Two-stage convolver-based DCT and IDCT algorithms
Ja‐Ling Wu, S.-H. Hsu, Wei-Jou Duh · IEE Proceedings I Communications Speech and Vision · 1991
Discrete cosine transform is the most popular solution for image coding owing to its near optimal performance, yet it is not signal dependent. A two-stage convolver-based DCT and IDCT algorithm with power-of-two length is presented. The transform matrix of IDCT is decomposed into the product of pre- and post processing matrices by using Möbius inversion formula. The pre-processing stage consists of just additions and subtractions; the post-processing stage performs circular convolution operations. A nearly recursive computational method for preprocessing calculation is given which considerably reduces the operation count and is valuable in practical usage. The post-processing is a circular convolution and can be computed using number theoretic transform, (semi-) systolic arrays or transversal filters.