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
% non-singleton 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
%
% L-1
% c(n+1) = sqrt(2/L) * sum f(m+1)*sin(pi*(n+.5)*(m+.5)/L)
% m=0
%
% Examples:
% ---------
%
% The following figures show the first 4 basis functions of the DSTIV of
% length 20:
%
% % The dstiv is its own adjoint.
% F=dstiv(eye(20));
%
% for ii=1:4
% subplot(4,1,ii);
% stem(F(:,ii));
% end;
%
% See also: dstii, dstiii, dctii
%
% 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/dstiv.html
% Copyright (C) 2005-2023 Peter L. Soendergaard <peter@sonderport.dk> and others.
% This file is part of LTFAT version 2.6.0
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
% AUTHOR: Peter L. Søndergaard
% TESTING: TEST_PUREFREQ
% REFERENCE: REF_DSTIV
complainif_argnonotinrange(nargin,1,3,mfilename);
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;
c = comp_dst(f,4);
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));