Fast Fourier Transforms by C. Sidney Burrus
Fast Fourier Transforms - Table of Contents
1. Preface: *Fast Fourier Transforms*
2. Introduction: *Fast Fourier Transforms*
3. Multidimensional Index Mapping
4. Polynomial Description of Signals
5. The DFT as Convolution or Filtering
6. Factoring the Signal Processing Operators
7. Winograd's Short DFT Algorithms
8. DFT and FFT: An Algebraic View
9. The Cooley-Tukey Fast Fourier Transform Algorithm
10. The Prime Factor and Winograd Fourier Transform Algorithms
11. Implementing FFTs in Practice
12. Algorithms for Data with Restrictions
13. Convolution Algorithms
14. Comments: *Fast Fourier Transforms*
15. Conclusions: *Fast Fourier Transforms*
Appendix 1. FFT Flowgraphs
Appendix 2. Operation Counts for General-Length FFT
Appendix 3. FFT Computer Programs
Appendix 4. Programs for Short FFTs
What You Will Learn in Fast Fourier Transforms
"Fast Fourier Transforms" by C. Sidney Burrus is a comprehensive guide to efficient computation of the "Discrete Fourier Transform (DFT)" and its widely used "Fast Fourier Transform (FFT)" algorithms. The book explains the mathematical foundations of fast Fourier methods, including "convolution", polynomial decomposition, and operator factorization, making it easier for readers to understand how to compute transforms quickly and accurately. Burrus emphasizes both theory and practical application, showing how these algorithms are essential in modern "signal processing".
The text goes beyond the classic Cooley-Tukey FFT, exploring advanced topics such as Winograd’s short DFT algorithms, prime factor algorithms, and other fast techniques. It also addresses "implementation strategies", including programming examples that demonstrate how to translate theory into functional software. Chapters contributed by other experts expand the theoretical coverage and illustrate practical considerations for real-world applications.
Designed for engineers, computer scientists, and mathematicians, "Fast Fourier Transforms" combines rigorous mathematical derivation with hands-on examples. By connecting "FFT", "DFT", and "convolution" theory to practical computation, the book equips readers with the knowledge to analyze and process signals efficiently in applications such as audio, image processing, communications, and scientific computing. It remains a vital resource for anyone working with fast Fourier methods.
Book Details & Specifications
Title:
Fast Fourier Transforms by C. Sidney Burrus
Publisher:
Samurai Media Limited
Year:
2018
Pages:
252
Type:
PDF
Language:
English
ISBN-10 #:
988840752X
ISBN-13 #:
978-9888407521
License:
CC BY 4.0
Amazon:
Amazon
About the Author: C. Sidney Burrus
The author
C. Sidney Burrus
is a pioneering "electrical engineer" and professor at "Rice University". Burrus is renowned for his contributions to "digital signal processing", "FFT algorithms", and "wavelet theory", advancing both theoretical and practical aspects of computation in engineering. His work explains the "Discrete Fourier Transform (DFT)" and its efficient implementations, blending rigorous mathematics with real-world applications. Ideal for students, researchers, and engineers, it provides a deep understanding of FFT methods and computational techniques essential for modern signal processing and applied mathematical analysis.
Read or Downloadable Fast Fourier Transforms
Free Fourier Analysis Books PDF | Signal Processing Resources