Fast Fourier Transforms
C. Burrus, Ivan Selesnick, Markus Pueschel, Steven Johnson, Matteo Frigo
Computers & Technology
Fast Fourier Transforms
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This book uses an index map, a polynomial decomposition, an operator factorization, and a conversion to a filter to develop a very general and efficient description of fast algorithms to calculate the discrete Fourier transform (DFT). The work of Winograd is outlined, chapters by Selesnick, Pueschel, and Johnson are included, and computer programs are provided.

Fast Fourier Transforms
1. Preface: Fast Fourier Transforms
2. Introduction: Fast Fourier Transforms
3. Multidimensional Index Mapping
4. Polynomial Description of Signals
5. The DFT as Convolution or Filtering
6. Factoring the Signal Processing Operators
7. Winograd's Short DFT Algorithms
8. DFT and FFT: An Algebraic View
9. The Cooley-Tukey Fast Fourier Transform Algorithm
10. The Prime Factor and Winograd Fourier Transform Algorithms
11. Implementing FFTs in Practice
12. Algorithms for Data with Restrictions
13. Convolution Algorithms
14. Comments: Fast Fourier Transforms
15. Conclusions: Fast Fourier Transforms
16. Appendix 1: FFT Flowgraphs
17. Appendix 2: Operation Counts for General Length FFT
18. Appendix 3: FFT Computer Programs
19. Appendix 4: Programs for Short FFTs
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