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function c=dstiv(f,L,dim)
%DSTIV Discrete Sine Transform type IV
% Usage: c=dstiv(f);
% c=dstiv(f,L);
% c=dstiv(f,[],dim);
% c=dstiv(f,L,dim);
%
% DSTIV(f) computes the discrete sine transform of type IV 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.
%
% DSTIV(f,L) zero-pads or truncates f to length L before doing the
% transformation.
%
% DSTIV(f,[],dim) applies the transformation along dimension dim.
% DSTIV(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. It is its own inverse.
%
% Let f be a signal of length _L and let c=DSTIV(f). Then
%
%M L-1
%M c(n+1) = sqrt(2/L) * sum f(m+1)*sin(pi*n*(m+.5)/L)
%M m=0
%F \[
%F c\left(n+1\right)=\sqrt{\frac{2}{L}}\sum_{m=0}^{L-1}f\left(m+1\right)\sin\left(\frac{\pi}{L}\left(n+\frac{1}{2}\right)\left(m+\frac{1}{2}\right)\right)
%F \]
%
% See also: dstii, dstiii, dctii
%
%R rayi90 wi94
% AUTHOR: Peter Soendergaard
% TESTING: TEST_PUREFREQ
% REFERENCE: REF_DSTIV
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,'DSTIV');
if ~isempty(L)
f=postpad(f,L);
end;
s1=zeros(2*L,W);
c=zeros(L,W);
m1=1/sqrt(2)*exp(-(0:L-1)*pi*i/(2*L)).';
m2=-1/sqrt(2)*exp((1:L)*pi*i/(2*L)).';
for w=1:W
s1(:,w)=[m1.*f(:,w);flipud(m2).*f(L:-1:1,w)];
end;
s1=i*exp(-pi*i/(4*L))*fft(s1)/sqrt(2*L);
% This could be done by a repmat instead.
for w=1:W
c(:,w)=s1(1:L,w).*m1+s1(2*L:-1:L+1,w).*m2;
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 algorithm.
%R=1/sqrt(2)*[diag(exp(-(0:L-1)*pi*i/(2*L)));...
% flipud(diag(-exp((1:L)*pi*i/(2*L))))];
%c=i*(exp(-pi*i/(4*L))*R.'*fft(R*f)/sqrt(2*L));

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