Yi Zhou, Parikshit Ram, et al.
ICLR 2023
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.
Yi Zhou, Parikshit Ram, et al.
ICLR 2023
Sonia Cafieri, Jon Lee, et al.
Journal of Global Optimization
Robert F. Gordon, Edward A. MacNair, et al.
WSC 1985
Ligang Lu, Jack L. Kouloheris
IS&T/SPIE Electronic Imaging 2002