waveform tilt and overshoot will create  at high frequencies than signals whose
there are three broad areas of concern.        incorrect readings. Modest amounts of    rise time is limited by interface band-
First are problems with interface wave-        tilt or overshoot are no cause for con-  width. More important than the effects
form parameters which affect the ability       cern since the information is conveyed   of rise time on high frequency energy
of the interface to reliably pass data         in the waveform edges, but the in-       content of the interface is the interac-
from one device to the next. Second are        creased level they imply may mask se-    tion between rise time and interface jit-
problems which, although allowing er-          rious problems with inadequate mini-     ter. This is illustrated in Fig. 24.
ror-free communication, affect the ulti-       mum amplitude in the body of the            Jitter is the deviation of the interface
mate audio performance. Last are prob-         waveform. The only way to see the        waveform zero crossing times from the
lems which manifest themselves only in         true effects of amplitude reduction,     zero crossings of a perfectly stable
a system environment when multiple             without being obscured by such wave-     clock whose period is one Unit Inter-
devices are interconnected in arbitrary        form artifacts, is with eye patterns or  val. It is not the deviation of the wave-
combinations.                                  histograms, as described below.          form pulse widths from the ideal Unit
   As described in Cabot (1990), the               The AES-3 interface operates with    Interval width. Simply measuring the
AES interface is a self-clocking, polar-       bits whose widths are multiples of       variations in pulse width by overlaying
ity-independent, Manchester coded              1/128th of the sampling interval (the    traces on a scope which are triggered
interface. The data, clocking and syn-         reciprocal of 128x the sample rate). At  by the edges of the incoming stream
chronization information are all con-          48 kHz sample rate this works out to be  will only indicate edge to edge jitter.
tained in the edge timing of the stream.       163 ns. This time period is called the   Variations in width which are corre-
This makes the proper detection of             Unit Interval (UI) since it defines the  lated from pulse to pulse (all being
edges and their location crucial not           minimum interval on the interface. (It   larger than normal or all being smaller
only to the interface functionality, but       should be noted that this definition is  than normal) can accumulate into sub-
to its performance as well.                    different from that used in other        stantially larger deviations from the
   The AES standard specifies mini-            branches of engineering such as          ideal edge locations.
mum and maximum waveform ampli-                telecom, where a Unit Interval refers to    The internal noise or instability of
tudes for signals transmitted on the in-       the width of a data bit and not the in-  the clock oscillator in a device will cre-
terface. It also specifies a minimum           terface pulses.) Data ones are com-      ate jitter in its digital output signal.
amplitude at which any properly func-          posed of two bits of opposite polarity,  With most devices, this inherent jitter is
tioning AES receiver must correctly re-        while data zeros consist of a single bit not large enough to cause problems
ceive data. This is intended to insure         of double this width (326 ns). The syn-  with the proper reception of the digital
that all devices have adequate inter-          chronization patterns, called pream-     signal. Some devices use digitally gen-
face signal to correctly recover clock         bles, consist of these two pulse widths  erated clocks created from a high fre-
and data information, without being            plus three unit interval wide pulses as  quency master clock which is divided
overloaded by excessive amplitude              illustrated in Fig. 22.                  down in a digital PLL to create an in-
signals. Although the interface signal             These short pulses
amplitude conveys no information, it           require considerable
is all in the edges, inadequate levels in-     bandwidth for proper             3

crease the receiver susceptibility to          transmission,       typi-       2.5



noise. Reduced amplitudes also in-             cally 20 MHz or more.
                                                                                2

                                                                               1.5


crease jitter in the recovered signals         This can be seen by              1

                                                                             500m

due to errors in the slicing level. Proper     transforming the in-      V      0


testing of an AES interface requires the       terface      waveform         -500m

                                                                                -1

ability to control the interface wave-         into the frequency             -1.5



form amplitude over a range at least as        domain as shown in
                                                                                -2

