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PULSE CODE MODULATION
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Pulse Code Modulation
Analogue to Digital Conversion
Quantizing
Encoding
PULSE CODE MODULATION
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 highspeed 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.
SAMPLING, QUANTIZING, AND
ENCODING
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The PCM signal is generated by carrying out three
basic operations:
1.
2.
3.
1.
2.
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
a)
b)
c)
3.
Sampling
Quantizing
Encoding
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.
ANALOG TO DIGITAL CONVERSION
Analog
Input
Signal
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.
Sample
ADC
Quantize
Encode
Digital Output
Signal
111 111 001 010 011 111 011
111
110
101
100
011
010
001
000
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.
UNIFORM QUANTIZATION
 Most
ADC’s 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.
QUANTIZATION EXAMPLE
Analogue signal
Sampling TIMING
Quantization levels.
Quantized to 5-levels
Quantization levels
Quantized 10-levels
QUANTIZATION
The used of a non-uniform quantizer is equivalent to passing the
baseband
Signal through a compressor and then appling the compressed
signal to a
uniform quantizer.
A particular form of compression law that used in practice is the
so-called μ-law is defined by
Another compression law is the socalled A-law defined by
ENCODING
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The output of the quantizer is one of M possible signal
levels.
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
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.
GRAY CODES


With gray codes adjacent samples differ only in one
bit position.
Example (3 bit quantization):
XQ Natural coding
+7
+5
+3
+1
-1
-3
-5
-7
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111
110
101
100
011
010
001
000
Gray Coding
110
111
101
100
000
001
011
010
With this gray code, a single bit error will result in an
amplitude error of only 2.
 Unless the MSB is in error.
PCM ENCODING
EXAMPLE
Levels are encoded
using this table
Table: Quantization levels with belonging code
words
Chart 1. Quantization and digitalization of a signal.
Signal is quantized in 11 time points & 8 quantization
segments.
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
WAVEFORMS IN A PCM SYSTEM FOR M=8
M  2n
n  log 2 ( M )
M is the number of Quantization levels
n is the number of bits per sample
PCM TRANSMISSION SYSTEM