Fast recursive algorithms for 2-D discrete cosine transform

Abstract

A new algorithm for computation of two-dimensional (2-D) type-III discrete cosine transform is presented. The algorithm is particularly suited to block size ( p 1∗2 m ) by ( p 2∗2 n ), where p 1 and p 2 are odd integers, and m and n are non-negative integers. It shows that the 2-D type-III DCT can be decomposed into cosine–cosine, cosine–sine, sine–cosine, sine–sine sequences, which can be further decomposed into similar sequences. The proposed algorithm provides the flexibility in choosing block size and has a simple indexing mapping scheme and a fairly regular computation structure. The algorithm also requires a smaller number of arithmetic operations for p 1= p 2=3.