Pulse Code Modulation (PCM)
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Formatting and transmission of baseband signal
Digital info.
Format
Textual
source info.
Analog
info.
Analog
info.
sink
Sample
Quantize
Encode
Bit stream
Format
Low-pass
filter
Pulse
modulate
Decode
Pulse
waveforms
Demodulate/
Detect
Textual
info.
Transmit
Channel
Receive
Digital info.
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Formatting and transmission of baseband signal
Digital info.
Format
Textual
source info.
Analog
info.
Bit stream
(Data bits)
Sample
Sampling at rate
f s  1 / Ts
(sampling time=Ts)
Quantize
Encode
Pulse waveforms
(baseband signals)
Pulse
modulate
Encoding each q. value to
l  log 2 L bits
(Data bit duration Tb=Ts/l)
Quantizing each sampled
value to one of the
L levels in quantizer.
Mapping every m  log 2 M data bits to a
symbol out of M symbols and transmitting
a baseband waveform with duration T
Rb  1 / Tb [bits/sec]
– Information (data) rate:
– Symbol rate : R  1 / T [symbols/s ec]
• For real time transmission: Rb  mR
Format analog signals
•
To transform an analog waveform into a
form that is compatible with a digital
communication system, the following steps
are taken:
1. Sampling
2. Quantization and encoding
3. Baseband transmission
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Sampling
Time domain
Frequency domain
xs (t )  x (t )  x(t )
X s ( f )  X ( f )  X ( f )
x(t )
| X(f )|
| X ( f ) |
x (t )
xs (t )
| Xs( f ) |
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Aliasing effect
LP filter
Nyquist rate
aliasing
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Sampling theorem
Analog
signal
Sampling
process
Pulse amplitude
modulated (PAM) signal
• Sampling theorem: A bandlimited signal
with no spectral components beyond , can
be uniquely determined by values sampled
at uniform intervals of
– The sampling rate,
Nyquist rate.
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Quantization
• Amplitude quantizing: Mapping samples of a continuous
amplitude waveform to a finite set of amplitudes.
Out
Average quantization noise power
Quantized
values
In
Signal peak power
Signal power to average 
quantization noise power
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Encoding (PCM)
• A uniform linear quantizer is called Pulse Code Modulation
(PCM).
• Pulse code modulation (PCM): Encoding the quantized signals
into a digital word (PCM word or codeword).
– Each quantized sample is digitally encoded into an l bits codeword
where L in the number of quantization levels and
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Example: Quantization
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Quantization error
• Quantizing error: The difference between the input and output of
e(t )  xˆ (t )  x(t )
a quantizer
Process of quantizing noise
Qauntizer
Model of quantizing noise
y  q (x )
AGC
xˆ (t )
x(t )
xˆ (t )
x(t )
x
e(t )
+
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e(t ) 
xˆ (t )  x(t )
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PCM waveforms
• PCM waveforms category:
 Nonreturn-to-zero (NRZ)  Phase encoded
 Return-to-zero (RZ)
 Multilevel binary
1
NRZ-L
0
1
1
0
+V
-V
+V
Manchester -V
Unipolar-RZ +V
0
+V
Bipolar-RZ 0
-V
0
1
Miller
0
1
1
0
+V
-V
+V
Dicode NRZ 0
-V
T
2T 3T 4T 5T
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2T 3T 4T
5T
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PCM waveforms …
• Criteria for comparing and selecting PCM
waveforms:
– Spectral characteristics (power spectral density
and bandwidth efficiency)
– Bit synchronization capability
– Error detection capability
– Interference and noise immunity
– Implementation cost and complexity
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Baseband transmission
• To transmit information through physical
channels, PCM sequences (codewords) are
transformed to pulses (waveforms).
– Each waveform carries a symbol from a set of size M.
– Each transmit symbol represents k  log 2 M bits of
the PCM words.
– PCM waveforms (line codes) are used for binary
symbols (M=2).
– M-ary pulse modulation are used for non-binary
symbols (M>2).
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Example: 4-PAM
For 4-PAM:
For M-PAM:
T=2Tb
Rs=Rb/2
Rs is the symbol rate
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1
𝑅𝑠 =
𝑇
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