Chapter 1: PCM, and Delta Modulation and Demodulation

Learning Objectives LO 1.1 - Understand various practical aspects of sampling such as methods of sampling, Nyquist sampling theorems, aliasing, PAM/TDM application. LO 1.2 - Analyze the functional processes (sampling, quantization and binary encoding) of pulse-code modulation (PCM) technique. LO 1.3 - Generate variants of PCM such as differential PCM (DPCM) and adaptive differential PCM (ADPCM). LO 1.4 - Implement delta modulation and adaptive delta modulation techniques.

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

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 ……..

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

A Typical Digital Communication Link Fig. 1B Block Diagram

1.1 Practical Aspects of Sampling 1.1.1 Sampling Theorem 1.1.2 Methods of Sampling 1.1.3 Significance of Sampling Rate 1.1.4 Anti-aliasing Filter 1.1.5 Applications of Sampling Theorem – PAM/TDM

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.

….. 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.

1.1.2 Methods of Sampling Ideal sampling - an impulse at each sampling instant Fig. 1.1.1 Ideal Sampling

….. Methods of Sampling Natural sampling - a pulse of short width with varying amplitude with natural tops Fig. 1.1.2 Natural Sampling

….. Methods of Sampling Flat-top sampling - a pulse of short width with varying amplitude with flat tops Fig. 1.1.3 Flat-top Sampling

1.1.3 Significance of Sampling Rate When fs < 2fm, spectral components of adjacent samples will overlap, known as aliasing Fig. 1.1.4 An Illustration of Aliasing

Fig. 1.1.5 Minimizing Aliasing 1.1.4 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. 1.1.5 Minimizing Aliasing

1.1.5 Application of Sampling Theorem – PAM/TDM Figure 1.1.10 Design of PAM/TDM System

1.2 Pulse Code Modulation (PCM) 1.2.1 Block Diagram of PCM 1.2.2 PCM Sampling 1.2.3 Quantization of Sampled Signal 1.2.4 Encoding of Quantized Sampled Signal 1.2.5 PCM System using Codec 1.2.6 PCM System Parameters

Block Diagram of PCM System Figure 1.2.1 Block Diagram of PCM System

The Process of Natural Sampling 1.2.2 PCM Sampling Figure 1.2.3 The Process of Natural Sampling

1.2.3 Quantization of Sampled Signal VL 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

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

Characteristics of Compressor, Uniform and Non-uniform Quantizer Figure 1.2.9 Figure 1.2.10

μ-law and A-law Compression Characteristics Figure 1.2.11 Figure 1.2.12

1.2.4 Encoding of Quantized Sampled Signal Figure 1.2.13 PCM – Functional Blocks

Figure 1.2.15 Functional Block Diagram 1.2.5 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 1.2.15 Functional Block Diagram

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

1.3 DPCM and Adaptive DPCM 1.3.1 DPCM Transmitter with Predictor 1.3.2 DPCM Receiver with Predictor 1.3.3 Adaptive Differential PCM

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 1.3.1 DPCM Transmitter with Predictor Figure 1.3.2 DPCM Receiver with Predictor

1.4 Delta Modulation 1.4.1 Slope Overload and Granular Noise 1.4.2 DM Encoder and Decoder 1.4.3 Delta-Sigma Modulation 1.4.4 Adaptive Delta Modulation (ADM) 1.4.5 Comparison of PCM and DM Techniques

Essence of Delta Modulation (DM) Delta modulation (DM) uses a single-bit DPCM code to achieve digital transmission of analog signals Figure 1.4.1 An Ideal Delta Modulation Waveform

Delta Modulation Encoding Figure 1.4.2 Basic Concept of Linear DM Encoding

DM Encoding Waveform Figure 1.4.3

Delta Modulation Decoding Figure 1.4.4 Basic Concept of DM Decoding

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.

1.4.2 DM Encoder and Decoder Figure 1.4.7 Figure 1.4.8

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.

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.

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

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 1990-92. He executed international assignment as Senior Network Consultant with Flextronics Network Services, Texas, USA during 2000-02. 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.

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