                                                                              -2.5


wide as that specified in AES-3. To in-        Fig. 23. The spectrum            -3
                                                                                 -1u      0            1u           2u          3u


sure margin for error when the device          has components from
                                                                                                      sec




is used in practice, testing over a wider      under 1 MHz to more
range is desirable.                            than 20 MHz. Dis-
   Similarly, a received signal’s ampli-       crete products are Fig. 22. AES/EBU data stream format
                                                                                                               terface clock signal of the correct aver-
                                                                                                               age frequency. This technique leads to
                                                                                                               notoriously jittery signals and has
                                                                                                               been responsible for generating sig-
                                                                                                               nals which cannot be received by
                                                                                                               many receivers.
                                                                                                                   An excellent way to view the jitter
                                                                                                               behavior of a clock or interface signal,
                                                                                                               especially when it is particularly noisy,
                                                                                                               is via a histogram. Fig. 25 is an exam-
                                                                                                               ple of a jitter histogram measured from
                                                                                                               a noisy interface. The horizontal axis is
                                                                                                               the deviation of the interface signal
                                                                                                               zero crossings from their ideal posi-
                                                                                                               tions. The vertical axis represents the
                                                                                                               likelihood of the zero crossing having
Fig. 24. Spectrum of interface waveform.
                                                                                                               that particular timing. A strongly bi-
                                                                                                               modal histogram is indicative of
                                                                                                               squarewave jitter, while a bimodal dis-
                                                                                                               tribution with a gradual transition be-
                                                                                                               tween modes is a sign of sinewave jit-
                                                                                      Fig. 23. Effect of       ter. Gaussian or skewed Gaussian
                                                                                      bandwidth reduction on   shapes are indicative of random jitter.
                                                                                      jitter.                      When several digital devices are
                                                                                                               cascaded without a system-wide mas-
                                                                                                               ter synchronization signal, each re-
                                                                                                               ceives its clock from the previous de-
                                                                                                               vice in the chain and provides the
                                                                                                               clock to the next one in the chain. The
                                                    “Perfect” AES/EBU Waveform
                                                                                                               individual devices extract the clock
         Actual AES/EBU
            Waveform                      Closeup of a portion of the data stream                              from the incoming interface signal and
                                            showing how the waveform crosses
                                                  the baseline with a slight time                              create an output signal from this clock.
                                                 offset which translates as jitter.
                          Zero-crossing                                                                        Unfortunately, it is common for equip-
                            time shift
                                                                                                               ment to not only pass jitter received at
                                                                                                               its input to its output, but to amplify the
                                                                                                               jitter if it is within a particular fre-
                                                                                                               quency range. This is caused by the re-
                                                                                                               sponse of the internal clock recovery
                                                                                                               phase locked loop (PLL). The loop is
                                                                                                               designed to track the incoming sample
                                                                                                               rate and will therefore follow slow vari-
                                                                                                               ations in clock frequency. As the fre-
                                                                                                               quency of sample rate variation is in-
                                                                                                               creased, the loop will (hopefully)
                                                                                                               attenuate the variations. The loop re-
                                                                                                               sponse is therefore a low pass filter, al-
                                                                                                               lowing low frequency jitter to pass
                                                                                                               unattenuated but reducing high fre-
                                                                                                               quency jitter. The loop response is ob-
                                                                                                               tained by plotting the amplitude of jit-
                                                                                                               ter on the device’s output signal for a
                                                                                                               fixed amplitude, but variable fre-
                                                                                                               quency, jittered signal at the input.
                                                                                                               Ideally this response is a lowpass func-
                                                                                                               tion with no peaking. However, in
                                                                                                               practice, many devices have several
                                                                                                               dB of jitter gain near the corner fre-
Fig. 25. Jitter histogram of a noisy signal.
                                                                                                               quency of this lowpass function. Such
Fundamentals of Modern Audio Measurement

