Author	Tolimieri, Richard. author
Title	Algorithms for Discrete Fourier Transform and Convolution [electronic resource] / by Richard Tolimieri, Chao Lu, Myoung An
Imprint	New York, NY : Springer New York : Imprint: Springer, 1997
Edition	Second Edition
Connect to	http://dx.doi.org/10.1007/978-1-4757-2767-8
Descript	XII, 268 p. online resource

This book is based on several courses taught during the years 1985-1989 at the City College of the City University of New York and at Fudan Univerยญ sity, Shanghai, China, in the summer of 1986. It was originally our intention to present to a mixed audience of electrical engineers, mathematicians and computer scientists at the graduate level a collection of algorithms that would serve to represent the vast array of algorithms designed over the last twenty years for computing the finite Fourier transform (FFT) and finite convolution. However, it was soon apparent that the scope of the course had to be greatly expanded. For researchers interested in the design of new algorithms, a deeper understanding of the basic mathematical concepts underlying algorithm design was essential. At the same time, a large gap remained between the statement of an algorithm and the implementation of the algorithm. The main goal of this text is to describe tools that can serve both of these needs. In fact, it is our belief that certain mathematical ideas provide a natural language and culture for understanding, unifying and implementing a wide range of digital signal processing (DSP) algoยญ rithms. This belief is reinforced by the complex and time-consuming effort required to write code for recently available parallel and vector machines. A significant part of this text is devoted to establishing rules and procedures that reduce and at times automate this task

1 Review of Applied Algebra -- 2 Tensor Product and Stride Permutation -- 3 Cooley-Tukey FFT Algorithms -- 4 Variants of FT Algorithms and Implementations -- 5 Good-Thomas PFA -- 6 Linear and Cyclic Convolutions -- 7 Agarwal-Cooley Convolution Algorithm -- 8 Multiplicative Fourier Transform Algorithm -- 9 MFTA: The Prime Case -- 10 MFTA: Product of Two Distinct Primes -- 11 MFTA: Composite Size -- 12 MFTA: p2 -- 13 Periodization and Decimation -- 14 Multiplicative Characters and the FT -- 15 Rationality

1. Engineering
2. Functional analysis
3. Engineering
4. Signal
5. Image and Speech Processing
6. Engineering
7. general
8. Functional Analysis