1. Chapter 1: PCM, and Delta Modulation and Demodulation

2. Learning Objectives
LO Understand various practical aspects of sampling such as methods of sampling, Nyquist sampling theorems, aliasing, PAM/TDM application.
LO Analyze the functional processes (sampling, quantization and binary encoding) of pulse-code modulation (PCM) technique.
LO Generate variants of PCM such as differential PCM (DPCM) and adaptive differential PCM (ADPCM).
LO Implement delta modulation and adaptive delta modulation techniques.

3. Introduction Digital representation of analog signals
Analog signal source
Waveform Coding (Codec)
Digital signal destination
Fig. 1A Analog-to-Digital Encoding

4. Advantages of Digital Transmissions
Noise immunity
Error detection and correction
Ease of multiplexing
Integration of analog and digital data
Use of signal regenerators
Data integrity and security
Ease of evaluation and measurements
More suitable for processing ……..

5. Disadvantages of Digital Transmissions
More bandwidth requirement
Need of precise time synchronization
Additional hardware for encoding/decoding
Integration of analog and digital data
Sudden degradation in QoS
Incompatible with existing analog facilities

6. A Typical Digital Communication Link
Fig. 1B Block Diagram

7. 1.1 Practical Aspects of Sampling
Sampling Theorem
Methods of Sampling
Significance of Sampling Rate
Anti-aliasing Filter
Applications of Sampling Theorem – PAM/TDM

8. 1.1.1 Sampling Theorem
Sampling Theorem for Baseband Signal - A baseband signal having no frequency components higher than fm Hz may be completely recovered from the knowledge of its samples taken at a rate of at least 2 fm samples per second, that is, sampling frequency fs ≥ 2 fm.
A baseband signal having no frequency components higher than fm Hz is completely described by its sample values at uniform intervals less than or equal to 1/(2fm) seconds apart, that is, the sampling interval Ts ≤ 1/(2fm) seconds.
The minimum sampling rate fs = 2 fm samples per second is called the Nyquist sampling rate.

9. ….. Sampling Theorem
Sampling Theorem for Bandpass Signal - If an analog information signal containing no frequency outside the specified bandwidth W Hz, it may be reconstructed from its samples at a sequence of points spaced 1/(2W) seconds apart with zero-mean squared error.
The reciprocal of Nyquist rate, 1/(2W), is called the Nyquist interval, that is, Ts = 1/(2W).
The phenomenon of the presence of high-frequency component in the spectrum of the original analog signal is called aliasing or simply foldover.
The minimum sampling rate of (2W) samples per second, for an analog signal bandwidth of W Hz, is called the Nyquist rate.

10. Methods of Sampling
Ideal sampling - an impulse at each sampling instant
Fig Ideal Sampling

11. ….. Methods of Sampling
Natural sampling - a pulse of short width with varying amplitude with natural tops
Fig Natural Sampling

12. ….. Methods of Sampling
Flat-top sampling - a pulse of short width with varying amplitude with flat tops
Fig Flat-top Sampling

13. 1.1.3 Significance of Sampling Rate
When fs < 2fm, spectral components of adjacent samples will overlap, known as aliasing
Fig An Illustration of Aliasing

14. Fig. 1.1.5 Minimizing Aliasing
Antialiasing Filter
An anti-aliasing filter is a low-pass filter of sufficient higher order which is recommended to be used prior to sampling.
Fig Minimizing Aliasing

15. 1.1.5 Application of Sampling Theorem – PAM/TDM
Figure
Design of PAM/TDM System

16. 1.2 Pulse Code Modulation (PCM)
Block Diagram of PCM
PCM Sampling
Quantization of Sampled Signal
Encoding of Quantized Sampled Signal
PCM System using Codec
PCM System Parameters

17. Block Diagram of PCM System
Figure 1.2.1
Block Diagram of PCM System

18. The Process of Natural Sampling
PCM Sampling
Figure 1.2.3
The Process of Natural Sampling

19. 1.2.3 Quantization of Sampled SignalVL
L01
L12
L34
L23
L45
L56
L67 VH Δ
Δ/2
s(t)
sq(t) Δ0 Δ1 Δ2 Δ3 Δ4 Δ5 Δ6 Δ7 s0 s1 s2 s3 s4 s5 s6 s7
Figure 1.2.6
Operation of Quantization

20. Quantization Error and Classification
Quantization error is defined as the difference between rounding off sample values of an analog signal to the nearest permissible level of the quantizer during the process of quantization.
Quantization is the conversion of an analog sample of the information signal into discrete form. Thus, an infinite number of possible levels are converted to a finite number of conditions.
Classification of Quantization Process
Uniform quantization
Non-uniform quantization