            Audio Precision                                                              12/06/95 17:03:53    This time from presentation of signal
      50n
                                                                                                              until locking is the receiver pll acquisi-
      45n                                                                                                     tion time. This can be assessed if the
                                                                                                              measurement system offers a time do-
      40n
  J                                                                                                           main display of interface bit rate.
  i
  t
      35n                                                                                                        Eye patterns are a display of the en-
  t
      30n
                                                                                                              velope of possible interface signal
  e
  r                                                                                                           waveshapes across one unit interval.
      25n

  s
                                                                                                              By triggering an oscilloscope from a
  e   20n                                                                                                     highly stable version of the recovered
  c
      15n
                                                                                                              interface clock and setting the sweep
                                                                                                              speed to put one unit interval on
      10n
                                                                                                              screen, an eye pattern will result. Each
      5n                                                                                                      successive sweep of the oscilloscope
            60     100        200   500      1k        2k            5k    10k     20k          50k    100k
                                                                                                              traces one trajectory of the interface
                                          Induced jitter frequency   Hz
                                                                                                              waveform across a unit interval. As the
                                                                                                              traces curve up or down at the begin-
Fig. 26. Jitter transfer function of a typical device.                                                        ning and end of the unit interval, the
                                                                                                              display closes down to show a hole in
devices will amplify jitter occurring in                        The transient behavior of clock re-           the middle where the cell edges do not
that frequency range. If several such                       covery circuits can be more easily as-            cross the horizontal axis.
devices are cascaded the results can be                     sessed with squarewave jitter. The                   The outer extremes of the eye pat-
disastrous for the later equipment in                       leading and trailing edge of a                    tern represent the maximum excursion
the chain (Dunn et al, 1993).                               squarewave create a sudden shift in in-           of the waveform during the interval
   For equipment with an external                           terface signal phase which must be fol-           and essentially display the maximum
sync reference input this jitter accumu-                    lowed by the device under test. This              peak-to-peak signal level. This is of
lation cannot occur, because each de-                       transient may cause the device to lose            limited utility. The inner extremes of
vice extracts its output clock from the                     lock or to oscillate around the new in-           the eye pattern (Fig. 27) represent the
reference input and ignores the jitter                      terface phase. The loop dynamics are              minimum excursion of the interface
on the signal input. However, the loop                      easy to view if the measurement                   waveform during the unit interval and
response from the reference input to                        equipment offers both a squarewave                represent the difficulty a receiver
the device output becomes the rele-                         jitter source and a time domain display           would have decoding the signal. The
vant parameter. Although jitter accu-                       of jitter.                                        AES-3 standard specifies the mini-
mulation is no longer a concern, the jit-                       Any AES-3 receiver will take some             mum eye-pattern size, or “opening”,
ter gain can produce excessive jitter in                    finite time to acquire lock on the in-            with which a correctly functioning re-
the output of an individual device.                         coming signal. It must lock before it             ceiver must operate. There is no speci-
   Sinewave jitter is useful to deter-                      can recover data and before it may                fication in the AES standard for how
mine the jitter transfer gain of a digital                  output a regenerated AES-3 signal.                the minimum eye opening is to be ob-
input / digital output device. It is also
useful to isolate the effect of jitter as a
function of frequency on a converter.
By stimulating the device under test
with a sinewave jittered AES-3 signal
whose jitter frequency is adjustable,
the jitter transfer function may be mea-
sured. An example of this for a typi-
cally medium priced digital processing
device is shown in Fig. 26. The re-
sponse has a broad peak in the 5 kHz
region which reaches 2 dB of gain.
When several of these devices are cas-
caded, jitter could rise to levels which
would cause later devices in the chain
to lose lock. Since the receiver design
used in this device is a common com-
