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Titlebook: Algorithms for Discrete Fourier Transform and Convolution; R. Tolimieri,Myoung An,Chao Lu,C. S. Burrus (Profe Book 19891st edition Springe

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发表于 2025-3-21 17:51:58 | 显示全部楼层 |阅读模式
期刊全称Algorithms for Discrete Fourier Transform and Convolution
影响因子2023R. Tolimieri,Myoung An,Chao Lu,C. S. Burrus (Profe
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学科分类Signal Processing and Digital Filtering
图书封面Titlebook: Algorithms for Discrete Fourier Transform and Convolution;  R. Tolimieri,Myoung An,Chao Lu,C. S. Burrus (Profe Book 19891st edition Springe
影响因子This book is based on several courses taught during the last five years at the City College of the City University of New York and at Fudan University, Shanghai, China in the Summer, 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 which would serve to represent the vast array of algorithms designed over the last twenty years for com­ puting 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 con­ cepts 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 which can serve both of these needs. In fact, it is our belief that certain mathematical ideas provide a natural lan­ guage and culture for understanding, unifying and implementing a wide range of digital signal processing (DSP) algorithms. This b
Pindex Book 19891st edition
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Partnerinnen und Töchter im Vergleichte the resulting factorization by combining Rader and Winograd small FFT algorithms. The basic factorization is . where . is a block diagonal matrix with small skew-circulant blocks (rotated Winograd cores) and tensor product of these small skew-circulant blocks, and . is a pre-addition matrix with all its entries being 0, 1 or −1.
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Good-Thomas PFA,r in structure to these additive algorithms, but no longer requiring the twiddle factor multiplication. The idea is due to Good [2] in 1958 and Thomas [8] in 1963, and the resulting algorithm is called the Good-Thomas Prime Factor algorithm (PFA).
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Partnerinnen und Töchter im Vergleich convolution theorem which returns the computation to an FFT computation. Since the size (.−1) is a composite number, the (.−1)-point FT can be handled by Cooley-Tukey FFT algorithms. The Winograd algorithm for small convolutions can also be applied to the skew-circulant action.
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https://doi.org/10.1007/978-3-658-11082-6 of Rader’s multiplicative FT algorithms, we derive the fundamental factorization . where . is a block-diagonal matrix having skew-circulant blocks (rotated Winograd cores) and tensor products of these skew-circulant blocks and . is a matrix of pre-additions, all of whose entries are 0, 1 or −1. Variants will then be derived.
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