Function: dctiv
DCTIV  Discrete Consine Transform type IV
  Usage:  c=dctiv(f);

  DCTIV(f) computes the discrete cosine transform of type IV of the
  input signal f. If f is multi-dimensional, the transformation is
  applied along the first non-singleton dimension.

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

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

  The transform is real (output is real if input is real) and
  orthonormal.  It is its own inverse.

  Let f be a signal of length L and let c=DCTIV(f). Then

                         L-1
    c(n+1) = sqrt(2/L) * sum f(m+1)*cos(pi*(n+.5)*(m+.5)/L) 
                         m=0 

  Examples:
  ---------

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

    % The dctiv is its own adjoint.
    F=dctiv(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/dctiv.html

See also: dctii, dctiii, dstii.

Package: ltfat