TY - JOUR

T1 - On algebras related to the discrete cosine transform

AU - Feig, Ephraim

AU - Ben-Or, Michael

PY - 1997/11/15

Y1 - 1997/11/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=30244447021&partnerID=8YFLogxK

U2 - 10.1016/S0024-3795(96)00634-9

DO - 10.1016/S0024-3795(96)00634-9

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AN - SCOPUS:30244447021

SN - 0024-3795

VL - 266

SP - 81

EP - 106

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1-3

ER -