1. discrete cosine transform DCT A technique for expressing a waveform as a weighted sum of cosines. The DCT is central to many kinds of signal processing, especially video compression. Given data Ai, where i is an integer in the range 0 to N-1, the forward DCT which would be used e. g. by an encoder is: Bk = sum Ai cospi k/N 2 i + 1/2 i=0 to N-1 Bk is defined for all values of the frequency-space variable k, but we only care about integer k in the range 0 to N-1. The inverse DCT which would be used e. g. by a decoder is: AAi= sum Bk 2-deltak-0 cospi k/N2 i + 1/2 k=0 to N-1 where deltak is the Kronecker delta. The main difference between this and a discrete Fourier transform DFT is that the DFT traditionally assumes that the data Ai is periodically continued with a period of N, whereas the DCT assumes that the data is continued with its mirror image, then periodically continued with a period of 2N. Mathematically, this transform pair is exact, i. e. AAi == Ai, resulting in lossless coding; only when some of the coefficients are approximated does compression occur. There exist fast DCT algorithms in analogy to the Fast Fourier Transform.
discrete cosine transform |
