DCTIV Discrete Consine Transform type IV
Usage: c=dctiv(f);
DCTIV(f) computes the discrete cosine transform of type IV of the
input signal f. If f is multi-dimensional, the transformation is
applied along the first non-singleton dimension.
DCTIV(f,L) zero-pads or truncates f to length L before doing the
transformation.
DCTIV(f,[],dim) or DCTIV(f,L,dim) applies the transformation along
dimension dim.
The transform is real (output is real if input is real) and
orthonormal. It is its own inverse.
Let f be a signal of length L and let c=DCTIV(f). Then
L-1
c(n+1) = sqrt(2/L) * sum f(m+1)*cos(pi*(n+.5)*(m+.5)/L)
m=0
Examples:
---------
The following figures show the first 4 basis functions of the DCTIV of
length 20:
% The dctiv is its own adjoint.
F=dctiv(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/dctiv.html
See also: dctii, dctiii, dstii.
Package: ltfat