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function [AF,BF]=nsgabframebounds(g,a,M)
%-*- texinfo -*-
%@deftypefn {Function} nsgabframebounds
%@verbatim
%NSGABFRAMEBOUNDS Frame bounds of non-stationary Gabor frame
% Usage: fcond=nsgabframebounds(g,a,M);
% [A,B]=nsgabframebounds(g,a,M);
%
% Input parameters:
% g : Cell array of windows
% a : Vector of time positions of windows.
% M : Vector of numbers of frequency channels.
% Output parameters:
% fcond : Frame condition number (B/A)
% A,B : Frame bounds.
%
% NSGABFRAMEBOUNDS(g,a,Ls) calculates the ratio B/A of the frame
% bounds of the non-stationary discrete Gabor frame defined by windows
% given in g at positions given by a. Please see the help on NSDGT
% for a more thourough description of g and a.
%
% [A,B]=NSGABFRAMEBOUNDS(g,a,Ls) returns the actual frame bounds A*
% and B instead of just the their ratio.
%
% The computed frame bounds are only valid for the 'painless case' when
% 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.
%
%
% References:
% P. Balazs, M. Doerfler, F. Jaillet, N. Holighaus, and G. A. Velasco.
% Theory, implementation and applications of nonstationary Gabor frames.
% J. Comput. Appl. Math., 236(6):1481--1496, 2011.
%
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/nonstatgab/nsgabframebounds.html}
%@seealso{nsgabtight, nsdgt, insdgt}
%@end deftypefn
% Copyright (C) 2005-2016 Peter L. Soendergaard <peter@sonderport.dk>.
% This file is part of LTFAT version 2.2.0
%
% 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 : Florent Jaillet
% TESTING: TEST_NSDGT
% Compute the diagonal of the frame operator.
f=nsgabframediag(g,a,M);
AF=min(f);
BF=max(f);
if nargout<2
% Avoid the potential warning about division by zero.
if AF==0
AF=Inf;
else
AF=BF/AF;
end;
end;
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