This paper presents stable, radix-2, completely recursive discrete cosine transformation algorithms DCT-I and DCT-III solely based on DCT-I, DCT-II, DCT-III, and DCT-IV having sparse and orthogonal factors. Error bounds for computing the completely recursive DCT-I, DCT-II, DCT-III, and DCT-IV algorithms having sparse and orthogonal factors are addressed. Image compression results are presented based on the recursive 2D DCT-II and DCT-IV algorithms for image size 512×512 pixels with transfer block sizes 8×8, 16×16, and 32×32 with 93.75% absence of coefficients in each transfer block. Finally signal flow graphs are demonstrated based on the completely recursive DCT-I, DCT-II, DCT-III, and DCT-IV algorithms having orthogonal factors.
@article{arxiv.1503.04106,
title = {Signal Processing based on Stable radix-2 DCT Algorithms having Orthogonal Factors},
author = {Sirani M. Perera},
journal= {arXiv preprint arXiv:1503.04106},
year = {2015}
}