The document discusses various topics related to digital communication systems including: - Advantages of digital over analog communication systems such as noise immunity and easier implementation of error control coding. - The process of analog to digital conversion including sampling, quantization, encoding, and pulse code modulation (PCM). - Digital modulation techniques like differential PCM (DPCM) and delta modulation (DM) that reduce redundancy before encoding. - Considerations for line coding binary data onto an analog channel such as bandwidth, noise immunity, power efficiency and self-clocking capability.

1. Communication Theory
Analog to Digital Conversion
and
Pulse Code Modulation (PCM)
Enjoy

2. 2
Advantages of Digital Communication
 Digital systems are less sensitive to noise and signal distortion. For long transmission line, the signal may
be regenerated effectively error-free at different points along the path.
 With digital systems, it is easier to integrate different services, e.g., video and the accompanying
soundtrack, into the same transmission scheme.
 The transmission scheme can be relatively independent of the source
 Circuitry for digital signals is easier to repeat and digital circuits are less sensitive to physical effects
such as vibration and temperature
 Digital signals are simpler to characterize and typically do not have the same amplitude range and
variability as analog signals. This makes the associated hardware design easier.
 Various media sharing strategies (known as multiplexing) are more easily implemented with digital
transmission strategies
 Source coding techniques can be used for removing redundancy from digital transmission
 Error-control coding can be used for adding redundancy, which can be used to detect and correct
errors at the receiver side
 Digital communication systems can be made highly secure by exploiting powerful encryption algorithms
 Digital communication systems are inherently more efficient than analog communication systems in
the tradeoff between transmission bandwidth and signal-to-noise ratio
 Various channel compensation techniques, such as, channel estimation and equalization, are easier to
implement

3. 3
Sampling (1)
 Sampling is an operation that is basic to digital signal processing and digital communications
 Through the use of sampling process, an analog signal is converted into a corresponding
sequence of samples that are usually spaced uniformly in time
Message
Sampled Signal
Sampling Signal
   



n
ssT nffffs


4. 4
Sampling (2)
Two types of practical sampling:
 Natural Sampling
 Flat-top sampling

5. 5
Sampling (3)
Frequency Domain:
or,

6. 6
Sampling (4)
fs > 2W:
fs = 2W:
fs < 2W:
Aliasing

7. 7
Sampling Theorem
 Sampling theorem is a fundamental bridge between continuous signals (analog
domain) and discrete signals (digital domain)
 It only applies to a class of mathematical functions whose Fourier transforms are
zero outside of a finite region of frequencies
Nyquist Sampling Theorem / Nyquist-Shanon Sampling Theorem:
fs = Sampling frequency
fs = 2W: Nyquist frequency / Nyquist rate / Minimum sampling frequency
A signal whose bandwidth is limited to W Hz can be reconstructed exactly
(without any error) from its samples uniformly taken at a rate fs ≥ 2W Hz

8. 8
Antialiasing Filter
 All practical signals are time-limited, i.e., non band-limited => Aliasing inevitable
 To limit aliasing, use anti-aliasing filter (LPF) before sampling
Original
Signal
Anti-aliasing
filter
Sample
Reconstruction
Filter
Reconstructed
Signal

9. 9
Reconstruction Filter
fs = 2W:
Ideal LPF
characteristic:
1/2W- 1/2W
Ts = 1/2W
(interpolation formula)
(interpolation filter /
interpolation function)

10. 10
Quantization (1)
Quantizer characteristic:
Here, k = 1, 2, 3, … , L
L = Number of representation levels
(Number of intervals)
It is the process of transforming the sample amplitude m(nTS) of a baseband signal at time t = nTS
into a discrete amplitude v(nTS) taken from a finite set of possible levels
kth interval:
Quantizer output equals to vk if the input signal sample m belongs to the interval Ik
mk: Decision levels / Decision thresholds
vk: Representation levels / Reconstruction levels
Δ=|vk +1 – vk|: Step-size / quantum
kk Imifvv 

