[1] : The Free On-line Dictionary of Computing (27 SEP 03)

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.
     
        1997-03-10
     
     
see also:
signal processing compression kronecker delta discrete fourier transform lossless coding algorithms 
fast fourier transform 

Transform >> T Words
Transform, definition of term: Transform
transform_pag1.html

Discrete >> D Words
Discrete, definition of term: Discrete
discrete_pag1.html

Cosine >> C Words
Cosine, definition of term: Cosine
cosine_pag1.html