Digital Signal Processing

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1 Digital Signal Processing Theory, Analysis and Digital-filter Design B. Somanathan Nair

2 DIGITAL SIGNAL PROCESSING Theory, Analysis and Digital-filter Design B. SOMANATHAN NAIR Principal SHM Engineering College Kadakkal Kerala Formerly Director Centre for Continuing Education Kerala Delhi

3 DIGITAL SIGNAL PROCESSING: Theory, Analysis and Digital-filter Design B. Somanathan Nair 2004 by PHI Learning Private Limited, Delhi. All rights reserved. No part of this book may be reproduced in any form, by mimeograph or any other means, without permission in writing from the publisher. ISBN The export rights of this book are vested solely with the publisher. Eighth Printing º º º January, 2013 Published by Asoke K. Ghosh, PHI Learning Private Limited, Rimjhim House, 111, Patparganj Industrial Estate, Delhi and Printed by Rajkamal Electric Press, Plot No. 2, Phase IV, HSIDC, Kundli , Sonepat, Haryana.

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6 Contents Preface 1 xiii BASIC PRINCIPLES OF SIGNAL PROCESSING Introduction Principles of Analog Signal Processing Principles of Optical Signal Processing Basic Principles of OSP Explanation of the Observed Spectrum Principles of an Optical Signal Processor Optical Signal Processor (or Optical Computer) 11 Review Questions 12 2 BASIC PRINCIPLES OF DIGITAL SIGNAL PROCESSING Introduction Why Digital Building Blocks of a Digital Signal Processor Comparison between OSP and DSP Analog-to-digital Conversion The Sampling Process Sampling and Holding The Nyquist Sampling Theorem Digital-to-analog Converters Analog-to-digital Converters The Counter-ramp-type ADC The Successive-approximation A/D Converter (SAADC) The Flash Converter The z-transformer and the Discrete Fourier-transformer 33 Review Questions 34 Problems 34 v

7 vi Contents 3 SIGNALS AND FUNCTIONS ENCOUNTERED IN SIGNAL PROCESSING Introduction The Delta (Impulse) Function The Unit-step Function The Unit-ramp Function The Parabolic and Exponential Functions The Sinusoidal Function Methods for Plotting Various Types of Signals Other Classification of Functions Even and Odd Functions Periodic and Nonperiodic Functions 56 Review Questions 60 Problems 61 4 SYSTEMS AND THEIR PROPERTIES Introduction Properties of Systems Linearity Causality Time-variance Convolution Stability Memory Worked-out Problems Problems on Linearity Problems on Causality Problems on Time-variance Problems on Stability Problems on Memory 96 Review Questions 97 Problems 97 5 TRANSFORMATIONS Introduction The Fourier, the Laplace and Other Transformations The Fourier Transformation The Laplace Transformation z-transforms and Discrete-time Fourier Transforms of Various Functions Region of Convergence (ROC), Causality and Stability 107

8 5.3 Properties of z-transforms and Discrete-time Fourier Transforms Inverse z-transformation (IZT) 128 Review Questions 131 Problems 131 Contents vii 6 DISCRETE FOURIER TRANSFORMATION Introduction Computation of DFT Inverse Discrete Fourier Transformation (IDFT) Periodicity and Symmetry Properties of DFT Periodicity in DFTs Reason for Choosing 0 and (N 1) as the Limits to Evaluate DFTs Conjugate Symmetry of DFTs Comparison between DTFT and DFT Circular Convolution Property of DFT Circular (Periodic) Shift Circular or Periodic Convolution Solving Convolutional Problems using Various Methods Additional Properties of DFT Linearity Time-shift Block Convolution Overlap-and-add Method Overlap-and-save Method 163 Review Questions 165 Problems 166 FAST-FOURIER TRANSFORMATION Introduction Decimation-in-time Radix-2 FFT Algorithm Saving Obtained in the Decimation-in-time FFT Algorithm Butterfly Diagrams Further Decimations In-place Computation Decimation-in-frequency FFT Algorithm Further Decimations in DIF Algorithm More about Butterflies in DIF Algorithm Composite-N FFT Algorithms Radix-4 DIT FFT Algorithm 201

9 viii Contents The Generalized Twiddle-factor Table for the N-point Radix-2 DIT FFT Algorithm Evaluation of 16-point DFT using Radix-2 DIT Algorithm 207 Review Questions 211 Problems 211 BASIC PRINCIPLES OF FILTERS AND FILTERING Introduction Low-pass Filters A Practical First-order RC Low-pass Filter Circuit A Practical Second-order RLC Low-pass Filter Circuit A Practical Second-order RC Low-pass Filter Circuit High-pass Filters Band-pass Filters Band-reject Filters Problems Associated with Passive Filters Theory of Analog Filter Design Introduction Filters using Operational Amplifiers Another Way of Representing the Structure of Analog Computers 227 Review Questions 228 Problems STEP-BY-STEP DESIGN OF ANALOG FILTERS Introduction The Butterworth Approximation Function Step-by-step Design of Butterworth Filters Introduction Design Procedure for Butterworth Filter Transfer Function of a Fourth-order Butterworth Filter Transfer Function of a Fifth-order Butterworth Filter Chebyshev Approximation Introduction Step-by-step Design of Chebyshev Low-pass Filter Comparison between Butterworth and Chebyshev Filters 252 Review Questions 254 Problems 254

10 Contents ix 10 STEP-BY-STEP DESIGN OF DIGITAL IIR FILTERS Introduction Theory of Infinite-impulse-response (IIR) Filters Finding the Expression for H(s) in the Digital Domain Step-by-step Design of Butterworth Digital IIR Filters Chebyshev Digital IIR Filters Introduction Step-by-step Design of Type-I Chebyshev Digital IIR Filters The Inverse (Type-II) Chebyshev IIR Filter Design Digital Filter Design using Bilinear Transformation Introduction Frequency Warping and Prewarping Design of Digital Filters using Bilinear Transformation Frequency Transformation Low-pass Frequency Transformation High-pass Frequency Transformation Band-pass Transformation Band-reject (Band-elimination or Notch-filter) Transformation Why the Name Infinite-impulse-response Filter 292 Review Questions 293 Problems 293 STRUCTURES FOR REALIZING DIGITAL IIR FILTERS Introduction Direct-form I Structure of IIR Filters Direct-form II (Canonical-form) Structure for IIR Filters Transposed-form Structure for IIR Filters Parallel Structure for IIR Filters Cascade-form Structures for IIR Filters Signal-flow Graphs in Filter-structure Realization Introduction Transposed-form Structure of Digital Filters Lattice Structure of IIR Filters 315 Review Questions 317 Problems 317

11 Digital Signal Processing Theory, Analysis And Digital-filter Design Publisher : PHI Learning ISBN : Author : B Somanathan Nair Type the URL : Get this ebook

B.Tech III Year II Semester (R13) Regular & Supplementary Examinations May/June 2017 DIGITAL SIGNAL PROCESSING (Common to ECE and EIE)

Code: 13A04602 R13 B.Tech III Year II Semester (R13) Regular & Supplementary Examinations May/June 2017 (Common to ECE and EIE) PART A (Compulsory Question) 1 Answer the following: (10 X 02 = 20 Marks)