An Evaluation of a Hybrid-Logarithmic Number System DCT/IDCT Algorithm

This paper presents an evaluation of an algorithm for performing the forward and inverse discrete cosine transforms (DCT) on digital images using a hybrid-logarithmic number system (hybrid-LNS) instead of linear binary arithmetic. The algorithm has been simulated using Matlab® where the accuracy of the fractional part of the logarithm has been limited to 8 bits and has been calculated using just 4, 6 or 8 binary address bits of the linear input data. The results show that it is possible to use this hybrid-LNS architecture to build multiplierless DCT and IDCT transforms having only a minimal reduction in image quality. The algorithm is suitable for implementation on existing mid-range FPGA technologies where there are limitations on the size of on-chip memory and high-speed computing elements.