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function c=dsti(f,L,dim)
%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 a matrix, then the transformation is applied to
% each column. For N-D arrays, the transformation is applied to the first
% dimension.
%
% DSTI(f,L) zero-pads or truncates f to length N before doing the
% transformation.
%
% DSTI(f,[],dim) applies the transformation along dimension dim.
% DSTI(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.
%
% This transform is its own inverse.
%
% Let f be a signal of length _L and let c=DSTI(f). Then
%
%M L-1
%M c(n+1) = sqrt(2/(L+1)) * sum sin(pi*(n+1)*(m+1)/(L+1))
%M m=0
%F \[
%F c\left(n+1\right)=\sqrt{\frac{2}{L+1}}\sum_{m=0}^{L-1}f\left(m+1\right)\sin\left(\frac{\pi \left(n+1\right)\left(m+1\right)}{L+1}\right)
%F \]
%
% The implementation of this functions uses a simple algorithm that require
% 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.
%
% See also: dcti, dstiii, dstiv
%
%R rayi90 wi94
% AUTHOR: Peter Soendergaard
% TESTING: TEST_PUREFREQ
% REFERENCE: REF_DSTI
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,'DSTI');
if ~isempty(L)
f=postpad(f,L);
end;
if L==1
c=f;
else
c=zeros(L,W);
s1=dft([zeros(1,W);...
f;...
zeros(1,W);...
-flipud(f)]);
% This could be done by a repmat instead.
for w=1:W
c(:,w)=s1(2:L+1,w)-s1(2*L+2:-1:L+3,w);
end;
c=c*i/2;
if isreal(f)
c=real(c);
end;
end;
c=assert_sigreshape_post(c,dim,permutedsize,order);

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