c=dctii(f); c=dctii(f,L); c=dctii(f,[],dim); c=dctii(f,L,dim);
dctii(f) computes the discrete cosine transform of type II of the input signal f. If f is multi-dimensional, the transformation is applied along the first non-singleton dimension.
dctii(f,L) zero-pads or truncates f to length L before doing the transformation.
dctii(f,[],dim) or dctii(f,L,dim) applies the transformation along dimension dim.
The transform is real (output is real if input is real) and orthonormal.
This is the inverse of dctiii.
Let f be a signal of length L, let c=dctii(f) and define the vector w of length L by
Then
The following figures show the first 4 basis functions of the DCTII of length 20:
% The dctiii is the adjoint of dctii. F=dctiii(eye(20)); for ii=1:4 subplot(4,1,ii); stem(F(:,ii)); end;
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.