Fast Discrete Cosine Transform via Computation of Moments

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 for computing moments is converted to compute DCT with only a few 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 VLSI implementation. We provide an estimate of the realizability of our array in a 0.5 m CMOS technology and comparisons with other methods. The execution time of the systolic array is only O(N log₂N/log₂ log₂N) in computing 1D N-point DCT if N is sufficiently large. The approach is also applicable to multiple dimensional DCT and DCT inverses.