Source : Free On-Line Dictionary of Computing

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 A(i), 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:
     
         B(k) =    sum    A(i) cos((pi k/N) (2 i + 1)/2)
                i=0 to N-1
     
        B(k) 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:
     
         AA(i)=    sum    B(k) (2-delta(k-0)) cos((pi k/N)(2 i + 1)/2)
                k=0 to N-1
     
        where delta(k) is the {Kronecker delta}.
     
        The main difference between this and a {discrete Fourier
        transform} (DFT) is that the DFT traditionally assumes that
        the data A(i) 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. AA(i) ==
        A(i), 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}.
     
        (1997-03-10)