Other Fast Algorithms for the FFT

Algorithms for the fast calculation of a discrete Fourier transform (DFT) are based on factorization of the matrix of the transform. In order to use these fast algorithms and thus to exploit to the full both the characteristics of the signals to be processed and the various technological possibiliti...

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Bibliographic Details
Published in:Digital Signal Processing p. 1
Main Author: Bellanger, Maurice
Format: Book Chapter
Language:English
Published: Chichester, UK Wiley 2024
John Wiley & Sons
John Wiley & Sons, Ltd
Edition:10
Subjects:
Computer Architecture
Computer Hardware Engineering
discrete Fourier transform
Electronic Devices
Electronics & Semiconductors
fast Fourier transform algorithms
Kronecker product
lapped transforms
matrix products
partial transforms
ISBN:9781394182664, 139418266X
Online Access:Get full text
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Summary:Algorithms for the fast calculation of a discrete Fourier transform (DFT) are based on factorization of the matrix of the transform. In order to use these fast algorithms and thus to exploit to the full both the characteristics of the signals to be processed and the various technological possibilities, one must use a suitable mathematical tool – the Kronecker product of matrices. The Kronecker product is a tensor operation which is a generalization of the multiplication of a matrix by a scalar. The Kronecker product can be combined with conventional matrix products. Factorization as Kronecker products forms the basis of algorithms which have various properties. It also applies to partial transforms, which are of great practical importance. In image compression, lapped transforms introduce smoothing and attenuate the so‐called blocking effects. Winograd algorithms generally introduce a reduction in the amount of computation. This reduction can be quite significant when compared to fast Fourier transform algorithms.
ISBN:9781394182664
139418266X
DOI:10.1002/9781394182695.ch3