《Computational Frameworks for the Fast Fourier Transform》 (Charles Van Loan)contains a very readable and up-to-date presentation of FFT techniques, their theory and application. Together with many explicit computational algorithms, the extensive annotated list of references add greatly to the scientific value of this reference text.

Preface

Preliminary Remarks

1 The Radix-2 Frameworks

 1.1 Matrix Notation and Algorithms

 1.2 The FFT Idea

 1.3 The Cooley-Tukey Radix-2 Factorization

 1.4 Weight and Butterfly Computations

 1.5 Bit Reversal and Transposition

 1.6 The Cooley-Tukey Framework

 1.7 The Stockham Autosort Frameworks

 1.8 The Pease Framework

 1.9 Decimation in Frequency and Inverse FFTs

2 General Radix Frameworks

 2.1 General Radix Ideas 

 2.2 Index Reversal and Transposition

 2.3 Mixed-Radix Factorizations

 2.4 Radix-4 and Radix-8 Frameworks

 2.5 The Split-Radix Framework

3 High-Performance Frameworks

 3.1 The Multiple DFT Problam

 3.2 Matrix Transposition

 3.3 The Large Single-Vector FFT Problem

 3.4 The Multidimensional FFT Problem

 3.5 Distributed-Memory FFT

 3.6 Shared-Memory FFTs

4 Selected Topics

 4.1 Prime Factor Frameworks

 4.2 Convolution

 4.3 FFTs of Real Data

 4.4 Fast Trigonometric Transforms

 4.5 Fast Poisson Solvers

Bibliography

Index