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So here is a book that I have written to meet the junior students’ needs and written with a student-oriented approach, based on many years of teaching courses at the junior level.
INTRODUCTION TO DIGITAL SIGNAL PROCESSING AND FILTER DESIGN B.A. Sheno WILEY INTERSCIENCE A JOHN WILEY SONS INC PUblIcatIon Copyright o 2006 by John Wiley sons, Inc. All rights reserved Published by John Wiley Sons, Inc, Hoboken, New Jersey Published simultaneously in Canad No part of this publication may be reproduced, stored in a retrieval system, or transmitted in an form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc, 222 Rosewood Drive, Danvers Ma01923,(978)750-8400,fax(978)750-4470,oronthewebatwww.copyright.comRequests to the Publisher for permission should be addressed to the Permissions Department, John Wiley Sons, Inc. lll River Street, Hoboken, NJ 07030, (201)748-6011, fax(201)748-6008, or online at http://www.wiley.com/go/permission Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other amages For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at(800)762-2974, outside the United States at(317)572-3993 or fax(317)5724002 Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about wiley products, visit our websiteatwww.wiley.com Library of Congress Cataloging-in-Publication Data: ISBN-13978-0-471-46482-2( cloth) ISBN-100-471-46482-1( cloth) Printed in the united states of america 10987654321 CONTENTS Preface 1 Introduction 1.1 Introduction 1.2 Applications of DSP 1. 3 Discrete-Time Signals 1.3. 1 Modeling and properties of discrete-Time Signals 1.3.2 Unit Pulse function 1.3.3 Constant Sequence 10 1.3.4 Unit Step Function 10 1.3.5 Real Exponential Function 12 1.3.6 Complex exponential function 12 1.3.7 Properties of cos(won) 1. 4 History of Filter Design 5 Analog and Digital Signal Processing 23 1.5.1 Operation of a Mobile Phone Network 1.6 Summary Problems 20 References 2 Time- Domain Analysis and z Transform 32 2.1 A Linear, Time-Invariant System 32 2.1.1 Models of the Discrete-Time system 3 2.1.2 Recursive algorithm 36 2.1.3 Convolution Sum 38 2.2 z Transform Theory 41 2. 2. 1 Definition 41 2.2.2 Zero Input and Zero State Response 4 CONTENTS 2.2.3 Linearity of the System 2.2.4 Time-Invariant System 2.3 USing z Transform to Solve Difference Equations 51 2.3. 1 More Applications of z Transform 56 2.3.2 Natural Response and Forced Response 58 2. 4 Solving Difference Equations Using the Classical Method 59 2.4.1 Transient Response and Steady-State Response 63 2.5 z Transform Method Revisited 2.6 Convolution revisited 65 2. 7 A Model from Other models 70 2.7.1 Review of model generation 2.8 Stability 77 2.8.1 Jury-Marden Test 78 2.9 Solution USing MATLAB Functions 81 2.10 Summary 93 Problems 94 R eferences 3 Frequency-Domain Analysis 112 3.1 Introduction 3.2 Theory of Sampling 113 3.2.1 Sampling of Bandpass Signals 120 3.3 dtft and IdtFt 122 3.3.1 Time-Domain analysis of noncausal Inputs 125 3.3.2 Time-Shifting property 3.3.3 Frequency-Shifting Property 127 3.3.4 Time Reversal Property 128 3.4 DtFT of Unit Step sequence 138 3.4.1 Differentiation Property 3.4.2 Multiplication Property 142 3.4.3 Conjugation Property 145 3.4.4 Symmetry property 145 3. 5 Use of matlab to Compute DtFt 14 3.6 DtFS and DFT 154 3.6.1 Introduction 154 CONTENTS 3.6.2 Discrete-Time Fourier Series 156 3.6.3 Discrete Fourier Transform 159 3.6.4 Reconstruction of dtft from DFt 160 3.6.5 Properties of dtFs and dFt 16l 3.7 Fast Fourier Transform 170 3.8 Use of matLaB to Compute DFT and IDFT 172 3.9 Summary 177 Problems 178 References 185 4 Infinite Impulse Response Filters 186 4.1 Introduction 186 4.2 Magnitude Approximation of Analog Filters 189 4.2. 1 Maximally Flat and Butterworth Approximation 191 4.2.2 Design Theory of Butterworth Lowpass filters 194 4.2.3 Chebyshev I Approximation 202 4.2.4 Properties of Chebyshev Polynomials 202 4.2.5 Design Theory of Chebyshev I Lowpass Filters 4.2.6 Chebyshev II Approximation 08 4.2.7 Design of Chebyshev II Lowpass Filters 10 4.2.8 Elliptic Function Approximation 212 4.3 Analog Frequency Transformations 12 4.3.1 Highpass Filter 12 4.3.2 Bandpass filter 213 4.3.3 Bandstop Filter 216 4.4 Digital Filters 219 4.5 Impulse-Invariant Transformation 4.6 Bilinear transformation 221 4.7 Digital Spectral transformation 226 4.8 Allpass Filters 230 4.9 IIR Filter Design Using MATLAB 231 4.10 Yule-Walker approximation 238 4.11 Summary 240 Problems 240 References 247 CONTENTS 5 Finite Impulse Response Filters 249 5.1 Introduction 5.1.1 Notations 250 5.2 Linear phase fir filters 251 5.2. 1 Properties of linear Phase FIR Filters 256 5.3 Fourier Series Method Modified by Windows 261 5.3.1 Gibbs phenomenon 263 5.3.2 Use of window functions 266 5.3.3 FIR Filter Design Procedures 268 5.4 Design of Windowed FIR Filters Using MATLaB 273 5.4.1 Estimation of filter order 273 5.4.2 Design of the fir filter 275 5.5 Equiripple linear Phase FIR Filters 280 5.6 Design of Equiripple FIR Filters Using MATLAB 285 5.6.1 USe of MATLAB Program to Design Equiripple FIR Filters 285 5.7 Frequency Sampling Method 289 5. 8 Summar 292 Problems 294 References 301 6 Filter realizations 303 6.1 Introduction 303 6.2 FIR Filter realizations 305 6.2.1 Lattice structure for fir filters 309 6.2.2 Linear phase fir filter realizations 310 6.3 IIR Filter realizations 312 6.4 Allpass Filters in Parallel 320 6. 4.1 Design Procedure 325 6. 4.2 Lattice-Ladder realization 326 6.5 Realization of FiR and IIR Filters Using MATLaB 327 6.5.1 MATLAB Program Used to Find allpass Filters in parallel 334 6.6 Summary 346 CONTENTS Problems 347 References 353 7 Quantized Filter Analysis 354 7.1 Introduction 354 7.2 Filter Design- Analysis Tool 355 7.3 Quantized Filter Analysis 360 7.4 Binary Numbers and Arithmetic 360 7.5 Quantization Analysis of IIR Filters 367 7.6 Quantization Analysis of FIR Filters 375 7.7 Summary 379 Problems 379 References 379 8 Hardware Design USing DsP Chips 381 8.1 Introducti 381 8.2 Simulink and Real-Time Workshop 381 8.3 Design Preliminaries 383 8.4 Code generation 385 8.5 Code Composer Studio 386 8.6 Simulator and emulator 388 8.6. 1 Embedded Target with Real-Time Workshop 389 8.7 Conclusion References 390 9 MATLAB Primer 391 9.1 Introduction 9.1.1 Vectors, Arrays, and Matrices 392 9.1.2 Matrix Operations 393 9. 1.3 Scalar Operations 398 9.1.4 Drawing plots 9.1.5 MATLAB Functions 400 9.1.6 Numerical Format 401

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