DCTIII Discrete Consine Transform type III
Usage: c=dctiii(f);
c=dctiii(f,L);
c=dctiii(f,[],dim);
c=dctiii(f,L,dim);
DCTIII(f) computes the discrete cosine transform of type III of the
input signal f. If f is multi-dimensional, the transformation is
applied along the first non-singleton dimension.
DCTIII(f,L) zero-pads or truncates f to length L before doing the
transformation.
DCTIII(f,[],dim) or DCTIII(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 DCTII.
Let f be a signal of length L, let c=DCTIII(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(m+1)*f(m+1)*cos(pi*(n+.5)*m/L)
m=0
Examples:
---------
The following figures show the first 4 basis functions of the DCTIII of
length 20:
% The dctii is the adjoint of dctiii.
F=dctii(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/dctiii.html
See also: dctii, dctiv, dstii.
Package: ltfat