mercially available chip used accord-
ing to the manufacturer’s recommen-
dations, such a cascade is not unlikely.
                                                            Fig. 27. Eye pattern inner traces.
tained. The height reduction may                                                                            Fig. 28. Comparison of
come from low signal level, cable                                                                           delay and data based
roll-off, interfering noise, or any com-                                                                    settling
bination of the three. The width reduc-
tion may come from cable roll-off, jit-
ter or a combination of the two.
   Long cables create high frequency
roll-off because of distributed capaci-
tance working against the wire resis-
tance. This high frequency attenuation
progressively increases the interface
signal rise time with increasing cable
length. The AES standard includes a
suggested equalizer to be inserted at
the receiver to compensate for the ca-
ble roll-off. To see what effect this will
have on signal recoverability, it is help-   added noise will shift the zero cross-      ment due to noise or sampling uncer-
ful to be able to switch such an equal-      ings due to the finite rise times.) When    tainty issues. The tradeoff is usually one
izer in line with the signal before view-    the eye closes, errors are unavoidable.     of accuracy, speed, or (in the case of
ing the signal on a scope. One test          If the noise level is sufficient to close   sampled signals and quantized signals)
equipment manufacturer has instead           the eye to 200 mV the AES-3 specifica-      sample density and converter resolu-
provided an automatically adjusting          tion requires the receiver to still cor-    tion. The concepts of repeatability and
equalizer which introduces a variable        rectly receive the data. By adding          accuracy are quite distinct. It is entirely
degree of high frequency boost and           noise of selectable amplitude to the        possible to have highly inaccurate read-
displays the amount of boost intro-          transmitted signal, the test equipment      ings which are very repeatable. Con-
duced. This number indicates the de-         can degrade the signal seen by the re-      versely, it is possible to have readings
gree of cable roll-off, giving a rough       ceiver to the threshold of error and de-    which, on average, are quite accurate
measure of cable quality and length as       termine the receiver margin.                but have variability in excess of their ac-
well as an indication of the fixed equal-        This paper has described several        curacy.
izer which should be permanently in-         impairments which can affect AES-3              One aspect to getting repeatable
stalled in the line.                         signals. In the real world these can        and accurate readings is that of set-
   The AES-3 standard specifies that         (and do) occur simultaneously. The          tling. Some measurement equipment
receiving devices should tolerate 7          AES-3 standard only specifies that a        depends on fixed delays between a
Volts peak of 20 kHz common-mode             receiver must correctly receive a signal    setting change and the taking of a
signal. The interface was originally         whose eye height and width have             reading to obtain stabilized results.
planned to carry an analog version of        shrunk to the values specified in the       Some of these delay-based schemes
the digital audio as a common-mode           standard. What combination of im-           are more intelligent than a single delay
signal. This was never exploited in          pairments are included is not speci-        value for all conditions. The more ad-
practical systems. However, in large         fied. The eye height may be reduced         vanced ones make the delay a func-
installations there may be consider-         by the effects of additive noise, inade-    tion of frequency and also depend on
able pickup of common-mode inter-            quate common-mode rejection, low            the measurement being performed,
ference from nearby power lines,             signal amplitude and cable roll-off. By     taking longer for THD+N measure-
video lines, data lines or ground po-        applying these in various combina-          ments than for amplitude measure-
tential differences. If the receiving de-    tions the robustness of a device under      ments for example.
vice has inadequate common-mode              test may be examined. Similarly, the            This is quite acceptable if the equip-
rejection there will be leakage of this      standard specifies that a receiver must     ment is only used for measuring itself
interference into the digital signal         correctly function down to an eye of        or for measuring some well behaved
path. If the interference is low fre-        one half nominal width. This narrow-        devices such as power amplifiers or
quency it will shift the slicing point of    ing of the eye might be caused by jitter,   gently sloping equalizers. Devices with
the data comparator, creating jitter         cable roll-off or shifting of the slicing   large response variations such as
and reducing data integrity.                 point by inadequate common-mode             high-Q notch filters, devices with dy-
   Interfering noise of sufficient magni-    rejection or additive noise.                namic characteristics such as compres-
tude will cause errors in a receiver of                                                  sors or limiters, devices with dynamic
an AES-3 signal. When viewed on an           Measurement stability or                    delays such as reverberators, etc. can
eye diagram, the noise reduces the eye       repeatability                               cause serious problems when mea-
height, often without significantly af-      The issue of measurement repeatability      sured with fixed delay schemes. The
fecting the eye width. (If the AES-3 sig-    was discussed with regard to amplitude      concept of device under test settling
nal suffers from limited bandwidth,          and frequency measurements. How-            being more stringent than the test
                                             ever, this is an issue with any measure-    equipment’s own settling is often ig-
Fundamentals of Modern Audio Measurement

