Front Matter and Index (Mertins - Signal Analysis (Revised Edition))
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Signal Analysis: Wavelets, Filter Banks, Time-Frequency Transforms andApplications. Alfred MertinsCopyright 0 1999 John Wiley & Sons LtdPrint ISBN 0-471-98626-7 ElectronicISBN 0-470-84183-4Signal AnalysisSignal AnalysisWavelets, Filter Banks,Time-Frequency Transformsand ApplicationsAlfred MertinsUniversity of Wollongong, AustraliaJOHN WILEY & SONSChichester . New York .
Weinheim . Brisbane . Singapore . Toronto@B.G. Teubner Stuttgart 1996, Mertins, SignaltheorieTranslation arranged with the approval of the publisherB.G. Teubner Stuttgart, from the originalGerman edition into English.English (revised edition) Copyright@ 1999 by John Wiley& Sons Ltd,Baffins Lane, Chichester,West Sussex P019 IUD, EnglandNational01243719717International (+44) 1243 119117e-mail (for orders and customer service enquiries): cs-books@wiley.co.ukVisit our Home Page on http://www.wiley.co.uk or http://www.wiley.comthis publication may be reproduced, stored in a retrieval system,All Rights Reserved. No part ofor transmitted, in any form or by any means, electronic, mechanical, photocopying, recording,scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 orunder the terms of a licence issued by the Copyright Licensing Agency, 90 Tottenham Court Road,London, W1P 9HE, UK, without the permission in writing of the publisher, with the exception of anymaterial supplied specifically for the purpose of being entered and executed on a computer system,for exclusive use by the purchaser of the publication.& Sons Ltd accept any responsibility or liability for loss orNeither the authors nor John Wileydamage occasioned to any person or property through using the material, instructions, methods orideas contained herein, or acting or refraining from acting as a result of such use.
The authors andPublisher expressly disclaim all implied warranties, including merchantability of fitness for anyparticular purpose.Designations used by companies to distinguish their products are often claimed as trademarks. In allinstances where John Wiley& Sons is aware of a claim, the product names appear in initial capitalor capital letters. Readers, however, should contact the appropriate companies for more completeinformation regarding trademarks and registration.Other wiley Editorial OficesJohn Wiley & Sons, Inc., 605 Third Avenue,New York, NY 10158-0012, USAWiley-VCH Verlag GmbH, Pappelallee 3,D-69469 Weinheim, GermanyJacaranda Wiley Ltd, 33 Park Road, Milton,Queensland 4064, AustraliaJohn Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01,Jin Xing Distripark, Singapore 129809John Wiley & Sons (Canada) Ltd, 22 Worcester Road,Rexdale, OntarioM9W 1L1, CanadaBritish Library Cataloguing in Publication DataA catalogue record for this book is available from the British Library.ISBN 0-471-98626-7Produced from PostScript files supplied by the author.Printed and bound in Great Britain by Bookcraft (Bath) Ltd.This book is printed on acid-free paper responsibly manufactured from sustainable forestry,in which at least two trees are planted for each one used in paper production.ContentsSpaces Signal1 Signals and11.1 Signal Spaces .
. . . . . . . . . . . . . . . . . . . . . . . . . . .11.1.1 Energyand Power Signals . . . . . . . . . . . . . . . . . 121.1.2 Normed Spaces . . . . . . . . . . . . . . . . . . . . . . .Spaces . . . . . . . . . . . . . . . . . . . . . . . .31.1.3 MetricProduct Spaces . . .
. . . . . . . . . . . . . . . . 41.1.4 InnerCorrelation . . . . . . . . . . . . . . . . . . 81.2 EnergyDensityand1.2.1 Continuous-Time Signals . . . . . . . . . . . . . . . . . 81.2.2 Discrete-Time Signals . . . . . . . . . . . . . . . . . . . 9101.3 Random Signals . . . . . . . . . .
. . . . . . . . . . . . . . . . .1.3.1 Properties of Random Variables . . . . . . . . . . . . . . 11Processes.....................131.3.2 Random1.3.3 Transmission of StochasticProcessesthroughLinearSystems . . . . . . . . . . . . . . . . . . . . . .
. . . ..2 Integral Signal Representations2.1 IntegralTransforms . . . . . . . . . . . . . . . . . . . . . . . . .2.2 The Fourier Transform . . . . . . . . . . . . . . . . . . . . . . .2.3 TheHartley Transform . . . . . . . . . . . . . . . . . . . . . . .2.4 The Hilbert Transform . . . . . . . . . .
. . . . . . . . . . . . .2.4.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . .2.4.2 Some Properties of the Hilbert Transform . . . . . . .2.5 Representation of Bandpass Signals . . . . . . . . . . . . . . .2.5.1 Analytic Signal and ComplexEnvelope . .
. . . . . .2.5.2 StationaryBandpass Processes . . . . . . . . . . . . .V20....22222629343435353643viContents3 Discrete Signal Representations3.1Introduction.............................3.2 Orthogonal Series Expansions . . . . . . . . . . . . . . . . . .3.2.1 Calculation of Coefficients . .
