Function: dcti
DCTI  Discrete Cosine Transform type I
  Usage:  c=dcti(f);
          c=dcti(f,L);
          c=dcti(f,[],dim);
          c=dcti(f,L,dim);

  DCTI(f) computes the discrete cosine transform of type I of the
  input signal f. If f is a matrix then the transformation is applied to
  each column. For N-D arrays, the transformation is applied to the first
  non-singleton dimension.

  DCTI(f,L) zero-pads or truncates f to length L before doing the
  transformation.

  DCTI(f,[],dim) or DCTI(f,L,dim) applies the transformation along
  dimension dim.

  The transform is real (output is real if input is real) and
  it is orthonormal.

  This transform is its own inverse.

  Let f be a signal of length L, let c=dcti(f) and define the vector
  w of length L by

     w = [1/sqrt(2) 1 1 1 1 ...1/sqrt(2)]

  Then

                             L-1
    c(n+1) = sqrt(2/(L-1)) * sum w(n+1)*w(m+1)*f(m+1)*cos(pi*n*m/(L-1))
                             m=0

  The implementation of this functions uses a simple algorithm that require
  an FFT of length 2L-2, which might potentially be the product of a large
  prime number. This may cause the function to sometimes execute slowly.
  If guaranteed high speed is a concern, please consider using one of the
  other DCT transforms.

  Examples:
  ---------

  The following figures show the first 4 basis functions of the DCTI of
  length 20:

    % The dcti is its own adjoint.
    F=dcti(eye(20));

    for ii=1:4
      subplot(4,1,ii);
      stem(F(:,ii));
    end;


  References:
    K. Rao and P. Yip. Discrete Cosine Transform, Algorithms, Advantages,
    Applications. Academic Press, 1990.
    
    M. V. Wickerhauser. Adapted wavelet analysis from theory to software.
    Wellesley-Cambridge Press, Wellesley, MA, 1994.
    

Url: http://ltfat.github.io/doc/fourier/dcti.html

See also: dctii, dctiv, dsti.

Package: ltfat