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Optimum Signal Processing An introduction
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Optimum Signal Processing An Introduction Second Edition Sophocles J. Orfanidis Rutgers University
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Optimum
Signal Processing
Optimum
Signal Processing
An Introduction
Second Edition
Sophocles J. Orfanidis
Rutgers University
http://www.ece.rutgers.edu/~orfanidi/osp2e
To my parents
John and Clio Orfanidis
Copyright © 1988 by McGraw-Hill Publishing Company
Copyright © 1996–2007 by Sophocles J. Orfanidis
This revised printing, first published in 2007, is a republication of the second edition of
this book published by McGraw-Hill Publishing Company, New York, NY, in 1988 (ISBN
0-07-047794-9), and also published earlier by Macmillan, Inc., New York, NY, 1988 (ISBN
0-02-389380-X). All copyrights to this work reverted to Sophocles J. Orfanidis in 1996.
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
R
is a registered trademark of The MathWorks, Inc.
Web page: http://www.ece.rutgers.edu/~orfanidi/osp2e
ISBN-13: 978-0-9793713-0-1 (softcover)
ISBN-10: 0-9793713-0-9
ISBN-13: 978-0-9793713-1-8 (hardcover)
ISBN-10: 0-9793713-1-7
Contents
Preface ix
1 Random Signals 1
1.1 Probability Density, Mean, Variance, 1
1.2 Chebyshev’s Inequality, 2
1.3 Joint and Conditional Densities, and Bayes’ Rule, 4
1.4 Correlation Canceling, 7
1.5 Gram-Schmidt Orthogonalization, 11
1.6 Partial Correlations, 19
1.7 Forward/Backward Prediction and LU/UL Factorization, 23
1.8 Random Signals, 38
1.9 Power Spectrum and Its Interpretation, 40
1.10 Sample Autocorrelation and the Periodogram, 42
1.11 Random Signal Models and Their Uses, 45
1.12 Filter Model of First Order Autoregressive Process, 51
1.13 Stability and Stationarity, 52
1.14 Parameter Estimation by the Maximum Likelihood Method, 53
1.15 Parameter Estimation by the Yule-Walker Method, 54
1.16 Linear Prediction and Signal Modeling, 56
1.17 Cram
´
er–Rao Bound and Maximum Likelihood, 58
1.18 Problems, 63
1.19 References, 70
2 Some Signal Processing Applications 72
2.1 Filtering of Stationary Random Signals, 72
2.2 System Identification by Cross-Correlation Methods, 75
2.3 Noise Reduction and Signal Enhancement Filters, 76
2.4 Quantization Noise, 83
2.5 Statistical Treatment of Multiplier Roundoff Error, 84
2.6 Introduction to Linear Prediction, 86
2.7 Gapped Functions, Levinson and Schur Recursions, 91
2.8 Introduction to Data Compression and DPCM, 97
2.9 Problems, 100
2.10 References, 104
3 Spectral Factorization 106
3.1 Minimum-Phase Signals and Filters, 106
3.2 Partial Energy and Minimal Delay, 107
3.3 Invariance of the Autocorrelation Function, 108
3.4 Minimum-Delay Property, 108
3.5 Minimum-Phase Property, 109
3.6 Spectral Factorization Theorem, 110
3.7 Minimum-Phase Property of the Prediction-Error Filter, 112
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