Book Description

The third edition of Transforms and Applications Handbook follows a similar approach to that of the second edition. The new edition builds upon the previous one by presenting additional important transforms valuable to engineers and scientists. Numerous examples and different types of applications are included in each chapter so that readers from different backgrounds will have the opportunity to become familiar with a wide spectrum of applications of these transforms. In this edition, we have added the following important transforms:

1. Finite Hankel transforms, Legendre transforms, Jacobi and Gengenbauer transforms, and Laguerre and Hermite transforms
2. Fraction Fourier transforms
3. Zak transforms
4. Continuous and discrete Chirp–Fourier transforms
5. Multidimensional discrete unitary transforms
6. Hilbert–Huang transforms

I would like to thank Richard Dorf, the series editor, for his help. Special thanks also go to Nora Konopka, the acquisitions editor for engineering books, for her relentless drive to finish the project.

Alexander D. Poularikas

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 and Samuel 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
Jacqueline Bertrand, Pierre Bertrand, and Jean-Philippe Ovarlez
13 Mixed Time–Frequency Signal Transformations ……… 13-1
G. Fay Boudreaux-Bartels
14 Fractional Fourier Transform …………… 14-1
Haldun M. Ozaktas, M. Alper Kutay, and Ça gatay Candan

15 Lapped Transforms ….. 15-1
Ricardo L. de Queiroz
16 Zak Transform … 16-1
Mark E. Oxley and Bruce W. Suter
17 Discrete Time and Discrete Fourier Transforms ….. 17-1
Alexander D. Poularikas
18 Discrete Chirp-Fourier Transform …….. 18-1
Xiang-Gen Xia
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, and Norden 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

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