Discrete Cosine Transform, type II and III

More Examples

Explanation of Notation

How does it work?

Discrete Cosine Transform, Type II and III

The discrete cosine transform of type III is given by the matrix

where a_k = sqrt(1/2) for k = 0, and a_k = 1 else. The DCT type II is the transpose of type III. The following structured, sparse matrix factorization represents a fast algorithm for a DCT, type III, size 8, and has been automatically generated (even in the presented Latex format) using the package AREP.

By transposition we obtain a fast algorithm for the DCT^(II):

Note that these algorithms require 13 multiplications and 29 additions and are thus among the best ones known.

O.k., you where not looking for math, but hoping to find good code for this (or other) transforms? No problem, get SPIRAL.