Fast fourier transforms (6x9 version)

OpenStax

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Preface: fast fourier transforms

1 Introduction: fast fourier transforms

2 Multidimensional index mapping

3 Polynomial description of signals

4 The dft as convolution or filtering

5 Factoring the signal processing operators

6 Winograd's short dft algorithms

7 Dft and fft: an algebraic view

8 The cooley-tukey fast fourier transform algorithm

9 The prime factor and winograd fourier transform algorithms

10 Implementing ffts in practice

11 Algorithms for data with restrictions

12 Convolution algorithms

12.1 Fast convolution by the fft

12.2 Fast convolution by overlap-add

12.3 Fast convolution by overlap-save

12.4 Block processing, a generalization of overlap methods

12.5 Introduction

12.6 Block signal processing

12.7 Block convolution

12.8 Block recursion

12.9 Block state formulation

12.10 Block implementations of digital filters

12.11 Multidimensional formulation

12.12 Periodically time-varying discrete-time systems

12.13 Multirate filters, filter banks, and wavelets

12.14 Distributed arithmetic

12.15 Direct fast convolution and rectangular transforms

12.16 Number theoretic transforms for convolution

12.17 Results from number theory

12.18 Number theoretic transforms

13 Comments: fast fourier transforms

14 Conclusions: fast fourier transforms

15 Appendix 1: fft flowgraphs

16 Appendix 2: operation counts for general length fft

17 Appendix 3: fft computer programs

18 Appendix 4: programs for short ffts

Source: OpenStax, Fast fourier transforms (6x9 version). OpenStax CNX. Aug 24, 2009 Download for free at http://cnx.org/content/col10683/1.5

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