On algebras related to the discrete cosine transform (Q1372961)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On algebras related to the discrete cosine transform |
scientific article; zbMATH DE number 1083211
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On algebras related to the discrete cosine transform |
scientific article; zbMATH DE number 1083211 |
Statements
On algebras related to the discrete cosine transform (English)
0 references
4 June 1998
0 references
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)].
0 references
Chebyshev polynomials
0 references
discrete cosine transform
0 references
discrete Fourier transform
0 references
Chinese-Remainder Theorem
0 references
0 references
