wilorth.m

来自「Matlab时频分析工具箱,希望能对大家有所帮助啊」· M 代码 · 共 127 行

function [gamma]=wilorth(p1,p2,p3)
%WILORTH  Wilson orthonormal window.
%   Usage:   gamma=wilorth(M,L);
%            gamma=wilorth(g,M);
%            gamma=wilorth(g,M,L);
%
%   Input parameters:
%         g     : Auxiliary window window function (optional).
%         M     : Number of modulations.
%         L     : Length of window (optional).
%   Output parameters:
%         gamma : Window generating an orthonormal Wilson basis.
%
%   gamma=WILORTH(M,L) computes a nice window of length L generating a
%   Wilson or MDCT orthonormal basis with M frequency bands for signal of
%   length L.
%
%   gamma=WILORTH(g,M) creates an orthonormal window from the window g, 
%   g must be whole-point even.
%
%   gamma=WILORTH(g,M,L) pads or truncates g to length L before
%   calculating the orthonormal window. gamma will also be of length L.
%
%   The input window g must be whole-point even. If g is not whole-point
%   even, then reconstruction using the dual window will not be perfect.
%
%   SEE ALSO:  DWILT, WILDUAL, ISEVEN

% 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/>.

error(nargchk(2,3,nargin));

wasrow=0;

% Detect which parameters was entered, and do simple transformations.
if nargin == 3
  g=p1;
  M=p2;
  L=p3;

  if size(g,2)>1
    if size(g,1)>1
      error('g must be a vector');
    else
      % g was a row vector.
      wasrow=1;
      g=g(:);
    end;
  end;

  assert_squarelat(M,M,1,'WILORTH',0);
  [b,N,L]=assert_L(L,length(g),L,M,2*M,'WILORTH');


  % fir2iir is now safe.
  g=fir2iir(g,L);

  wasreal=isreal(g);
else

  if numel(p1)>1
    % First parameter is a vector.
    g=p1;
    M=p2;
    
    if size(g,2)>1
      if size(g,1)>1
        error('g must be a vector');
      else
        % g was a row vector.
        wasrow=1;
        g=g(:);
      end;
    end;

    assert_squarelat(M,2*M,1,'WILORTH',0);
    [b,N,L]=assert_L(length(g),length(g),[],M,2*M,'WILORTH');
    
    wasreal=isreal(g);
  else
    
    M=p1;
    L=p2;
    
    assert_squarelat(M,M,1,'WILORTH',0);
    [b,N,L]=assert_L(L,L,L,M,2*M,'WILORTH');

    a=M;
    b=L/(2*M);
        
    % Create default window, a Gaussian.
    g=comp_pgauss(L,a/b,0);
    
    wasreal=1;
  end;

end;

a=M;
b=L/(2*M);

% Multiply by sqrt(2), because comp_cantight will return a normalized
% tight frame, i.e. the framebounds are A=B=1 instead of A=B=2. This means
% that the returned gamma only has norm=.701 and not norm=1.

gf=comp_wfac(g,a,2*M);
gammaf=comp_cantight_fac(gf,L,a,2*M);
gamma=sqrt(2)*comp_iwfac(gammaf,L,a,2*M);

if wasrow
  gamma=gamma.';
end;

if wasreal
  gamma=real(gamma);
end;