Inside the FFT Black Box: Serial and Parallel Fast Fourier Transform Algorithms / Edition 1

Inside the FFT Black Box: Serial and Parallel Fast Fourier Transform Algorithms / Edition 1

by Eleanor Chu, Alan George
     
 

ISBN-10: 0849302706

ISBN-13: 9780849302701

Pub. Date: 11/11/1999

Publisher: Taylor & Francis

Examples and diagrams explain algorithms completely, with consistent n otation. This approach connects the algorithms explicitly to the under lying mathematics. Reviews and explanations of FFT ideas taken from en gineering, mathematics, and computer science journals teach the comput ational techniques relevant to FFT. Two appendices familiarize readers with the

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Overview

Examples and diagrams explain algorithms completely, with consistent n otation. This approach connects the algorithms explicitly to the under lying mathematics. Reviews and explanations of FFT ideas taken from en gineering, mathematics, and computer science journals teach the comput ational techniques relevant to FFT. Two appendices familiarize readers with the design and analysis of computer algorithms, as well. This v olume employs a unified and systematic approach to FFT. It closes the gap between brief textbook introductions and intimidating treatments i n the FFT literature. Inside the FFT Black Box provides an up-to-date, self-contained guide for learning the FFT and the multitude of ideas and computing techniques it employs.

Product Details

ISBN-13:
9780849302701
Publisher:
Taylor & Francis
Publication date:
11/11/1999
Series:
Computational Mathematics Series
Pages:
336
Product dimensions:
7.00(w) x 10.00(h) x 0.81(d)

Table of Contents

PRELIMINARIES
An Elementary Introduction to the Discrete Fourier Transform
Some Mathematical and Computational Preliminaries
SEQUENTIAL FFT ALGORITHMS
The Divide-and-Conquer Paradigm and Two Basic FFT Algorithms
Deciphering the Scrambled Output from In-Place FFT Computation
Bit-Reversed Input to the Radix-2 DIF FFT
Performing Bit-Reversal by Repeated Permutation of Intermediate Results
An In-Place Radix-2 DIT FFT for Input in Natural Order
An In-Place Radix-2 DIT FFT for Input in Bit-Reversed Order
An Ordered Radix-2 DIT FFT
Ordering Algorithms and Computer Implementation of Radix-2 FFTs
The Radix-4 and the Class of Radix-2s FFTs
The Mixed-Radix and Split-Radix FFTs
FFTs for Arbitrary N
FFTs for Real Input
FFTs for Composite N
Selected FFT Applications
PARALLEL FFT ALGORITHMS
Parallelizing the FFTs: Preliminaries on Data Mapping
Computing and Communications on Distributed-Memory Multiprocessors
Parallel FFTs without Inter-Processor Permutations
Parallel FFTs with Inter-Processor Permutations
A Potpourri of Variations on Parallel FFTs
Further Improvement and a Generalization of Parallel FFTs
Parallelizing Two-Dimensional FFTs
Computing and Distributing Twiddle Factors in the Parallel FFTs
APPENDICES
Fundamental Concepts of Efficient Scientific Computation
Solving Recurrence Equations by Substitution
Bibliography

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