DCTII Discrete Consine Transform type II Usage: 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 w = [1/sqrt(2) 1 1 1 1 ...] Then L-1 c(n+1) = sqrt(2/L) * sum w(n+1)*f(m+1)*cos(pi*n*(m+.5)/L) m=0 Examples: --------- 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; 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/dctii.html
See also: dctiii, dctiv, dstii.
Package: ltfat