Mario Blaum, John L. Fan, et al.
IEEE International Symposium on Information Theory - Proceedings
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.
Mario Blaum, John L. Fan, et al.
IEEE International Symposium on Information Theory - Proceedings
Y.Y. Li, K.S. Leung, et al.
J Combin Optim
Imran Nasim, Michael E. Henderson
Mathematics
Alfred K. Wong, Antoinette F. Molless, et al.
SPIE Advanced Lithography 2000