On algebras related to the discrete cosine transform
type: Item
instance of: scholarly article
title: On algebras related to the discrete cosine transform
zbMATH Open document ID: 0888.65145
DOI: 10.1016/S0024-3795(96)00634-9
author: Ephraim Feig
author: Michael Ben-Or
published in: Linear Algebra and its Applications
publication date: 1998-06-04T00:00:00Z
review text: The authors present an algebraic theory for the discrete cosine transform (modified DCT-II) which is analogous to the well-known theory of the discrete Fourier transform (DFT). To design fast DCT-algorithms we have to replace \(\mathbf C[x]/(x^n- 1)\) (DFT-setting) by \(\mathbf R[x]/(x- 1)U_N(x)\) and to use the Chinese-Remainder Theorem similar to the DFT-case. See also \textit{G. Steidl} and \textit{M. Tasche} [Math. Comput. 56, No. 193, 281-296 (1991; Zbl 0725.65145)].
Mathematics Subject Classification ID: 65T50
zbMATH DE Number: 1083211
zbMATH Keywords: Chebyshev polynomials
zbMATH Keywords: discrete cosine transform
zbMATH Keywords: discrete Fourier transform
zbMATH Keywords: Chinese-Remainder Theorem
reviewed by: Gabriele Steidl
MaRDI profile type: Publication
cites work: Discrete Cosine Transform
cites work: The multiplicative complexity of the discrete Fourier transform
cites work: Abelian semi-simple algebras and algorithms for the discrete Fourier transform
cites work: Fast discrete transforms by means of eigenpolynomials
cites work: A Fast Computational Algorithm for the Discrete Cosine Transform
cites work: Symplectic factorizations and parallel iterative algorithms for tridiagonal systems of equations
cites work: THE COLLEAGUE MATRIX, A CHEBYSHEV ANALOGUE OF THE COMPANION MATRIX
cites work: A Sinusoidal Family of Unitary Transforms
cites work: A new algorithm to compute the discrete cosine Transform
cites work: A fast cosine transform in one and two dimensions
cites work: On the Computation of the Discrete Cosine Transform
cites work: Some remarks on multivariate Chebyshev polynomials
cites work: Multi-iterative methods
cites work: On Computing the Discrete Cosine Transform
cites work: Simple FFT and DCT algorithms with reduced number of operations.
cites work: On Computing the Discrete Fourier Transform
cites work: Q4003887
Wikidata QID: Q126590404
description: scientific article; zbMATH DE number 1083211