Fast Fourier Transforms书

Table of Contents 1 Preface: Fast Fourier Transforms ................................................ 1 2 Introduction: Fast Fourier Transforms .......................................... .5 3 Multidimensional Index Mapping ............................................... 7 4 Polynomial Description of Signals .............................................. 21 5 The DFT as Convolution or Filtering .......................................... 27 6 Factoring the Signal Processing Operators .................................... 39 7 Winog rad's Short DFT Algorithms ............................................ 43 8 DFT and FFT: An Algebraic View ............................................. 6.5 9 The Cooley-Tukey Fast Fourier Transform Algorithm ........................ 79 10 The Prime Factor and Winograd Fourier Transform Algo rithms.......................................................................... 97 11 Implementing FFTs in Practice .............................................. 109 12 Algorithms for Data with Restrictions ....................................... 137 13 Convolution Algorithms ....................................................... 139 14 Comments: Fast Fourier Transforms ......................................... 1.53 15 Conclusions: Fast Fourier Transforms ....................................... 1.57 16 Appendix 1: FFT Flowgraphs ................................................ 1.59 17 Appendix 2: Operation Counts for General Length FFT .................. 16.5 18 Appendix 3: FFT Computer Programs ...................................... 167 19 Appendix 4: Programs for Short FFTs ...................................... 207 Bibliography....................................................................... 210 Index............................................................................... 242 Attributions........................................................................244