. . . . . . . . . . . . . .3.2.2 OrthogonalProjection . . . . . . . . . . . . . . . . . .3.2.3 The Gram-Schmidt OrthonormalizationProcedure . .3.2.4 Parseval’s Relation . . . . . . . . . . . . . . . . . . . . .3.2.5 CompleteOrthonormalSets...............3.2.6 Examples of CompleteOrthonormalSets.......3.3GeneralSeries Expansions .
. . . . . . . . . . . . . . . . . . . .3.3.1 Calculating the Representation . . . . . . . . . . . . .3.3.2 OrthogonalProjection . . . . . . . . . . . . . . . . . .3.3.3 OrthogonalProjection of n-Tuples . . . . . . . . . . .3.4 Mathematical Tools . . . . . . . . . . . . . . . . . . . . . . .
.3.4.1 The&R Decomposition . . . . . . . . . . . . . . . . .3.4.2 The Moore-Penrose Pseudoinverse . . . . . . . . . . .3.4.3 The Nullspace . . . . . . . . . . . . . . . . . . . . . . .3.4.4 The Householder Transform . . . . . . . . . . . . . . .3.4.5 Givens Rotations . . . . . . . . . . . . . . . . . . . . . .4 Examples of Discrete Transforms4.1 The z-Transform . . . . . . . . .
. . . . . . . . . . . . . . . . .4.2 The Discrete-TimeFourierTransform.............4.3 The Discrete Fourier Transform (DFT) . . . . . . . . . . . . .4.4 The FastFourierTransform....................4.4.1 Radix-2 Decimation-in-Time FFT . . . . . . . . . . .4.4.2Radix-2Decimation-in-FrequencyFFT . . .
. . . . . .4.4.3 Radix-4 FFT . . . . . . . . . . . . . . . . . . . . . . . .4.4.4 Split-Radix FFT . . . . . . . . . . . . . . . . . . . . . .4.4.5 Further FFT Algorithms . . . . . . . . . . . . . . . . .4.5 Discrete Cosine Transforms . . . . . . . . . . . . . . . . . . . .4.6 Discrete Sine Transforms . .
. . . . . . . . . . . . . . . . . . . .4.7 The DiscreteHartleyTransform . . . . . . . . . . . . . . . . .4.8 TheHadamardand Walsh-Hadamard Transforms . . . . . ..........4747494950515152535657606264. 64. 6668. 69737575. 80.8285. 85. 889091. 929396. 97. 1005 TransformsandFilters for Stochastic Processes1015.1The Continuous-Time Karhunen-Loitve Transform . . .
. . . . 1015.2 The Discrete Karhunen-Loitve Transform . . . . . . . . . . . . 1035.3 The KLT of Real-Valued AR(1) Processes . . . . . . . . . . . . 1095.4 WhiteningTransforms . . . . . . . . . . . . . . . . . . . . . . .1115.5LinearEstimation.........................113viiContents5.5.1Least-SquaresEstimation.................5.5.2 The Best Linear Unbiased Estimator (BLUE) . . . . . .5.5.3 MinimumMean SquareErrorEstimation........5.6 LinearOptimalFilters . .
. . . . . . . . . . . . . . . . . . . . .5.6.1 Wiener Filters . . . . . . . . . . . . . . . . . . . . . . .5.6.2 One-StepLinearPrediction................5.6.3 Filter Design on the Basis of Finite Data Ensembles . .5.7 Estimation of Autocorrelation Sequences and Power SpectralDensities . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . .5.7.1Estimation of Autocorrelation Sequences . . . . . . . . .5.7.2 Non-Parametric Estimation of Power Spectral Densities5.7.3 Parametric Methods in SpectralEstimation . . . . . . .6 Filter Banks6.1 Basic MultirateOperations . . . .
. . . . . . . . . . . . . . . .6.1.1Decimation andInterpolation . . . . . . . . . . . . . .6.1.2 Polyphase Decomposition . . . . . . . . . . . . . . . .6.2 Two-ChannelFilterBanks . . . . . . . . . . . . . . . . . . . . .6.2.1 P R Condition . . . . . . . . . . .
. . . . . . . . . . . . .6.2.2 Quadrature MirrorFilters . . . . . . . . . . . . . . . .6.2.3GeneralPerfectReconstructionTwo-ChannelFilterBanks . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.2.4 MatrixRepresentations.................6.2.5 Paraunitary Two-ChannelFilterBanks........6.2.6 Paraunitary Filter Banks in Lattice Structure . . . . .6.2.7 Linear-PhaseFilterBanks in LatticeStructure . . . .6.2.8 Lifting Structures . . .
. . . . . . . . . . . . . . . . . . .6.3Tree-StructuredFilterBanks..................6.4 UniformM-Channel FilterBanks . . . . . . . . . . . . . . . .6.4.1 Input-Output Relations . . . . . . . . . . . . . . . . .6.4.2 The PolyphaseRepresentation .
. . . . . . . . . . . .6.4.3 ParaunitaryFilter Banks . . . . . . . . . . . . . . . .6.4.4 Design of Critically Subsampled M-Channel FIR FilterBanks . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.5 DFTFilter Banks . . . . . . . . . . . . . . . . . . . . . . . . .6.6 Cosine-ModulatedFilterBanks.................6.6.1 CriticallySubsampled Case . . . . . . . . .
