Eeng 360 1

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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
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PULSE CODE MODULATION (PCM)

• 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.

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Sampling, Quantizing, and Encoding

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

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Analog to Digital Conversion

• The Analog-to-digital Converter (ADC) performs
  three functions
• Sampling
• 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.
• Quantization
• Makes the signal discrete in amplitude.
• Round off to one of q discrete levels.
• Encode
• Maps the quantized values to digital words that
  are ? bits long.
• If the (Nyquist) Sampling Theorem is satisfied,
  then only quantization introduces distortion to
  the system.

Analog Input Signal
Sample
ADC
Quantize
Encode
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Quantization

• 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 --gt 3.8 0.001 --gt 0

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Illustration of the Quantization Error
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PCM TV transmission

• 5-bit resolution
• 8-bit resolution.

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Uniform Quantization

• Most ADCs use uniform quantizers.
• The quantization levels of a uniform quantizer
  are equally spaced apart.
• Uniform quantizers are optimal when the input
  distribution is uniform. When all values within
  the Dynamic Range of the quantizer are equally
  likely.

Input sample X
Example Uniform ? 3 bit quantizer q8 and XQ
?1,?3,?5,?7
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Quantization Example
Analogue signal
Sampling TIMING
Quantization levels. Quantized to 5-levels
Quantization levels Quantized 10-levels
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PCM encoding example
Levels are encoded using this table
Table Quantization levels with belonging code
words
M8
Chart 2. Process of restoring a signal. PCM
encoded signal in binary form 101 111 110 001
010 100 111 100 011 010 101 Total of 33 bits were
used to encode a signal
Chart 1. Quantization and digitalization of a
signal. Signal is quantized in 11 time points
8 quantization segments.
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Encoding

• 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.
• 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 encoding.
• 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.

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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.

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Waveforms in a PCM system for M8
M8
(a) Quantizer Input output characteristics
(b) Analog Signal, PAM Signal, Quantized PAM
Signal
(c) Error Signal
(d) PCM Signal
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PCM Transmission System
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Practical PCM Circuits

• Three popular techniques are used to implement
  the analog-to-digital converter (ADC) encoding
  operation
• The counting or ramp, ( Maxim ICL7126 ADC)
• Serial or successive approximation, (AD 570)
• 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 SIOs

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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
• Rnfs
• Where n is the number of bits in the PCM
  word (M2n) and fs is the sampling rate.
• 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 is
• Bpcm R nfs