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Signal Processing: a Mathematical Approach, Second Edition Mathematics MONOGRAPHS AND RESEARCH NOTES IN MATHEMATICS MONOGRAPHS AND RESEARCH NOTES IN MATHEMATICS Second Edition Second Signal Processing: A Mathematical Approach is designed to show how many of the mathematical tools the reader knows can be used to understand and employ signal processing techniques in an applied environment. Assuming an advanced undergraduate- or graduate- level understanding of mathematics—including familiarity with Fouri- er series, matrices, probability, and statistics—this Second Edition: Signal Processing , Contains new chapters on convolution and the vector DFT, Processing Signal plane-wave propagation, and the BLUE and Kalman lters A Mathematical Approach , Expands the material on Fourier analysis to three new chapters to provide additional background information Second Edition , Presents real-world examples of applications that demonstrate how mathematics is used in remote sensing Featuring problems for use in the classroom or practice, Signal Processing: A Mathematical Approach, Second Edition covers topics such as Fourier series and transforms in one and several vari- ables; applications to acoustic and electro-magnetic propagation models, transmission and emission tomography, and image recon- struction; sampling and the limited data problem; matrix methods, singular value decomposition, and data compression; optimization techniques in signal and image reconstruction from projections; autocorrelations and power spectra; high-resolution methods; de- tection and optimal ltering; and eigenvector-based methods for array processing and statistical ltering, time-frequency analysis, and wavelets. Charles L. Byrne “A PDF version of this book is available for free in Open Byrne Access at www.taylorfrancis.com. It has been made available under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 license.” Signal Processing A Mathematical Approach Second Edition MONOGRAPHS AND RESEARCH NOTES IN MATHEMATICS Series Editors John A. Burns Thomas J. Tucker Miklos Bona Michael Ruzhansky Chi-Kwong Li Published Titles Iterative Optimization in Inverse Problems, Charles L. Byrne Signal Processing: A Mathematical Approach, Second Edition, Charles L. Byrne Modeling and Inverse Problems in the Presence of Uncertainty, H. T. Banks, Shuhua Hu, and W. Clayton Thompson Sinusoids: Theory and Technological Applications, Prem K. Kythe Blow-up Patterns for Higher-Order: Nonlinear Parabolic, Hyperbolic Dispersion and Schrödinger Equations, Victor A. Galaktionov, Enzo L. Mitidieri, and Stanislav Pohozaev Set Theoretical Aspects of Real Analysis, Alexander B. Kharazishvili Special Integrals of Gradshetyn and Ryzhik: the Proofs – Volume l, Victor H. Moll Forthcoming Titles Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions, Irina V. Melnikova and Alexei Filinkov Monomial Algebra, Second Edition, Rafael Villarreal Groups, Designs, and Linear Algebra, Donald L. Kreher Geometric Modeling and Mesh Generation from Scanned Images, Yongjie Zhang Difference Equations: Theory, Applications and Advanced Topics, Third Edition, Ronald E. Mickens Method of Moments in Electromagnetics, Second Edition, Walton C. Gibson The Separable Galois Theory of Commutative Rings, Second Edition, Andy R. Magid Dictionary of Inequalities, Second Edition, Peter Bullen Actions and Invariants of Algebraic Groups, Second Edition, Walter Ferrer Santos and Alvaro Rittatore Practical Guide to Geometric Regulation for Distributed Parameter Systems, Eugenio Aulisa and David S. Gilliam Analytical Methods for Kolmogorov Equations, Second Edition, Luca Lorenzi Handbook of the Tutte Polynomial, Joanna Anthony Ellis-Monaghan and Iain Moffat Application of Fuzzy Logic to Social Choice Theory, John N. Mordeson, Davendar Malik and Terry D. Clark Microlocal Analysis on Rˆn and on NonCompact Manifolds, Sandro Coriasco Forthcoming Titles (continued) Cremona Groups and Icosahedron, Ivan Cheltsov and Constantin Shramov Special Integrals of Gradshetyn and Ryzhik: the Proofs – Volume ll, Victor H. Moll Symmetry and Quantum Mechanics, Scott Corry Lineability and