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