On algebras related to the discrete cosine transform

Autor:	Ephraim Feig, Michael Ben-Or
Rok vydání:	1997
Předmět:	Chebyshev polynomials Polynomial Factor theorem Numerical Analysis Algebra and Number Theory Algebra Reciprocal polynomial Discrete Fourier transform (general) Finite field Factorization of polynomials Algebra representation Discrete Mathematics and Combinatorics Geometry and Topology Mathematics
Zdroj:	Linear Algebra and its Applications. 266:81-106
ISSN:	0024-3795
DOI:	10.1016/s0024-3795(96)00634-9
Popis:	An algebraic theory for the discrete cosine transform (DCT) is developed, which is analogous to the well-known theory of the discrete Fourier transform (DFT). Whereas the latter diagonalizes a convolution algebra, which is a polynomial algebra modulo a product of various cyclotomic polynomials, the former diagonalizes a polynomial algebra modulo a product of various polynomials related to the Chebyshev types. When the dimension of the algebra is a power of 2, the DCT diagonalizes a polynomial algebra modulo a product of Chebyshev polynomials of the first type. In both DFT and DCT cases, the Chinese remainder theorem plays a key role in the design of fast algorithms.
Databáze:	OpenAIRE
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