DSTI Discrete Sine Transform type I
Usage: c=dsti(f);
c=dsti(f,L);
c=dsti(f,[],dim);
c=dsti(f,L,dim);
DSTI(f) computes the discrete sine transform of type I of the
input signal f. If f is multi-dimensional, the transformation is
applied along the first non-singleton dimension.
DSTI(f,L) zero-pads or truncates f to length L before doing the
transformation.
DSTI(f,[],dim) or DSTI(f,L,dim) applies the transformation along
dimension dim.
The transform is real (output is real if input is real) and orthonormal.
This transform is its own inverse.
Let f be a signal of length L and let c=DSTI(f). Then
L-1
c(n+1) = sqrt(2/(L+1)) * sum sin(pi*(n+1)*(m+1)/(L+1))
m=0
The implementation of this functions uses a simple algorithm that requires
an FFT of length 2N+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 DST transforms.
Examples:
---------
The following figures show the first 4 basis functions of the DSTI of
length 20:
% The dsti is its own adjoint.
F=dsti(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/dsti.html
See also: dcti, dstiii, dstiv.
Package: ltfat