dstiii.m

Matlab时频分析工具箱,希望能对大家有所帮助啊

function c=dstiii(f,L,dim)
%DSTIII  Discrete sine transform type III
%   Usage:  c=dstiii(f);
%           c=dstiii(f,L);
%           c=dstiii(f,[],dim);
%           c=dstiii(f,L,dim);
%
%   DSTIII(f) computes the discrete sine transform of type III 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.
%
%   DSTIII(f,L) zero-pads or truncates f to length L before doing the
%   transformation.
%
%   DSTIII(f,[],dim) applies the transformation along dimension dim. 
%   DSTIII(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 is the inverse of DSTII
%
%   Let f be a signal of length L, let c=DSTIII(f) and define the vector
%   w of length L by  
%     w = [1 1 1 1 ... 1/sqrt(2)]
%   Then 
% 
%                          L-1
%     c(n+1) = sqrt(2/L) * sum w(n+1)*f(m+1)*sin(pi*(n+.5)*m/L) 
%                          m=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/>.

%   SEE ALSO:  DCTII, DSTII, DSTIV
%
%R  rayi90 wi94

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,'DSTIII');

if ~isempty(L)
  f=postpad(f,L);
end;

c=zeros(2*L,W);
  
m1=1/sqrt(2)*exp((1:L)*pi*i/(2*L)).';
m1(L)=i;
  
m2=-1/sqrt(2)*exp(-(L-1:-1:1)*pi*i/(2*L)).';
  
for w=1:W
  c(:,w)=[0;m1.*f(:,w);m2.*f(L-1:-1:1,w)];
end;

c=-sqrt(L)*2*i*ifft(c);
c=c(1:L,:);

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;
%
%c2=-sqrt(L)*2*i*ifft(R*f);
%
%c=c2(1:L,:);