Transforms and Applications Handbook, Third Edition (Electrical Engineering Handbook)

914 Pages·2010·17.61 MB·English

by  Alexander D. Poularikas

T H I R D E D I T I O N
TRANSFORMS
A N D
APPLICATIONS
H A N D B O O K
The Electrical Engineering Handbook Series
Series Editor
Richard C. Dorf
University of California, Davis
Titles Included in the Series
The Avionics Handbook, Second Edition, Cary R. Spitzer
The Biomedical Engineering Handbook, Third Edition, Joseph D. Bronzino
The Circuits and Filters Handbook, Third Edition, Wai-Kai Chen
The Communications Handbook, Second Edition, Jerry Gibson
The Computer Engineering Handbook, Vojin G. Oklobdzija
The Control Handbook, William S. Levine
CRC Handbook of Engineering Tables, Richard C. Dorf
Digital Avionics Handbook, Second Edition, Cary R. Spitzer
The Digital Signal Processing Handbook, Vijay K. Madisetti and Douglas Williams
The Electrical Engineering Handbook, Third Edition, Richard C. Dorf
The Electric Power Engineering Handbook, Second Edition, Leonard L. Grigsby
The Electronics Handbook, Second Edition, Jerry C. Whitaker
The Engineering Handbook, Third Edition, Richard C. Dorf
The Handbook of Ad Hoc Wireless Networks, Mohammad Ilyas
The Handbook of Formulas and Tables for Signal Processing, Alexander D. Poularikas
Handbook of Nanoscience, Engineering, and Technology, Second Edition,
William A. Goddard, III, Donald W. Brenner, Sergey E. Lyshevski, and Gerald J. Iafrate
The Handbook of Optical Communication Networks, Mohammad Ilyas and
Hussein T. Mouftah
The Industrial Electronics Handbook, J. David Irwin
The Measurement, Instrumentation, and Sensors Handbook, John G. Webster
The Mechanical Systems Design Handbook, Osita D.I. Nwokah and Yidirim Hurmuzlu
The Mechatronics Handbook, Second Edition, Robert H. Bishop
The Mobile Communications Handbook, Second Edition, Jerry D. Gibson
The Ocean Engineering Handbook, Ferial El-Hawary
The RF and Microwave Handbook, Second Edition, Mike Golio
The Technology Management Handbook, Richard C. Dorf
Transforms and Applications Handbook, Third Edition, Alexander D. Poularikas
The VLSI Handbook, Second Edition, Wai-Kai Chen
T H I R D E D I T I O N
TRANSFORMS
A N D
APPLICATIONS
H A N D B O O K
Editor-in-Chief
ALEXANDER D. POULARIKAS
Boca Raton London New York
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Library of Congress Cataloging-in-Publication Data
Transforms and applications handbook / editor, Alexander D. Poularikas. -- 3rd ed.
p. cm. -- (Electrical engineering handbook ; 43)
Includes bibliographical references and index.
ISBN-13: 978-1-4200-6652-4
ISBN-10: 1-4200-6652-8
1. Transformations (Mathematics)--Handbooks, manuals, etc. I. Poularikas, Alexander D., 1933- II. Title. III. Series.
QA601.T73 2011
515’.723--dc22 2009018410
Visit the Taylor & Francis Web site at
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and the CRC Press Web site at
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Contents
Preface to the Third Edition........................................................................................................................................................vii
Editor..................................................................................................................................................................................................ix
Contributors .....................................................................................................................................................................................xi
1 Signals and Systems...........................................................................................................................................................1-1
Alexander D. Poularikas
2 Fourier Transforms............................................................................................................................................................2-1
Kenneth B. Howell
3 Sine and Cosine Transforms............................................................................................................................................3-1
Pat Yip
4 Hartley Transform .............................................................................................................................................................4-1
Kraig J.Olejniczak
5 Laplace Transforms............................................................................................................................................................5-1
Alexander D. Poularikas andSamuel Seely
6 Z-Transform........................................................................................................................................................................6-1
Alexander D. Poularikas
7 Hilbert Transforms ............................................................................................................................................................7-1
Stefan L. Hahn
8 Radon and Abel Transforms ........................................................................................................................................... 8-1
Stanley R. Deans
9 Hankel Transform..............................................................................................................................................................9-1
Robert Piessens
10 Wavelet Transform..........................................................................................................................................................10-1
Yulong Sheng
11 Finite Hankel Transforms, Legendre Transforms, Jacobi and Gegenbauer Transforms,
and Laguerre and Hermite Transforms......................................................................................................................11-1
Lokenath Debnath
12 Mellin Transform.............................................................................................................................................................12-1
JacquelineBertrand,Pierre Bertrand,andJean-PhilippeOvarlez
13 Mixed Time–Frequency Signal Transformations......................................................................................................13-1
G.Fay Boudreaux-Bartels
14 Fractional Fourier Transform........................................................................................................................................14-1
Haldun M. Ozaktas, M. AlperKutay, andÇa(cid:1)gatay Candan
v
vi Contents
15 Lapped Transforms..........................................................................................................................................................15-1
Ricardo L.de Queiroz
16 Zak Transform..................................................................................................................................................................16-1
Mark E. Oxley andBruce W. Suter
17 Discrete Time and Discrete Fourier Transforms......................................................................................................17-1
Alexander D. Poularikas
18 Discrete Chirp-Fourier Transform...............................................................................................................................18-1
Xiang-GenXia
19 Multidimensional Discrete Unitary Transforms.......................................................................................................19-1
Artyom M.Grigoryan
20 Empirical Mode Decomposition and the Hilbert–Huang Transform .................................................................20-1
Albert Ayenu-Prah,Nii Attoh-Okine, andNorden E.Huang
Appendix A: Functions of a Complex Variable................................................................................................................ A-1
Appendix B: Series and Summations....................................................................................................................................B-1
Appendix C: Definite Integrals...............................................................................................................................................C-1
Appendix D: Matrices and Determinants ..........................................................................................................................D-1
Appendix E: Vector Analysis...................................................................................................................................................E-1
Appendix F: Algebra Formulas and Coordinate Systems...............................................................................................F-1
Index.............................................................................................................................................................................................IN-1
Preface to the Third Edition
ThethirdeditionofTransformsandApplicationsHandbookfollowsasimilarapproachtothatofthesecondedition.Thenewedition
buildsuponthepreviousonebypresentingadditionalimportanttransformsvaluabletoengineersandscientists.Numerousexamples
anddifferenttypesofapplicationsareincludedineachchaptersothatreadersfromdifferentbackgroundswillhavetheopportunity
tobecomefamiliarwithawidespectrumofapplicationsofthesetransforms.Inthisedition,wehaveaddedthefollowingimportant
transforms:
1. FiniteHankeltransforms,Legendretransforms,JacobiandGengenbauertransforms,andLaguerreandHermitetransforms
2. FractionFouriertransforms
3. Zaktransforms
4. ContinuousanddiscreteChirp–Fouriertransforms
5. Multidimensionaldiscreteunitarytransforms
6. Hilbert–Huangtransforms
IwouldliketothankRichardDorf,theserieseditor,forhishelp.SpecialthanksalsogotoNoraKonopka,theacquisitionseditorfor
engineeringbooks,forherrelentlessdrivetofinishtheproject.
AlexanderD.Poularikas
1
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vii

