<title>Fast scaled-DCT algorithm</title>

Abstract

ABSTRACTThe Discrete Cosine Transform (DCT) followed by scaling and quantiza.tion is an ml- portant operation in image processing. Because of the scaling, the DCT itself need not he computed, but rather a scalar mu]tiple of the DCT might do, with appropriate compensationincorporated into the scaling. We present a fast method for computing such scaled output ofthe 2-dimensional DCT on 8 x 8 points. We also present a similar algorithm for the inversescaled DCT.1. INTRODUCTIONThe discrete cosine transform (DCT) plays an important role in digital image processing.Of particular interest is the two-dimensional DCT followed by scaling and quantiza.tion. This has applications in data compression of continuous tone images [1, 11]. Because the DCT is so often used, research into fast algorithms for its implementation has been rather active[3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15].Given an array y(k) , 0 k  K — 1, of input data, its one-dimensional DCT output is K—i (irn(2k+1) y(n) = c(n) cost i y(),