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dstii.m    88 lines (72 with data), 2.3 kB

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function c=dstii(f,L,dim)
%DSTII Discrete Sine Transform type II
% Usage: c=dstii(f);
% c=dstii(f,L);
% c=dstii(f,[],dim);
% c=dstii(f,L,dim);
%
% DSTII(f) computes the discrete sine transform of type II 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
% dimension.
%
% DSTII(f,L) zero-pads or truncates f to length L before doing the
% transformation.
%
% DSTII(f,[],dim) applies the transformation along dimension dim.
% DSTII(f,L,dim) does the same, but pads or truncates to length L.
%
% The transform is real (output is real if input is real) and
% it is orthonormal.
%
% The inverse transform of DSTII is DSTIII.
%
% Let f be a signal of length _L, let c=DSTII(f) and define the vector
% _w of length _L by
%N w = [1 1 1 1 ... 1/sqrt(2)]
%L \[w\left(n\right)=\begin{cases}\frac{1}{\sqrt{2}} & \text{if }n=L-1\\1 & \text{otherwise}\end{cases}\]
% Then
%
%M L-1
%M c(n+1) = sqrt(2/L) * sum w(n+1)*f(m+1)*sin(pi*n*(m+.5)/L)
%M m=0
%F \[
%F c\left(n+1\right)=\sqrt{\frac{2}{L}}\sum_{m=0}^{L-1}w\left(n\right)f\left(m+1\right)\sin\left(\frac{\pi}{L}n\left(m+\frac{1}{2}\right)\right)
%F \]
%
% See also: dctii, dstiii, dstiv
%
%R rayi90 wi94
% AUTHOR: Peter Soendergaard
% TESTING: TEST_PUREFREQ
% REFERENCE: REF_DSTII
error(nargchk(1,3,nargin));
if nargin<3
dim=[];
end;
if nargin<2
L=[];
end;
[f,L,Ls,W,dim,permutedsize,order]=assert_sigreshape_pre(f,L,dim,'DSTII');
if ~isempty(L)
f=postpad(f,L);
end;
c=zeros(L,W);
m1=1/sqrt(2)*exp(-(1:L)*pi*i/(2*L)).';
m1(L)=-i;
m2=-1/sqrt(2)*exp((1:L-1)*pi*i/(2*L)).';
s1=i*fft([f;-flipud(f)])/sqrt(L)/2;
% This could be done by a repmat instead.
for w=1:W
c(:,w)=s1(2:L+1,w).*m1+[s1(2*L:-1:L+2,w).*m2;0];
end;
if isreal(f)
c=real(c);
end;
c=assert_sigreshape_post(c,dim,permutedsize,order);
% This is a slow, but convenient way of expressing the above algorithm.
%R=1/sqrt(2)*[zeros(1,L); ...
% diag(exp((1:L)*pi*i/(2*L)));...
% [flipud(diag(-exp(-(1:L-1)*pi*i/(2*L)))),zeros(L-1,1)]];
%R(L+1,L)=i;
%c=i*(R'*fft([f;-flipud(f)])/sqrt(L)/2);