                                                   Fig. 29. Spectrum of a              AudioPrecision                                                      16:22:51
                                                                                                                                                    12/06/95
nored by instrument manufacturers                                               +10
(especially when demonstrating their               5kHz signal with 3kHz         +0

products).                                         sinewave induced jitter.     -10

    To deal with real-world devices Au-                                         -20

dio Precision devised a comprehen-                                              -30

sive settling algorithm which starts                                          d
                                                                                -40

from minimum delay values based on                                            B -50
                                                                              V
the variables mentioned above. It then
                                                                                -60

                                                                                -70
performs an additional step of com-
                                                                                -80
paring new data values to previous                                              -90
data to see when the readings have                                              -100
stabilized. Although this carries a slight                                      -110
time penalty for collecting the addi-                                                  0        2k      4k   6k       8k    10k
                                                                                                                            Hz
                                                                                                                                  12k   14k   16k       18k      20k

tional data readings, in a well designed
implementation it is generally faster              cut-off frequency, improving the audio                         the device under test behavior. The jit-
overall than the longer delays that                performance of the device. It is incorrect                     ter is normally reduced by the filtering
must be used to insure adequate set-               to assume that an interface with more                          action of the receiver circuits in the de-
tling for the device under test. Fig. 28           jitter will perform worse than one with                        vice under test. These will filter out
shows the response of a typical DUT                less jitter. Similarly, it is incorrect to as-                 high frequency jitter components by
with       delay-based    settling    and          sume that a converter running from a                           virtue of the limited bandwidth of the
data-based settling overlaid. The er-              clock with higher jitter will perform                          phase lock loop. This behavior may be
rors become significant when the de-               worse than one operating from a clock                          non-linear, depending on jitter ampli-
vice’s response deviates from flat.                with lower jitter.                                             tude, since many phase detectors have
    It is common to make a direct link                 Jitter on an interface or on a D/A                         dead band behavior for small phase
between generator operation and ana-               converter clock may appear to some                             deviations. This is sometimes inten-
lyzer operation. This makes use of the             degree on the reconstructed signal.                            tional to facilitate locking to noisy sig-
knowledge about the generator wave-                This may be tested by introducing jitter                       nals.
form and frequency to set the analysis             on the interface and measuring the                                Jitter on a reference input can affect
averaging time, measurement filters                degradation of the reconstructed sig-                          A/D conversion performance if, as is
and any delays required for settling.              nal output. Jitter is a phase or time                          normal, the device extracts its sample
This avoids the time required for mea-             modulation effect, producing modula-                           clock from the reference input. If the
suring the input signal frequency in the           tion sidebands on an audio signal. For                         device has no reference input, as with
analyzer before setting these measure-             sinewave jitter, the sidebands will gen-                       inexpensive processing equipment, jit-
ment parameters. Although this works               erally also be sinusoidal and their am-                        ter on the digital audio input will be the
very well for situations where the gen-            plitude proportional to the jitter mag-                        relevant parameter to test. To properly
erator and analyzer are co-located, it             nitude as illustrated in Fig. 29. The                          characterize an A/D converter, it is
falls apart when the equipment is sep-             transfer function of the jitter amplitude                      therefore necessary to stimulate it with
arated by any substantial distance or              to the sideband amplitude as a func-                           a low distortion analog signal while si-
when making measurements from re-                  tion of jitter frequency may be charac-                        multaneously driving its reference in-
cord/replay devices such as tape re-               terized. For random jitter, the side-                          put or digital audio input with a jittered
corders.                                           bands will also be random, creating an                         digital signal. This apparatus is dia-
                                                   elevated noise floor.                                          grammed in Fig. 30. Measuring con-
Jitter measurements on                                 Jitter on an A/D converter clock                           verter performance with only the ana-
converters                                         may appear to some degree on the                               log signal input or only the jittered
Jitter exists in all digital signals, it is only   sampled signal. This may be tested by                          digital input would not indicate the au-
a question of magnitude. Interface jitter          introducing jitter on the clock and                            dio degradation. A medium-priced
is jitter on the signal between two digital        measuring the degradation of the digi-                         combined analog and digital signal
devices. Sampling jitter is jitter on the          tal signal output. Jitter will produce                         processor was used for the DUT and
clock of an A/D or D/A converter. The              modulation sidebands on the digital                            was stimulated with 35 ns of jitter on its
degradation introduced by jitter on an             signal. As with the D/A case, sinewave                         digital input when the analog input
interface depends on the design of the             jitter will produce sinusoidal sidebands                       was driven with a 997 Hz sinewave.
interface receiver. The degradation in-            which may be measured to quantify                              Fig. 31 shows the THD+N as a func-
troduced by jitter on a sampling clock             the jitter. The transfer function of the                       tion of jitter frequency. The distortion
depends on the design of the converter.            jitter to the sideband level and its effect                    is seen to rise for jitter frequencies be-
On better designed equipment, there is             on the noise floor may be measured as                          tween 5 kHz and 20 kHz.
a stage between the interface clock re-            described previously.                                             Jitter on the digital signal input or
covery and the converter clock genera-                 Varying the frequency of the jitter                        reference input similarly affects D/A
tion which filters out jitter above some           signal may have a significant effect on                        performance. To properly characterize
         DIGITAL SIGNAL                                                         JITTER                                                                                                          JITTER
          GENERATOR                              VCO                            SIGNAL                                               VCO
                                                                                                                                                                                                SIGNAL

