Transforms and Applications Handbook  book cover
3rd Edition

Transforms and Applications Handbook

ISBN 9781420066524
Published January 19, 2010 by CRC Press
911 Pages 411 B/W Illustrations

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Book Description

Updating the original, Transforms and Applications Handbook, Third Edition solidifies its place as the complete resource on those mathematical transforms most frequently used by engineers, scientists, and mathematicians. Highlighting the use of transforms and their properties, this latest edition of the bestseller begins with a solid introduction to signals and systems, including properties of the delta function and some classical orthogonal functions.
It then goes on to detail different transforms, including lapped, Mellin, wavelet, and Hartley varieties. Written by top experts, each chapter provides numerous examples and applications that clearly demonstrate the unique purpose and properties of each type. The material is presented in a way that makes it easy for readers from different backgrounds to familiarize themselves with the wide range of transform applications.
Revisiting transforms previously covered, this book adds information on other important ones, including:

  • Finite Hankel, Legendre, Jacobi, Gengenbauer, Laguerre, and Hermite
  • Fraction Fourier
  • Zak
  • Continuous and discrete Chirp-Fourier
  • Multidimensional discrete unitary
  • Hilbert-Huang

Most comparable books cover only a few of the transforms addressed here, making this text by far the most useful for anyone involved in signal processing—including electrical and communication engineers, mathematicians, and any other scientist working in this field.

Table of Contents

Signals and Systems, A.D. Poularikas
Fourier Transforms, K.B. Howell
Sine and Cosine Transform, P. Yip
Hartley Transform, K.J. Olejniczak
Laplace Transforms, A.D. Poularikas and S. Seely
Z-Transform, A.D. Poularikas
Hilbert Transforms, S.L. Hahn
Radon and Abel Transforms, S.R. Deans
Hankel Transform, R. Piessens
Wavelet Transform, Y. Sheng
Finite Hankel Transforms, Legendre Transforms, Jacobi and Gegenbauer Transforms,
and Laguerre and Hermite Transforms, L. Debnath
Mellin Transform, J. Bertrand, P. Bertrand, and J.-P. Ovarlez
Mixed Time–Frequency Signal Transformations, G. F. Boudreaux-Bartels
Fractional Fourier Transform, H.M. Ozaktas, M. Alper Kutay, and Ç. Candan
Lapped Transforms, R.L. de Queiroz
Zak Transform, M.E. Oxley and B.W. Suter
Discrete Time and Discrete Fourier Transforms, A.D. Poularikas
Discrete Chirp–Fourier Transform, X.-G. Xia
Multidimensional Discrete Unitary Transforms, A.M. Grigoryan
Empirical Mode Decomposition and the Hilbert–Huang Transform, A. Ayenu-Prah, N. Attoh-Okine, and N.E. Huang

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Alexander D. Poularikas received his Ph.D from the University of Arkansas, Fayetteville, Arkansas, and became a professor at the University of Rhode Island, Kingston, Rhode Island. He became the chairman of the engineering department at the University of Denver, Denver, Colorado, and then became the chairman of the electrical and computer engineering department at the University of Alabama in Huntsville, Huntsville, Alabama. Dr. Poularikas has published seven books and has edited two. He has served as the editor in chief of the Signal Processing series (1993–1997) with Artech House, and is now the editor in chief of the Electrical Engineering and Applied Signal Processing series as well 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 Educators Award of the IEEE, Huntsville Section. He is now a professor emeritus at the University of Alabama in Huntsville.