Amir Ali Ahmadi, Raphaël M. Jungers, et al.
SICON
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. © 1997 Elsevier Science Inc.
Amir Ali Ahmadi, Raphaël M. Jungers, et al.
SICON
Harpreet S. Sawhney
IS&T/SPIE Electronic Imaging 1994
John S. Lew
Mathematical Biosciences
Yi Zhou, Parikshit Ram, et al.
ICLR 2023