                                                                                                                                           CLOCK
                                                                               DIGITAL
        ANALOG SIGNAL                                                                                                                                                                                                            ANALOG
                                                                             DISTORTION                                 DIGITAL SIGNAL
         GENERATOR                                                                                                                                                                                                             DISTORTION
                                                                              ANALYZER                                   GENERATOR
                                                                                                                                                                                                                                ANALYZER
                                                       REFERENCE
                                                         INPUT

                                         DEVICE UNDER                                                                                                             DEVICE UNDER
                                                                                                                                       AES/EBU                        TEST                                       ANALOG
                             ANALOG          TEST                        AES/EBU
                                                                                                                                        SIGNAL                                                                   OUTPUT
                          INPUT SIGNAL                                OUTPUT SIGNAL




Fig. 30. Evaluating a device for jitter susceptibility.                                                  Fig. 32. D/A jitter susceptibility characterization


         AudioPrecision                                                               12/06/95
                                                                                             15:42:19              Audio Precision                                                                                                             12/06/95 16:59:45
                                                                                                             -50
  -80
                                                                                                                                                                                                          Digital Freq
  -82                                                                                                        -55
                                                                                                                                                                                                           20.0 kHz
D
i -84
                                                                                                                                                                                           Digital Freq                         Digital Freq
g                                                                                                            -60
                                                                                                                                                                                           7.962 kHz                             200.0 Hz
i                                                                                                        T
  -86
t                                                                                                                                                                                Digital Freq
                                                                                                         H -65
a                                                                                                                                                                                3.170 kHz
l -88                                                                                                    D
                                                                                                         +                                                        Digital Freq
                                                                                                             -70                                   Digital Freq
T -90                                                                                                    N                                         502.38 Hz
                                                                                                                                                                  1.262 kHz
H
D -92
                                                                                                         d -75
+
N -94                                                                                                    B
                                                                                                             -80
d -96
B
  -98                                                                                                        -85


  -100                                                                                                       -90
           60       100        200       500            1k       2k            5k        10k       20k             60          100         200             500           1k               2k               5k            10k        20k           50k        100k
                                         Jitter frequency (Hz)                                                                                                                    Induced Jitter Hz


