Guo-Jun Qi, Charu Aggarwal, et al.
IEEE TPAMI
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.
Guo-Jun Qi, Charu Aggarwal, et al.
IEEE TPAMI
Arnon Amir, Michael Lindenbaum
IEEE Transactions on Pattern Analysis and Machine Intelligence
W.C. Tang, H. Rosen, et al.
SPIE Optics, Electro-Optics, and Laser Applications in Science and Engineering 1991
Juliann Opitz, Robert D. Allen, et al.
Microlithography 1998