11. 11
Quantization(2): Two types
Mid-tread quantization Mid-rise quantization
Mid-rise quantizer:
Decision threshold value is exactly zero
Mid-tread quantizer:
Reconstruction value is exactly zero
Reconstruction
levels

12. 12
Quantization(3): Two types
Uniform quantization Non-uniform quantization

13. 13
Quantization Error for Uniform Quantization (1)
Quantization error (noise)
q = m – v => Q = M – V
 If mean of M is zero and the quantizer is
symmetric, then V is also a RV of zero mean
 Q is also a RV variable of zero mean in the
range [– Δ/2, Δ/2]
 If Δ is sufficiently small, Q can be assumed
a uniform RV with zero mean
– Δ/2 0 Δ/2 q
fQ(q)
1/Δ
Quantization noise power
 




2/
2/
2
22
12
dqqfq QQ
22
12


PP
SNR
Q
Signal-to-nose-ratio (SNR): P = Average power of m(t)

14. 14
Quantization Error for Uniform Quantization (2)
Special case:
m(t) is a sinusoidal signal with amplitude equal to mmax
R
m
L
m
2
22 maxmax

Suppose m(t) of continuous amplitude in the range [-mmax, mmax]:
R
m
P
SNR 2
2
max
2
3







R
SNR 2
2
2
3













 2
max
3
log1002.6
m
P
RSNRdB
8.16  RSNRdB
 Each additional bit increases the SNR by 6.02 dB and
a corresponding increase in required channel BW
R = Number of bits for presenting each level (bits/sample)

15. 15
Non-Uniform Quantization
 SNR of weak signals is much lower than that of strong signal
 Instantaneous SNR is also lower for the smaller amplitudes compared to that of the
larger amplitudes

16. 16
Non-Uniform Quantization
- Step size increases as the separation from the origin of the input–output amplitude
characteristic is increased
- First Compression and then uniform quantization
- Achieve more even SNR over the
dynamic range using fewer bits (e.g.,
8 bits instead of 13/14 bits)
Receiver side: Expansion required
Compression + Expansion = Companding
Original
Signal
Compression
Uniform
Quantization
Reconstruction Expansion
Original
Signal

17. 17
Non-Uniform Quantization
Compressor Input Compressor Output
 The compression here occurs in the amplitude values
 Compression in amplitudes means that the amplitudes of the compressed signal
are more closely spaced in comparison to the original signal
 To do so, the compressor boosts the small amplitudes by a large amount. However,
the large amplitude values receive very small gain and the maximum value remains
the same

18. 18
Non-Uniform Quantization
μ-Law: Used in North America, Japan (μ = 255 is mostly used)
 More uniform SNR is achieved over a larger dynamic range

19. 19
Non-Uniform Quantization
Used in Europe and many other countries
A = 87.6 is mostly used and comparable to μ = 255
A-Law:

20. 20
Encoding
 Each quantized samples is encoded into a code word
 Each element in a code word is called code element
Binary code:
 Each code element is either of two distinct
values, customarily denoted as 0 and 1
 Binary symbol withstands a relatively high
level of noise and also easy to regenerate
 Each binary code word consists of R bits and
hence, this code can represent 2R distinct
numbers (i.e., at best R bit quantizer can be
used)

21. 21
Pulse Code Modulation (PCM)
In PCM, a message signal is represented by a sequence of coded pulses, which is accomplished
by representing the signal in discrete form in both time and amplitude
Three basic operations in a PCM Transmitter:
- Sampling
- Quantization
- Encoding
Transmitter
Receiver
Transmission
Path