Fig. 31. THD+N as a function of jitter frequency.                                                        Fig. 33. THD+N as a function of jitter frequency for various signal
                                                                                                         frequencies.
a D/A, it is necessary to stimulate it                                    performance of digital to digital pro-                                                  and its application to converter mea-
with a jittered digital audio signal                                      cessing equipment may also be                                                           surements was explained. The
which carries audio information as                                        affected if the equipment contains any                                                  advantages of simultaneous measure-
shown in Fig. 32. Normally, jitter                                        sample rate conversion stages. They                                                     ment in multiple domains was simi-
would pass from the digital input to the                                  may be tested in much the same way                                                      larly detailed.
D/A clock circuits, but the converter                                     as D/A converters, although the distor-                                                    Novel      techniques    employing
might be more affected by the refer-                                      tion measurements are made in the                                                       multitone signals for fast audio mea-
ence input if the signal is internally                                    digital domain. If there is no sample                                                   surements were examined and appli-
reclocked with the reference clock.                                       rate conversion, the digital input jitter                                               cations of sampling frequency correc-
Using the same device under test as                                       will pass through to the output with                                                    tion technology to this and
the last example, the D/A distortion                                      some gain or loss. This may cause in-                                                   conventional FFT measurement were
was measured as a function of jitter fre-                                 terfacing problems if the jitter gain is                                                covered. Synchronous averaging of
quency. Again, the digital input was jit-                                 excessive. Excessive jitter gain may                                                    FFT data was presented and the sub-
tered with 35 ns of sinewave jitter and                                   cause the performance of the final dig-                                                 sequent noise reduction demon-
the THD+N was measured as a func-                                         ital to analog conversion stage to suffer                                               strated.
tion of jitter frequency. The perfor-                                     but it will not introduce any audio deg-
mance, shown in Fig. 33, rapidly de-                                      radation within the device itself.
grades for jitter above 500 Hz.                                                                                                                                   Acknowledgments
   Jitter on a digital input can affect                                   Summary                                                                                   Dual      Domain,        FASTTEST,
performance in an analog to analog                                           Various analog and digital audio                                                     AUDIO.TST, System Two, System One
system through its effect on the inter-                                   measurements were described. The                                                        and Audio Precision are trademarks of
nally recovered sampling clocks. Ulti-                                    architectures typically used in audio                                                   Audio Precision, Inc.
mately, it comes down to how well the                                     test equipment were reviewed. The                                                         Wayne Jones provided invaluable
clock recovery circuits can extract a                                     strong need for simultaneity of digital                                                 assistance with preparation of the fig-
stable clock from the interface. Audio                                    and analog generation was presented                                                     ures and the manuscript. Bob Metzler
Fundamentals of Modern Audio Measurement

