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