Editor
Alexander D. Poularikas received his PhD from the University of Arkansas, Fayetteville, Arkansas, and became a professor at
theUniversityofRhodeIsland,Kingston,RhodeIsland.HebecamethechairmanoftheengineeringdepartmentattheUniversityof
Denver,Denver,Colorado,andthenbecamethechairmanoftheelectricalandcomputerengineeringdepartmentattheUniversity
ofAlabamainHuntsville,Huntsville,Alabama.
Dr.Poularikashaspublished sevenbooks and hasedited two.Hehasserved astheeditorin chiefof the SignalProcessing series
(1993–1997)withArtechHouseandisnowtheeditorinchiefoftheElectricalEngineeringandAppliedSignalProcessingseriesaswell
as the Engineering and Science Primer series (1998 to present) with Taylor & Francis. He is a Fulbright scholar, a lifelong senior
member of the IEEE, and a member of Tau Beta Pi, Sigma Nu, and Sigma Pi. In 1990 and in 1996, he received the Outstanding
EducatorsAwardoftheIEEE,HuntsvilleSection.HeisnowaprofessoremeritusattheUniversityofAlabamainHuntsville.
Dr.Poularikashasauthored,coauthored,andeditedthefollowingbooks:
Electromagnetics,MarcelDekker,NewYork,1979.
ElectricalEngineering:IntroductionandConcepts,MatrixPublishers,Beaverton,OR,1982.
Workbook,MatrixPublishers,Beaverton,OR,1982.
SignalsandSystems,Brooks=Cole,Boston,MA,1985.
ElementsofSignalsandSystems,PWS-Kent,Boston,MA,1988.
SignalsandSystems,2ndedn.,PWS-Kent,Boston,MA,1992.
TheTransformsandApplicationsHandbook,CRCPress,BocaRaton,FL,1995.
TheHandbookforFormulasandTablesforSignalProcessing,CRCPress,BocaRaton,FL,1998,2ndedn.(2000),3rdedn.(2009).
AdaptiveFilteringPrimerwithMATLAB,Taylor&Francis,BocaRaton,FL,2006.
SignalsandSystemsPrimerwithMATLAB,Taylor&Francis,BocaRaton,FL,2007.
DiscreteRandomSignalProcessingandFilteringPrimerwithMATLAB,Taylor&Francis,BocaRaton,FL,2009.
ix