基本信息
- 原书名：Computational Frameworks for the Fast Fourier Transform
- 原出版社： Society for Industrial Mathematics
- 作者： Charles Van Loan
- 丛书名： 国际著名数学图书--影印版
- 出版社：清华大学出版社
- ISBN：9787302244974
- 上架时间：2011-3-21
- 出版日期：2011 年2月
- 开本：16开
- 页码：273
- 版次：1-1
- 所属分类：数学 > 分析 > 傅里叶分析与小波分析
内容简介
书籍
数学书籍
The fast Fourier transform (FFT) family of algorithms has revolutionized many areas of scientific computation. The FFT is one of the most widely used algorithms in science and engineering, with applications in almost every discipline. This volume is the most comprehensive treatment of FFTs to date.
Van Loan captures the interplay between mathematics and the design of effective numerical algorithms-a critical connection as more advanced machines become available. He uses a stylized Matlab notation, which is familiar to those engaged in high-performance computing.
This volume is essential for professionals interested in linear algebra as well as those working with numerical methods. The FFT is also a great vehicle for teaching key aspects of scientific computing.
数学书籍
The fast Fourier transform (FFT) family of algorithms has revolutionized many areas of scientific computation. The FFT is one of the most widely used algorithms in science and engineering, with applications in almost every discipline. This volume is the most comprehensive treatment of FFTs to date.
Van Loan captures the interplay between mathematics and the design of effective numerical algorithms-a critical connection as more advanced machines become available. He uses a stylized Matlab notation, which is familiar to those engaged in high-performance computing.
This volume is essential for professionals interested in linear algebra as well as those working with numerical methods. The FFT is also a great vehicle for teaching key aspects of scientific computing.
作译者
Charles Van Loan has been with the department of computer science at Cornell University since 1975 and is the author of other books on this subject.
目录
《快速傅里叶变换的计算框架(英文影印版)》
Preface ix
Preliminary Remarks xi
1 The Radix-2 Frameworks
1.1 Matrix Notation and Algorithms 2
1.2 The FFT Idea 11
1.3 The Cooley-Tukey Radix-2 Factorization 17
1.4 Weight and Butterfly Computations 22
1.5 Bit Reversal and Transposition 36
1.6 The Cooley-Tukey Framework 44
1.7 The Stockham Autosort Frameworks 49
1.8 The Pease Framework 60
1.9 Decimation in Frequency and Inverse FFTs 64
2 General Radix Frameworks
2.1 General Radix Ideas 76
2.2 Index Reversal and Transposition 84
2.3 Mixed-Radix Factorizations 95
2.4 Radix-4 and Radix-8 Frameworks 101
2.5 The Split-Radix Framework 111
3 High-Performance Frameworks
Preface ix
Preliminary Remarks xi
1 The Radix-2 Frameworks
1.1 Matrix Notation and Algorithms 2
1.2 The FFT Idea 11
1.3 The Cooley-Tukey Radix-2 Factorization 17
1.4 Weight and Butterfly Computations 22
1.5 Bit Reversal and Transposition 36
1.6 The Cooley-Tukey Framework 44
1.7 The Stockham Autosort Frameworks 49
1.8 The Pease Framework 60
1.9 Decimation in Frequency and Inverse FFTs 64
2 General Radix Frameworks
2.1 General Radix Ideas 76
2.2 Index Reversal and Transposition 84
2.3 Mixed-Radix Factorizations 95
2.4 Radix-4 and Radix-8 Frameworks 101
2.5 The Split-Radix Framework 111
3 High-Performance Frameworks
媒体评论
"This finely crafted work fills a gap in the library of books on the fast Fourier transform (FFT). It provides a complete and elegant mathematical formulation of the family of algorithms thai compute FFTs. It is written for students and professionals who already have a working knowledge of computational linear algebra... This work is an excellent contribution to the modern FFT literature."
——J. R. Hubbard, Computing Reviews, September 1993.
"... an excellent survey on the FFT, which will be valuable to all who wish to use it."
——S. Hitotumatu, Mathematical Reviews, Issue g3a.
"...This book 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."
——Short Book Reviews, August 1992, Vol.12, No.2.
——J. R. Hubbard, Computing Reviews, September 1993.
"... an excellent survey on the FFT, which will be valuable to all who wish to use it."
——S. Hitotumatu, Mathematical Reviews, Issue g3a.
"...This book 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."
——Short Book Reviews, August 1992, Vol.12, No.2.
