Algebraic Signal Processing Theory: Cooley-Tukey Type Algorithms for DCTs and DSTs

This paper presents a systematic methodology to derive and classify fast algorithms for linear transforms. The approach is based on the algebraic signal processing theory. This means that the algorithms are not derived by manipulating the entries of transform matrices, but by a stepwise decompositio...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 56; no. 4; pp. 1502 - 1521
Main Authors: Puschel, M., Moura, J.M.F.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.04.2008
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algebra
Application specific processors
Applied sciences
Chinese remainder theorem
discrete cosine transform (DCT)
Discrete cosine transforms
discrete Fourier transform (DFT)
Discrete Fourier transforms
discrete sine transform (DST)
Discrete transforms
Exact sciences and technology
fast Fourier transform (FFT)
Fast Fourier transforms
Filters
Fourier transforms
Information, signal and communications theory
Miscellaneous
polynomial algebra
Polynomials
representation theory
Signal processing
Signal processing algorithms
Telecommunications and information theory
Fast Fourier transformation
Chinese remainder theorem
Signal theory
Discrete Fourier transformation
discrete Fourier transform (DFT)
fast Fourier transform (FFT)
Discrete sine transform
discrete cosine transform (DCT)
discrete sine transform (DST)
Linear transformation
Signal processing
representation theory
Chinese
Fast algorithm
Discrete cosine transforms
polynomial algebra
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Description
Summary:This paper presents a systematic methodology to derive and classify fast algorithms for linear transforms. The approach is based on the algebraic signal processing theory. This means that the algorithms are not derived by manipulating the entries of transform matrices, but by a stepwise decomposition of the associated signal models, or polynomial algebras. This decomposition is based on two generic methods or algebraic principles that generalize the well-known Cooley-Tukey fast Fourier transform (FFT) and make the algorithms' derivations concise and transparent. Application to the 16 discrete cosine and sine transforms yields a large class of fast general radix algorithms, many of which have not been found before.
Bibliography:ObjectType-Article-2
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2007.907919