22. 22
Differential PCM (DPCM)
Transmitter
 When a signal is sampled at a rate slightly higher than the Nyquist rate, there exists a
high degree correlation between adjacent samples, i.e., in an average sense, the signal
does not change rapidly from one sample to the next
 When these highly correlated samples are encoded as in a standard PCM system, the
resulting encoded signal contains redundant information implying that symbols that are not
absolutely essential to the transmission of information are generated
 DPCM removes this redundancy before encoding by taking the difference between the
actual sample m(nTS) and its predicted value
 The quantized version of the prediction error e(nTS) are encoded instead of encoding
the samples of the original signal
 This will result in much smaller quantization intervals leading to less quantization noise
and much higher SNR
     SSS nTmnTmnTe ˆ
Prediction error
 SnTmˆ

23. 23
Predictor for DPCM:
Liner predictor of order p:
Transversal filter (tapped-delay-line filter) used as a linear predictor
    

p
k
SqkS TknmwnTm
1
ˆ

24.  SnTm'
24
Differential PCM (DPCM)
Transmitter
Receiver
 Sq nTe
 SnTmˆ      SqSS nTenTmnTm  ˆ'
Reconstruction error          SSqSSS nTqnTenTenTmnTm  '
= Quantization error
     SSS nTmnTmnTe ˆ
Prediction error

25. 25
Delta Modulation (DM) … (1)
 DM encodes the difference between the current sample and the previous sample using just one bit
 Correlation between samples are increased by oversampling (i.e., at a rate much higher, typically 4 times
higher than the Nyquist rate)
 DM involves the generation of the staircase approximation of the oversampled version message
 The difference between the input and the approximation is quantized into only two levels:
 1-bit version of DPCM (i.e., 2-level quantization) requiring less bandwidth than that of DPCM and PCM


26. 26
Delta Modulation (DM)…(2)
Transmitter
Receiver
  .qe
- Digital equivalent of integration

27. 27
Predictor for DM
Transmitter
Note:
(1) DPCM uses a higher order filter.
(2) DM uses a 1st order predictor with w1 = 1. Thus, the predicted output is the previous sample.

28. 28
Delta Modulation (DM)…(3)
Two types of quantization error:
(2) Granular noise(1) Slope overload distortion/noise
Comments:
(1) For avoiding slope overload distortion: larger Δ is desired
(2) For avoiding granular noise: smaller Δ is desired
 An optimal step size (Δ) has to be chosen for minimum overall noise
mq(t)
eq(nTS)
Example:
  s
s
mm f
T
Atm 

 max||   tAtm mm cos  
m
s
m
f
A


max
  
r
s
Voicem
f
A


max
8002  r

29. 29
Line Coding (1)
 PCM, DPCM and DM are different strategies for source
encoding, which converts an analog signal into digital form
 Once a binary sequence of 1s and 0s is produced, the
sequence is transformed into electrical pulses or
waveforms for transmission over a channel and this is
known as line coding
 Multi-level line coding is possible
Various line coding
(binary) methods:
(0 means transition)
(f) Split-phase
or Manchester
Or RZ-AMI
Or NRZ-L

30. 30
Line Coding (2)
Book:
Digital Communications:
Fundamentals and Applications
- Bernard Sklar
Applications:
 Polar NRZ / NRZ-L: Digital logic circuits
 NRZ-M/NRZ-S: Magnetic tap recording
 RZ line codes: Base band transmission and magnetic recording (e.g., Bipolar RZ / RZ-AMI
is used for telephone system)
 Manchester Coding: Magnetic recording, optical communications and satellite telemetry
Polar NRZ /

31. 31
Line Coding (3)
Desired properties (i.e., design criteria) for line coding:
 Transmission bandwidth: should be as small as possible
 Noise immunity: should be immune to noise
 Power efficiency: for a given bandwidth and given error probability, transmission power
requirement should be as small as possible
 Error detection and correction capability: should be possible to detect and correct errors
 Favorable power spectral density (PSD): should have zero PSD at zero (i.e., DC)
frequency, otherwise the ac coupling and the transformers used in communication systems
would block the DC component
 Adequate timing information / self-clocking: should carry the timing or clock information
which can be used for self-synchronization
 Transparency: should be possible to transmit a digital signal correctly regardless of the
patterns of 1’s and 0’s (by preventing long string of 0s and 1s)