Joy Y. Cheng, Daniel P. Sanders, et al.
SPIE Advanced Lithography 2008
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.
Joy Y. Cheng, Daniel P. Sanders, et al.
SPIE Advanced Lithography 2008
S.F. Fan, W.B. Yun, et al.
Proceedings of SPIE 1989
Chai Wah Wu
Linear Algebra and Its Applications
Donald Samuels, Ian Stobert
SPIE Photomask Technology + EUV Lithography 2007