Fast Discrete Cosine Transform via Computation of Moments

Authors:
J. G. Liu;H. F. Li;F. H. Y. Chan;F. K. Lam
Affiliations:
Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong;Department of Computer Science, University of Concordia, 1455 De Maisonneuve West, Montreal, Quebec, H3G 1M8, Canada;Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong;Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong
Venue:
Journal of VLSI Signal Processing Systems
Year:
1998

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Abstract

Discrete cosine transform (DCT) is widely used in signal processing.This paper presents a novel approach to perform DCT. DCT is expressed in terms of discrete moments via triangle function transforms and later Taylor series expansion. From this, a fast systolic array forcomputing moments is converted to compute DCT with only afew multiplications and without any cosine evaluations.The systolic array has advantages of pipelinability,regularity, modularity, local connectivity and scalability,thus making it to be very suitable for VLSIimplementation. We provide an estimate of therealizability of our array in a 0.5 μm CMOS technologyand comparisons with other methods. The execution time ofthe systolic array is only O(N \log_2 N/\log_2 \log_2N) in computing 1D N-point DCT if N is sufficiently large. The approach is also applicable to multiple dimensional DCT and DCTinverses.