21. Characteristics of Compressor, Uniform and Non-uniform Quantizer
Figure 1.2.9
Figure

22. μ-law and A-law Compression Characteristics
Figure
Figure

23. 1.2.4 Encoding of Quantized Sampled Signal
Figure PCM – Functional Blocks

24. Figure 1.2.15 Functional Block Diagram
PCM System using Codec
Analog signal IN/OUT
Hybrid
LPF
A/D
converter
(Tx side)
D/A
(Rx side)
CODEC
PCM signal
Digital MUX
Digital DeMUX
To other codecs
From other codecs
Tx signal
Rx signal
Figure Functional Block Diagram

25. 1.2.6 PCM System Parameters PCM Data Rate (bps) = 2nfm
PCM Bandwidth (Hz) = (1/2) PCM Data Rate = nfm
Dynamic Range (dB) = 20 log (2n – 1)
Coding Efficiency (%) = [(minimum bits)/(actual bits)] x 100
Where n is number of PCM encoding bits and fm is the highest frequency component of information signal

26. 1.3 DPCM and Adaptive DPCM 1.3.1 DPCM Transmitter with Predictor
DPCM Receiver with Predictor
Adaptive Differential PCM

27. DPCM Transmitter and Receiver with Predictor
The difference in the amplitude levels of two successive samples is transmitted rather than the absolute value of the actual sample
Figure DPCM Transmitter with Predictor
Figure DPCM Receiver with Predictor

28. 1.4 Delta Modulation 1.4.1 Slope Overload and Granular Noise
DM Encoder and Decoder
Delta-Sigma Modulation
Adaptive Delta Modulation (ADM)
Comparison of PCM and DM Techniques

29. Essence of Delta Modulation (DM)
Delta modulation (DM) uses a single-bit DPCM code to achieve digital transmission of analog signals
Figure An Ideal Delta Modulation Waveform

30. Delta Modulation Encoding
Figure Basic Concept of Linear DM Encoding

31. DM Encoding Waveform
Figure 1.4.3

32. Delta Modulation Decoding Figure 1.4.4 Basic Concept of DM Decoding

33. 1.4.1 Slope Overload and Granular Noise
Figure 1.4.5
Figure 1.4.6
REMEMBER: In DM, the step size is related to the sampling frequency. In order to avoid slope overload distortion, the maximum slope of the staircase approximation must be equal to or greater than the maximum slope of the signal.

34. DM Encoder and Decoder
Figure 1.4.7
Figure 1.4.8

35. 1.4.3 Delta-Sigma Modulation
Combines the operation of transmitter integrator (in the accumulator part) and the receiver integrator, and then shift it prior to the encoder in the transmitter
High over-sampling is employed in sigma-delta modulation systems, they are mostly useful in low-frequency applications such as digital telephony, digital audio encoders (compact-disc) and digital spectrum analyzers.
The input to the delta modulator is actually the difference between the integral of the analog signal and the integrated output pulses.

36. 1.4.4 Adaptive Delta Modulation (ADM)
The step size is automatically varied, depending on the level of the derivative of the input analog signal
A common algorithm followed for an ADM is that when three consecutive 1s or 0s occur, the step size is increased or decreased by a factor of 1.5.
The receiver must be able to adapt step sizes in exactly the same manner as the transmitter
NOTE: Continuous Variable Slope Delta Modulation (CVSDM) is an improvement over ADM.

37. 1.4.5 Comparison of PCM and DM Techniques
S. No.
Parameter
PCM
DPCM DM
ADM 1.
Number of bits per sample
4/8/16 bits
More than one bit but less than PCM
One bit 2.
Number of levels
Depends on number of bits
Fixed number of levels
Two levels 3.
Step size
Fixed or variable
Fixed
Variable 4.
Transmission bandwidth
More bandwidth needed
Lesser than PCM
Lowest 5.
Feedback
Does not exist
Exists 6.
Quantization noise/distortion
Quantization noise depends on number of bits
Quantization noise & slope overload
slope overload & granular noise
Quantization noise only 7.
Complexity of implementation
Complex
Simple

38. About the Author
T. L. Singal graduated from National Institute of Technology, Kurukshetra and post-graduated from Punjab Technical university in Electronics & Communication Engineering. He began his career with Avionics Design Bureau, HAL, Hyderabad in 1981 and worked on Radar Communication Systems. Then he led R&D group in a Telecom company and successfully developed Multi- Access VHF Wireless Communication Systems. He visited Germany during
He executed international assignment as Senior Network Consultant with Flextronics Network Services, Texas, USA during He was associated with Nokia, AT&T, Cingular Wireless and Nortel Networks, for optimization of 2G/3G Cellular Networks in USA. Since 2003, he is in teaching profession in reputed engineering colleges in India. He has number of technical research papers published in the IEEE Proceedings, Journals, and International/National Conferences. He has authored three text-books `Wireless Communications (2010)’, `Analog & Digital Communications (2012)’, and `Digital Communication (2015) with internationally renowned publisher McGraw-Hill Education.

39. THANKS!