Spaceability in Mathematics, Juan B. Seoane Sepulveda, Richard W. Aron, Luis Bernal-Gonzalez, and Daniel M. Pellegrinao Line Integral Methods and Their Applications, Luigi Brugnano and Felice Iaverno Reconstructions from the Data of Integrals, Victor Palamodov Lineability: The Search for Linearity in Mathematics, Juan B. Seoane Sepulveda Partial Differential Equations with Variable Exponents: Variational Methods and Quantitative Analysis, Vicentiu Radulescu Complex Analysis: Conformal Inequalities and the Bierbach Conjecture, Prem K. Kythe MONOGRAPHS AND RESEARCH NOTES IN MATHEMATICS Signal Processing A Mathematical Approach Second Edition Charles L. Byrne University of Massachusetts Lowell Lowell, Massachusetts, USA FirstFirst editionedition publishedpublished inin 20052005 byby AA KK Peters,Peters, Ltd.Ltd. First edition published in 2005 by A K Peters, Ltd. First edition published in 2005 by A K Peters, Ltd. First edition published in 2005 by A K Peters, Ltd. CRCCRC PressPress CRC Press TaylorTaylor && FrancisFrancis GroupGroup Taylor & Francis Group 60006000 BrokenBroken SoundSound ParkwayParkway NW,NW, SuiteSuite 300300 6000 Broken Sound Parkway NW, Suite 300 BocaBoca Raton,Raton, FLFL 33487-274233487-2742 Boca Raton, FL 33487-2742 ©© 20152015 byby TaylorTaylor && FrancisFrancis Group,Group, LLCLLC © 2015 by Taylor & Francis Group, LLC CRCCRC PressPress isis anan imprintimprint ofof TaylorTaylor && FrancisFrancis Group,Group, anan InformaInforma businessbusiness CRC Press is an imprint of Taylor & Francis Group, an Informa business CRCNoNo claimclaim Press toto originaloriginal U.S.U.S. GovernmentGovernment worksworks CRCNo claim Press to original U.S. Government works Taylor & Francis Group Taylor & Francis Group Printed on acid-free paper 6000PrintedPrinted Broken onon acid-freeacid-free Sound Parkway paperpaper NW, Suite 300 6000Printed Broken on acid-free Sound Parkwaypaper NW, Suite 300 Version Date: 20140730 BocaVersionVersion Raton, Date:Date: FL 2014073020140730 33487-2742 BocaVersion Raton, Date: FL 20140730 33487-2742 ©InternationalInternational 2015 by Taylor StandardStandard & Francis BookBook Group, Number-13:Number-13: LLC 978-1-4822-4184-6978-1-4822-4184-6 (Hardback)(Hardback) ©International 2015 by Taylor Standard & Francis Book Group, Number-13: LLC 978-1-4822-4184-6 (Hardback) CRC Press is an imprint of Taylor & Francis Group, an Informa business CRC Press is an imprint of Taylor & Francis Group, an Informa business ThisThis bookbook containscontains informationinformation obtainedobtained fromfrom authenticauthentic andand highlyhighly regardedregarded sources.sources. ReasonableReasonable effortsefforts This book contains information obtained from authentic and highly regarded sources. Reasonable efforts Nohavehave claim beenbeen to mademade original toto U.S.publishpublish Government reliablereliable datadata works andand information,information, butbut thethe authorauthor andand publisherpublisher cannotcannot assumeassume Nohave claim been to made original to U.S.publish Government reliable data works and information, but the author and publisher cannot assume responsibilityresponsibility forfor thethe validityvalidity ofof allall materialsmaterials oror thethe consequencesconsequences ofof theirtheir use.use. TheThe authorsauthors andand publisherspublishers responsibility for the validity of all materials or the consequences of their use. The authors and publishers Printedhavehave attemptedattempted on acid-free toto tracetrace paper thethe copyrightcopyright holdersholders ofof allall materialmaterial reproducedreproduced inin thisthis publicationpublication andand apologizeapologize toto Printedhave attempted on acid-free to trace paper the copyright holders of all material reproduced in this publication and apologize to Versioncopyrightcopyright Date: holdersholders 20140730 ifif permissionpermission toto publishpublish inin thisthis formform hashas notnot beenbeen obtained.obtained. IfIf anyany copyrightcopyright materialmaterial hashas Versioncopyright Date: holders 20140730 if permission to publish in this form has not been obtained. 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