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Also abbreviated DCT, the transform is closely related to the fast Fourier transform; it plays a role in coding signals and images [Jain89], e.g. in the widely used standard JPEG compression.
transform is defined by
where s is the array of N original values, t is the array of N
transformed values, and the coefficients c are given by
The discrete cosine transform in two dimensions,
for a square matrix, can be written as
with an analogous notation for N, s, t, and the c(i,j) given by c (0,j) = 1/N, c (i,0) = 1/N,
and c (i,j) = 2/N for both i and .
The DCT has an inverse, defined by
for the one-dimensional case, and
for two dimensions.
The DCT is included in commercial image processing packages, e.g. in Matlab (see [MATLAB97]).
Rudolf K. Bock, 7 April 1998