On algebras related to the discrete cosine transform
The authors present an algebraic theory for the discrete cosine transform (modified DCT-II) which is analogous to the well-known theory of the discrete Fourier transform (DFT). To design fast DCT-algorithms we have to replace \(\mathbf C[x]/(x^n- 1)\) (DFT-setting) by \(\mathbf R[x]/(x- 1)U_N(x)\) and to use the Chinese-Remainder Theorem similar to the DFT-case. See also \textit{G. Steidl} and \textit{M. Tasche} [Math. Comput. 56, No. 193, 281-296 (1991; Zbl 0725.65145)].
scientific article; zbMATH DE number 1083211
scientific article