Fast transforms : algorithms, analyses, applications

This book has grown from notes used by the authors to instruct fast transform classes. One class was sponsored by the Training Department of Rockwell International, and another was sponsored by the Department of Electrical Engineering of The University of Texas at Arlington. Some of the material was also used in a short course sponsored by the University of Southern California. The authors are indebted to their students for motivating the writing of this book and for suggestions to improve it. COVER......Page 1 TITLE PAGE\r......Page 3 CONTENTS......Page 7 1\rINTRODUCTION......Page 23 2\rFOURIER SERIES AMD THE FOURIER TRANSFORM......Page 28 3\rDISCRETE FOURIER TRANSFORMS......Page 55 4\rFAST FOURIER TRANSFORM ALGORITHMS......Page 80 5 FFT ALGORITHMS THAT REDUCE MULTIPLICATIONS......Page 121 6\rDFT FILTER SHAPES AND SHAPING......Page 200 7 SPECTRAL ANALYSIS USING THE FFT......Page 274 8 WALSH-HADAMARD TRANSFORMS......Page 323 9\rTHE GENERALIZED TRANSFORM......Page 356 10 DISCRETE ORTHOGONAL TRANSFORMS......Page 384 11 NUMBER THEORETIC TRANSFORMS......Page 439 APPENDIX......Page 466 REFERENCES......Page 476 INDEX......Page 505 Many signals can be expressed as a series that is a linear combination of orthogonal basis functions.