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									                      Chapter 3:
          Pulse Code Modulation
   Pulse Code Modulation
   Quantizing
   Encoding
   Analogue to Digital Conversion
   Bandwidth of PCM Signals

                            Huseyin Bilgekul
                   Eeng360 Communication Systems I
            Department of Electrical and Electronic Engineering
                    Eastern Mediterranean University              Eeng 360 1
 DEFINITION: Pulse code modulation (PCM) is essentially
  analog-to-digital conversion of a special type where the
  information contained in the instantaneous samples of an analog
  signal is represented by digital words in a serial bit stream.

 The advantages of PCM are:
   • Relatively inexpensive digital circuitry may be used extensively.
   • PCM signals derived from all types of analog sources may be merged with
     data signals and transmitted over a common high-speed digital
     communication system.
   • In long-distance digital telephone systems requiring repeaters, a clean PCM
     waveform can be regenerated at the output of each repeater, where the input
     consists of a noisy PCM waveform.
   • The noise performance of a digital system can be superior to that of an
     analog system.
   • The probability of error for the system output can be reduced even further
     by the use of appropriate coding techniques.

                                                                       Eeng 360 2
        Sampling, Quantizing, and Encoding
    The PCM signal is generated by carrying out three basic operations:
           1. Sampling
           2. Quantizing
           3. Encoding
1.   Sampling operation generates a flat-top PAM signal.
2.   Quantizing operation approximates the analog values by using a
     finite number of levels. This operation is considered in 3 steps
       a) Uniform Quantizer
       b) Quantization Error
       c) Quantized PAM signal output
3.   PCM signal is obtained from the quantized PAM signal by encoding
     each quantized sample value into a digital word.

                                                               Eeng 360 3
                Analog to Digital Conversion
                                              The Analog-to-digital Converter (ADC)
                                               performs three functions:
Analog                                           – Sampling
Input                                                • Makes the signal discrete in time.
                                                     • If the analog input has a bandwidth
                                                       of W Hz, then the minimum sample
                                                       frequency such that the signal can be
                                                       reconstructed without distortion.
ADC                                              – Quantization
         Quantize                                    • Makes the signal discrete in
                                                     • Round off to one of q discrete levels.
                                                 – Encode
          Encode                       000

                                                     • Maps the quantized values to digital
                                                        words that are  bits long.
                                              If the (Nyquist) Sampling Theorem is
          Digital Output                       satisfied, then only quantization introduces
              Signal                           distortion to the system.
         111 111 001 010 011 111 011
                                                                                  Eeng 360 4
 The output of a sampler is still continuous in amplitude.
   – Each sample can take on any value e.g. 3.752, 0.001, etc.
   – The number of possible values is infinite.

 To transmit as a digital signal we must restrict the number of
  possible values.

 Quantization is the process of “rounding off” a sample according to
  some rule.
   – E.g. suppose we must round to the nearest tenth, then:
            3.752 --> 3.8    0.001 --> 0

                                                                   Eeng 360 5
Illustration of the Quantization Error

                                   Eeng 360 6
                         Uniform Quantization
               Dynamic Range:                        • Most ADC’s use uniform
                   (-8, 8)
     Output sample
                                                     • The quantization levels of a
                                                       uniform quantizer are

                                                       equally spaced apart.
-8   -6   -4    -2       -1 2   4      6    8
                                                     • Uniform quantizers are
                                    Input sample X
                                                       optimal when the input
                         -5                            distribution is uniform.
                         -7                            When all values within the
      Quantization Characteristic                      Dynamic Range of the
Example: Uniform  =3 bit quantizer                    quantizer are equally likely.
   q=8 and XQ = {1,3,5,7}

                                                                             Eeng 360 7
Quantization Example

                 Analogue signal

                 Sampling TIMING

                 Quantization levels.
                 Quantized to 5-levels

                  Quantization levels
                  Quantized 10-levels

                                   Eeng 360 8
                               PCM encoding example

                                                                              Levels are encoded
                                                                               using this table

   Table: Quantization levels with belonging code words


                                                                       Chart 2. Process of restoring a signal.
      Chart 1. Quantization and digitalization of a signal.             PCM encoded signal in binary form:
Signal is quantized in 11 time points & 8 quantization segments.   101 111 110 001 010 100 111 100 011 010 101
                                                                    Total of 33 bits were used to encode a signal

                                                                                                   Eeng 360 9
• The output of the quantizer is one of M possible signal levels.
   – If we want to use a binary transmission system, then we need to map
     each quantized sample into an n bit binary word.

                        M  2n , n  log 2 ( M )
• Encoding is the process of representing each quantized sample
  by an  bit code word.
   – The mapping is one-to-one so there is no distortion introduced by
   – Some mappings are better than others.
      • A Gray code gives the best end-to-end performance.
      • The weakness of Gray codes is poor performance when the sign bit
        (MSB) is received in error.

                                                                    Eeng 360 10
                        Gray Codes
• With gray codes adjacent samples differ only in one bit position.
• Example (3 bit quantization):
     XQ        Natural coding         Gray Coding
     +7           111                    110
     +5           110                    111
     +3           101                    101
     +1           100                    100
     -1           011                    000
     -3           010                    001
     -5           001                    011
     -7           000                    010
• With this gray code, a single bit error will result in an amplitude
  error of only 2.
   – Unless the MSB is in error.

                                                               Eeng 360 11
  Waveforms in a PCM system for M=8

(a) Quantizer Input output characteristics

(b) Analog Signal, PAM Signal, Quantized PAM Signal

                                                        M  2n    n  log 2 ( M )
                                                      M is the number of Quantization levels
(c) Error Signal                                      n is the number of bits per sample

(d) PCM Signal                                                                      Eeng 360 12
PCM Transmission System

                          Eeng 360 13
             Practical PCM Circuits
•   Three popular techniques are used to implement the
    analog-to-digital converter (ADC) encoding
      1.   The counting or ramp, ( Maxim ICL7126 ADC)
      2.   Serial or successive approximation, (AD 570)
      3.   Parallel or flash encoders. ( CA3318)
•   The objective of these circuits is to generate the
    PCM word.
•   Parallel digital output obtained (from one of the
    above techniques) needs to be serialized before
    sending over a 2-wire channel
•   This is accomplished by parallel-to-serial
    converters [Serial Input-Output (SIO) chip]
•   UART,USRT and USART are examples for SIO’s

                                                          Eeng 360 14
           Bandwidth of PCM Signals
•   The spectrum of the PCM signal is not directly related to the spectrum of the
    input signal.
•   The bandwidth of (serial) binary PCM waveforms depends on the bit rate R
    and the waveform pulse shape used to represent the data.
•   The Bit Rate R is

    Where n is the number of bits in the PCM word (M=2n) and fs is the sampling
•   For no aliasing case (fs≥ 2B), the MINIMUM Bandwidth of PCM Bpcm(Min) is:

                             Bpcm(Min) = R/2 = nfs//2

    The Minimum Bandwidth of nfs//2 is obtained only when sin(x)/x pulse is used
    to generate the PCM waveform.

•   For PCM waveform generated by rectangular pulses, the First-null Bandwidth

                                 Bpcm = R = nfs
                                                                       Eeng 360 15

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