A Unified Algorithm for Subband-Based Discrete Cosine Transform

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)/3multiplication time forn-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.