discrete cosine transform

1 definition found

discrete cosine transform - Free On-line Dictionary of Computing (26 May 2007) :

  discrete cosine transform
  
     <mathematics> (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)