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Abstract: It is well-known that the discrete Fourier transform (DFT) can be characterized as decomposition matrix for the polynomial algebra C [x]=(x 1). This property gives deep insight into the DFT and can be used to explain and derive its fast algorithms. In this paper we present the polynomial algebras associated to the 16 discrete cosine and sine transforms. Then we derive important algorithms by manipulating algebras rather than matrix entries. This makes the derivation more transparent and... (Update)
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BibTeX entry: (Update)
@misc{ schel-discrete,
author = "Markus Püschel and José M. F. Moura",
title = "The Discrete Trigonometric Transforms And Their Fast Algorithms: An Algebraic
Symmetry Perspective",
url = "citeseer.ist.psu.edu/553556.html" }
Citations (may not include all citations):156 An Introduction to Orthogonal Polynomials (context) - Chihara - 1978
137 Discrete Cosine Transform: Algorithms (context) - Rao, Yip - 1990
37 Fast Algorithms for the Discrete W Transform and for the Dis.. (context) - Wang - 1984
24 Fast Algorithms for the Discrete Cosine Transform (context) - Feig, Winograd - 1992
23 A Polynomial Approach to Fast Algorithms for Discrete Fourie.. (context) - Steidl, Tasche - 1991
16 The Discrete Cosine Transform - Strang - 1999
13 Displacement structure approach to discrete trigonometric tr.. - Kailath, Olshevsky - 1996
4 Automatic Generation of Fast Discrete Signal Transforms - Egner, Puschel - 1992
4 Direct methods for computing discrete sinusoidal transforms (context) - Chan, Ho - 1990
3 Diagonalizing Properties of the Discrete Cosine Transforms (context) - Sanchez, Garca et al. - 1995
2 The Discrete W Transform (context) - Wang, Hunt - 1985
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