# Digital Audio

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```					Digital Audio

Part 1
Mechanical
(seismic waves, sound,…)
exists in a medium (which on
deformation is capable of
producing elastic restoring
forces),

Waves
(A wave is a disturbance that propagates through space, and transfer energy. )

Others
visible light, ultraviolet rays, x-rays, and gamma rays, and
can travel through vacuum without a medium
1-Reflection – the change of direction of
waves, due to hitting a reflective surface.
2-Refraction – the change of direction of
waves due to them entering a new
medium.
   Characteristic   3-Interference – the superposition of two
properties       waves that come into contact with each
other.
4-Dispersion – the splitting up of waves by
frequency.
5-Rectilinear propagation – the movement
of waves in straight lines.
vibrations perpendicular to the direction of
the propagation of the wave; examples
include waves on a string and
electromagnetic waves.

Transverse
 and
longitudinal waves

vibrations parallel to the direction of
the propagation of the wave; examples
include most sound waves.
What is Sound?

• Minute disturbances in the air, caused by
a vibrating object

• Air molecules bunch together, then spread
out

• Changes in density (air pressure, or
sound pressure)

• Causes a chain reaction; sound pressure
wave propagates
Sound Pressure

High

Normal

Low

Time

Time domain plot of a waveform
   Unit of sound

Generally, 0 dB refers to the threshold of
hearing at 1000 Hz. Note that 0 dB does not mean zero sound
intensity or absence of sound wave.
The threshold of pain is about 120 decibels, representing a
sound intensity of 1,000,000,000,000 (or 1012) times greater
than 0 decibels.
Amplitude

1 Cycle

Period: How long does one cycle last?
Frequency: How many cycles per second?

• Period = 1 / Frequency
(for A440: 0.0023 sec.)
Frequency and Pitch
• Frequency is an acoustic fact.
Pitch is a human perception.

• Our sense of pitch has a logarithmic relation to
frequency — it’s based on ratios.

• Our ear is like a microphone. It changes the
physical wave (acoustic energy) into an electrical
signal.

• Range of human hearing

•20Hz to 20,000 Hz (20 kHz), approximately
(for young folks; old folks can’t hear as high)
Math of waves
Harmonics in Music
F*w=Length *1/w
Noises
White Noise White noise is defined as a noise that has equal amount of energy
per frequency.

Pink Noise
Pink noise is noise that has an equal amount of energy per octave.

Blue Noise
doubles the
amount of power each time you go up 1 octave.

Red Noise
Extensive of the pink noise.

Purple Noise
It increases in power
by 6.02 dB for every increase in frequency of 1 octave.
Black Noise
It is essentially silence with the occasional randomly spaced
spike
Analogue vs. Digital
 Analogue signals vary continuously over
time
 Digital signals are made up of discrete
values, usually representing the amplitude
of an analogue signal
PCM - Pulse Code Modulation
   The most common method of
converting an analog audio signal to
digital audio data. At regular intervals
(i.e. pulse; Fs) a snapshot is taken of
the incoming signal.
Analog to Digital Overview
Sampling Rate
How often analog signal is measured
[samples per second, Hz]
Example: 44,100 Hz

Sampling Resolution
[a.k.a. “sample word length,” “bit depth”]
Precision of numbers used for
measurement: the more bits, the higher
the resolution.
Example: 16 bit
Dynamic Range
Sampling Rate
Determines the highest frequency that you
can represent with a digital signal.

Nyquist Theorem:
Sampling rate must be at least twice as high as
the highest frequency you want to represent.

Capturing just the crest and trough of a sine
wave will represent the wave exactly.
Aliasing
What happens if sampling rate not high enough?

A high frequency signal

sampled at too low a rate

looks like …

… a lower frequency signal.

That’s called aliasing.
Common Sampling Rates
Which rates can represent the range of
frequencies audible by (fresh) ears?

Sampling Rate        Uses
44.1 kHz (44100)     CD, DAT
48 kHz (48000)       DAT, DV, DVD-Video
96 kHz (96000)       DVD-Audio
22.05 kHz (22050)    Old samplers

Most software can handle all these rates.
3-bit Quantization
A 3-bit binary (base 2) number has 23 = 8 values.

7
6
5
Amplitude

4
3
2
1
0
Time — measure amp. at each tick of sample clock

A rough approximation
16-bit Sample Word Length
A 16-bit integer can represent 216, or
65,536, values (amplitude points).
We typically use signed 16-bit integers,
and center the 65,536 values around 0.

32,767

0

-32,768
Quantization Noise
Round-off error: difference between actual
signal and quantization to integer values…

Random errors: sounds
like low-amplitude noise
End of Part 1

For Part 2
Samples-Midi-DSP-Effect-TTS-Speech
Recognition
VST

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