INTRODUCTION TO Signal Processing
INTRODUCTION TO Signal Processing
INTRODUCTION TO Signal Processing Sophocles I.Orfanidis Rutgers University http://www.ece.rutgers.edu/~orfanidi/intro2sp
INTRODUCTION TO Signal Processing Sophocles J. Orfanidis Rutgers University http://www.ece.rutgers.edu/~orfanidi/intro2sp
To my lifelong friend George Lazos Copyright O 2010 by Sophocles J.Orfanidis This book was previously published by Pearson Education,Inc. Copyright 1996-2009 by Prentice Hall,Inc.Previous ISBN 0-13-209172-0. All rights reserved.No parts of this publication may be reproduced,stored in a retrieval system,or transmitted in any form or by any means,electronic,mechanical,photocopy- ing,recording or otherwise,without the prior written permission of the author. MATLAB is a registered trademark of The MathWorks,Inc. Web page:www.ece.rutgers.edu/~orfanidi/i2sp
To my lifelong friend George Lazos Copyright © 2010 by Sophocles J. Orfanidis This book was previously published by Pearson Education, Inc. Copyright © 1996–2009 by Prentice Hall, Inc. Previous ISBN 0-13-209172-0. All rights reserved. No parts of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the author. MATLABR is a registered trademark of The MathWorks, Inc. Web page: www.ece.rutgers.edu/~orfanidi/i2sp
Contents Preface xiii 1 Sampling and Reconstruction 1 1.1 Introduction,I 1.2 Review of Analog Signals,1 1.3 Sampling Theorem,4 1.3.1 Sampling Theorem,6 1.3.2 Antialiasing Prefilters,7 1.3.3 Hardware Limits,8 1.4 Sampling of Sinusoids,9 1.4.1 Analog Reconstruction and Aliasing,10 1.4.2 Rotational Motion,27 1.4.3 DSP Frequency Units,29 1.5 Spectra of Sampled Signals*,29 1.5.1 Discrete-Time Fourier Transform,31 1.5.2 Spectrum Replication,33 1.5.3 Practical Antialiasing Prefilters,38 1.6 Analog Reconstructors*,42 1.6.1 Ideal Reconstructors,43 1.6.2 Staircase Reconstructors,45 1.6.3 Anti-Image Postfilters,46 1.7 Basic Components of DSP Systems,53 1.8 Problems,55 2 Quantization 61 2.1 Quantization Process,61 2.2 Oversampling and Noise Shaping*,65 2.3 D/A Converters,71 2.4 A/D Converters,75 2.5 Analog and Digital Dither*,83 2.6 Problems,90 3 Discrete-Time Systems 95 3.1 Input/Output Rules,96 3.2 Linearity and Time Invariance,100 3.3 Impulse Response,103 i
Contents Preface xiii 1 Sampling and Reconstruction 1 1.1 Introduction, 1 1.2 Review of Analog Signals, 1 1.3 Sampling Theorem, 4 1.3.1 Sampling Theorem, 6 1.3.2 Antialiasing Prefilters, 7 1.3.3 Hardware Limits, 8 1.4 Sampling of Sinusoids, 9 1.4.1 Analog Reconstruction and Aliasing, 10 1.4.2 Rotational Motion, 27 1.4.3 DSP Frequency Units, 29 1.5 Spectra of Sampled Signals∗, 29 1.5.1 Discrete-Time Fourier Transform, 31 1.5.2 Spectrum Replication, 33 1.5.3 Practical Antialiasing Prefilters, 38 1.6 Analog Reconstructors∗, 42 1.6.1 Ideal Reconstructors, 43 1.6.2 Staircase Reconstructors, 45 1.6.3 Anti-Image Postfilters, 46 1.7 Basic Components of DSP Systems, 53 1.8 Problems, 55 2 Quantization 61 2.1 Quantization Process, 61 2.2 Oversampling and Noise Shaping∗, 65 2.3 D/A Converters, 71 2.4 A/D Converters, 75 2.5 Analog and Digital Dither∗, 83 2.6 Problems, 90 3 Discrete-Time Systems 95 3.1 Input/Output Rules, 96 3.2 Linearity and Time Invariance, 100 3.3 Impulse Response, 103 vii
viii CONTENTS 3.4 FIR and IIR Filters,105 3.5 Causality and Stability,112 3.6 Problems.117 4 FIR Filtering and Convolution 121 4.1 Block Processing Methods,122 4.1.1 Convolution,122 4.1.2 Direct Form,123 4.1.3 Convolution Table,126 4.1.4LTΠFom,127 4.1.5 Matrix Form,129 4.1.6 Flip-and-Slide Form,131 4.1.7 Transient and Steady-State Behavior,132 4.1.8 Convolution of Infinite Sequences,134 4.1.9 Programming Considerations,139 4.1.10 Overlap-Add Block Convolution Method,143 4.2 Sample Processing Methods,146 4.2.1 Pure Delays,146 4.2.2 FIR Filtering in Direct Form,152 4.2.3 Programming Considerations,160 4.2.4 Hardware Realizations and Circular Buffers,162 4.3 Problems,178 5 Z-Transforms 183 5.1 Basic Properties,183 5.2 Region of Convergence,186 5.3 Causality and Stability,193 5.4 Frequency Spectrum,196 5.5 Inverse z-Transforms,202 5.6 Problems,210 6 Transfer Functions 214 6.1 Equivalent Descriptions of Digital Filters,214 6.2 Transfer Functions,215 6.3 Sinusoidal Response,229 6.3.1 Steady-State Response,229 6.3.2 Transient Response,232 6.4 Pole/Zero Designs,242 6.4.1 First-Order Filters,242 6.4.2 Parametric Resonators and Equalizers,244 6.4.3 Notch and Comb Filters,249 6.5 Deconvolution,Inverse Filters,and Stability,254 6.6 Problems,259
viii CONTENTS 3.4 FIR and IIR Filters, 105 3.5 Causality and Stability, 112 3.6 Problems, 117 4 FIR Filtering and Convolution 121 4.1 Block Processing Methods, 122 4.1.1 Convolution, 122 4.1.2 Direct Form, 123 4.1.3 Convolution Table, 126 4.1.4 LTI Form, 127 4.1.5 Matrix Form, 129 4.1.6 Flip-and-Slide Form, 131 4.1.7 Transient and Steady-State Behavior, 132 4.1.8 Convolution of Infinite Sequences, 134 4.1.9 Programming Considerations, 139 4.1.10 Overlap-Add Block Convolution Method, 143 4.2 Sample Processing Methods, 146 4.2.1 Pure Delays, 146 4.2.2 FIR Filtering in Direct Form, 152 4.2.3 Programming Considerations, 160 4.2.4 Hardware Realizations and Circular Buffers, 162 4.3 Problems, 178 5 z-Transforms 183 5.1 Basic Properties, 183 5.2 Region of Convergence, 186 5.3 Causality and Stability, 193 5.4 Frequency Spectrum, 196 5.5 Inverse z-Transforms, 202 5.6 Problems, 210 6 Transfer Functions 214 6.1 Equivalent Descriptions of Digital Filters, 214 6.2 Transfer Functions, 215 6.3 Sinusoidal Response, 229 6.3.1 Steady-State Response, 229 6.3.2 Transient Response, 232 6.4 Pole/Zero Designs, 242 6.4.1 First-Order Filters, 242 6.4.2 Parametric Resonators and Equalizers, 244 6.4.3 Notch and Comb Filters, 249 6.5 Deconvolution, Inverse Filters, and Stability, 254 6.6 Problems, 259