Computational Frameworks for the Fast Fourier Transform

1. The Radix-2 Frameworks. Matrix Notation and Algorithms; The FFT Idea; The Cooley-Tukey Factorization; Weight and Butterfly Computations; Bit Reversal and Transposition; The Cooley-Tukey Framework; The Stockham Autosort Frameworks; The Pease Framework; Decimation in Frequency and Inverse FFTs; 2. General Radix Frameworks. The General Radix Ideas; Index Reversal and Transposition; Mixed-Radix Factorizations; Radix-4 and Radix-8 Frameworks; The Split-Radix Frameworks; 3. High Performance Frameworks. The Multiple DFT Problem; Matrix Transposition; The Large Single-Vector FFT Problem; Multi-Dimensional FFT Problem; Distributed Memory FFTs; Shared Memory FFTs; 4. Selected Topics. Prime Factor FFTs; Convolution; FFTs of Real Data; Cosine and Sine Transforms; Fast Poisson Solvers; Bibliography; Index.