Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 912194, 31 pages
http://dx.doi.org/10.1155/2012/912194
Research Article

A Unified Algorithm for Subband-Based Discrete Cosine Transform

Lu-Ting Ko,1 Jwu-E Chen,1 Hsi-Chin Hsin,2 Yaw-Shih Shieh,3 and Tze-Yun Sung3

1Department of Electrical Engineering, National Central University, Chungli City 320-01, Taiwan
2Department of Computer Science and Information Enginering, National United University, Miaoli City 360-03, Taiwan
3Department of Electronics Engineering, Chung Hua University, Hsinchu City 300-12, Taiwan

Received 13 April 2011; Revised 22 May 2011; Accepted 4 June 2011

Academic Editor: Shengyong Chen

Copyright © 2012 Lu-Ting Ko et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Discrete cosine transform (DCT) and inverse DCT (IDCT) have been widely used in many image processing systems and real-time computation of nonlinear time series. In this paper, the unified DCT/IDCT algorithm based on the subband decompositions of a signal is proposed. It is derived from the data flow of subband decompositions with factorized coefficient matrices in a recursive manner. The proposed algorithm only requires (4(log2n)−1−1) and (4(log2n)−1−1)/3 multiplication time for n-point DCT and IDCT, with a single multiplier and a single processor, respectively. Moreover, the peak signal-to-noise ratio (PSNR) of the proposed algorithm outperforms the conventional DCT/IDCT. As a result, the subband-based approach to DCT/IDCT is preferable to the conventional approach in terms of computational complexity and system performance. The proposed reconfigurable architecture of linear array DCT/IDCT processor has been implemented by FPGA.