made many of the comparative mea-                   R. C. Cabot, “Testing Digital Audio De-     for Digital Audio Interface Jitter,” presented
surements and graciously supplied the          vices in the Digital Domain,” presented at       at the 95th Convention of the Audio Engi-
                                               the 86th Convention of the Audio Engi-           neering Society, J. Audio Eng. Soc. (Ab-
material excerpted from his book. My           neering Society, J. Audio Eng. Soc. (Ab-         stracts), vol. 41, p. 1051 (1993 Dec),
wife Liane patiently waited while I oc-        stracts), vol. 37, p. 399 (1989 May),            preprint 3705.
casionally gave this paper more atten-         preprint 2800.                                       R. A. Finger, “On the Use of Com-
                                                    R. C. Cabot, “Performance Limitations       puter-Generated Dithered Test Signals,” J.
tion than her.                                 of Digital Filter Architectures,” presented at   Audio Eng. Soc., vol. 35, pp. 434-445
   The FASTTEST frequency correc-              the 89th Convention of the Audio Engi-           (1987 June).
tion technology, FASTTEST total dis-           neering Society, J. Audio Eng. Soc. (Ab-             R. A. Finger, “Review of Frequencies
                                               stracts), vol. 38, p. 871 (1990 Nov.),           and Levels for Digital Audio Performance
tortion technique, FASTTEST trigger-           preprint 2964.                                   Measurements. J. Audio Eng. Soc., vol. 34,
ing technology, synchronous FFT                     R. C. Cabot, “Measuring AES/EBU Digi-       pp. 36-48 (1986 Jan./Feb.).
averaging, and other technologies de-          tal Interfaces,” J. Audio Eng. Soc., vol. 38,        M. Mahoney, DSP-Based Testing of An-
                                               pp. 459-468 (1990 June).                         alog and Mixed Signal Circuits, IEEE Press
scribed in this paper are the subject of            R. C. Cabot, “Noise Modulation in Digi-     (1987).
US patents issued, pending or applied          tal Audio Equipment,” presented at the               R. E. Metzler, Audio Measurement
for.                                           90th Convention of the Audio Engineering         Handbook,       Audio      Precision      Inc.,
                                               Society, J. Audio Eng. Soc., vol. 39, p. 382     Beaverton, OR, USA (1993).
                                               (1991 May), preprint 3021.                           R. E. Metzler, “Test and Calibration Ap-
                                                    R. C. Cabot, “Comparison of Nonlinear       plications of Multitone Signals,” in Proc.
References                                     Distortion Measurement Methods,” in Proc.        AES 11th Int. Conf. On Audio Test & Mea-
    Data sheet for the AD536A rms to DC        AES 11th Int. Conf. On Audio Test & Mea-         surement, pp. 29-36 (1992).
converter, Analog Devices, Norwood MA,         surement, pp. 53-65 (1992).                          E. Rosenfeld, “Accuracy and Repeat-
1992                                                R. C. Cabot, “Measurements on Low           ability with DSP Test Methods,” IEEE 1986
    Audio Engineering Society, AES stan-       Bit Rate Coders,” Proc. AES 11th Int. Conf.      International Test Conference, paper 21.5,
dard method for digital audio engineer-        On Audio Test & Measurement, pp.                 pp. 788-795.
ing–Measurement of digital audio equip-        216-222 (1992).                                      E. Rosenfeld, “DSP Measurement of
ment, AES17-1992                                    R. C. Cabot, “Measuring the Effects of      Frequency,” IEEE 1986 International Test
    Audio Engineering Society, AES stan-       Sampling Jitter,” presented at the 99th of       Conference, paper 26.2, pp. 981-986.
dard method for digital audio engineer-        the Audio Engineering Society, Workshop              J. Tierney, C. Rader, and B. Gold, “A
ing–Serial   transmission     format     for   Jitter: Is it a Problem? (1995 Oct.).            Digital Frequency Synthesizer,” IEEE Trans.
two-channel linearly represented digital au-        R. C. Cabot, “Synchronous FFTs; Its         on Audio and Electroacoustics, vol. AU-19,
dio data, AES3-1996                            importance With Multitone Testing,”              No. 1, (1971 Mar.).
    Owners manual for the Model 5500 Au-       AUDIO.TST, vol. 11 #2 (1996).                        J. Vanderkooy and S. P Lipshitz,.
dio Measurement System, Amber Electro               J. Dunn, B. McKibbon, R. Taylor and C.      “Dither in Digital Audio,” J. Audio Eng.
Design, Montreal Canada, 1986                  Travis, “Towards Common Specifications           Soc., vol. 35, pp. 966–975 (1987 Dec.).




                                                      THE AUTHOR




    Richard C. Cabot received B.S.,             sponsible for all engineering and               zations. He holds 10 patents and
  Masters and Ph.D. degrees from                product development.                            has written extensively for industry
  Rensselaer Polytechnic Institute,               Dr. Cabot is active in the AES,               publications. He is a registered pro-
  Troy, N.Y.       After teaching at            having served as President, Vice                fessional engineer in both Electrical
  Rensselaer, he joined Tektronix,              President and Governor, and is cur-             Engineering and Acoustics. He
  and later left to help found Audio            rently chairman of the AES working              was also appointed to a term on the
  Precision Inc., a firm specializing in        group on digital audio measure-                 Oregon Central Business Registra-
  audio test and measurement equip-             ments. Dr. Cabot is a Fellow of the             tion Coordinating Council, advising
  ment for the professional audio in-           AES, a Senior Member of the IEEE                state government on streamlining
  dustry. He holds the position of              and a member of numerous related                the registration and regulation of
  Chief Technology Officer and is re-           technical and professional organi-              businesses in Oregon.
                       ®

Audio Precision, Inc.
PO Box 2209
Beaverton, Oregon 97075-2209
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