www.gusucode.com > 线性时频分析工具箱 - ltfat-1.0.1源码程序 > 线性时频分析工具箱 - LTFAT\nonstatgab\nsgabdual.m
function gd=nsgabdual(g,a,M,varargin) %NSGABDUAL Canonical dual window for nsionnary Gabor frames % Usage: gd=nsgabdual(g,a,L) % % Input parameters: % g : Cell array of windows. % a : Vector of time shift. % M : Vector of numbers of channels. % L : Transform length. % Output parameters: % gd : Cell array of canonical dual windows % % NSGABDUAL(g,a,M,L) computes the canonical dual windows of the % nsionary discrete Gabor frame defined by windows given in g an % time-shifts given by a. % % NSGABDUAL is designed to be used with functions NSDGT and INSDGT. % See the help on NSDGT for more details about the variables structure. % % The computed dual windows are only valid for the 'painless case', that % is to say that they ensure perfect reconstruction only if for each % window the number of frequency channels used for computation of NSDGT is % greater than or equal to the window length. This correspond to cases % for which the frame operator is diagonal. % % See also: nsgabtight, nsdgt, insdgt % % References: % F. Jaillet, M. Dörfler, and P. Balazs. LTFAT-note 10: Nonstationary % Gabor Frames. In Proceedings of SampTA, 2009. % % Copyright (C) 2005-2011 Peter L. Soendergaard. % This file is part of LTFAT version 1.0.1 % 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 : Florent Jaillet % TESTING: TEST_NSDGT % REFERENCE: if nargin<3 error('%s: Too few input parameters.',upper(mfilename)); end; definput.keyvals.L=sum(a); [flags,kv,L]=ltfatarghelper({'L'},definput,varargin); timepos=cumsum(a)-a(1); N=length(a); % Number of time positions f=zeros(L,1); % Diagonal of the frame operator % Compute the diagonal of the frame operator: % sum up in time (overlap-add) all the contributions of the windows as if % we where using windows in g as analysis and synthesis windows for ii=1:N shift=floor(length(g{ii})/2); temp=abs(circshift(g{ii},shift)).^2*length(g{ii}); tempind=mod((1:length(g{ii}))+timepos(ii)-shift-1,L)+1; f(tempind)=f(tempind)+temp; end % Initialize the result with g gd=g; % Correct each window to ensure perfect reconstrution for ii=1:N shift=floor(length(g{ii})/2); tempind=mod((1:length(g{ii}))+timepos(ii)-shift-1,L)+1; gd{ii}(:)=circshift(circshift(g{ii},shift)./f(tempind),-shift); end