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function [AF,BF]=gabframebounds(g,a,M,varargin)
%-*- texinfo -*-
%@deftypefn {Function} gabframebounds
%@verbatim
%GABFRAMEBOUNDS Calculate frame bounds of Gabor frame
% Usage: fcond=gabframebounds(g,a,M);
% [A,B]=gabframebounds(g,a,M);
% [A,B]=gabframebounds(g,a,M,L);
% [A,B]=gabframebounds(g,a,M,'lt',lt);
%
% Input parameters:
% g : The window function.
% a : Length of time shift.
% M : Number of channels.
% L : Length of transform to consider.
% lt : Lattice type (for non-separable lattices).
% Output parameters:
% fcond : Frame condition number (B/A)
% A,B : Frame bounds.
%
% GABFRAMEBOUNDS(g,a,M) calculates the ratio B/A of the frame bounds
% of the Gabor system with window g, and parameters a, M.
%
% [A,B]=GABFRAMEBOUNDS(...) returns the frame bounds A and B*
% instead of just the ratio.
%
% The window g may be a vector of numerical values, a text string or a
% cell array. See the help of GABWIN for more details.
%
% GABFRAMEBOUNDS(g,a,M,L) will cut or zero-extend the window to length
% L.
%
% GABFRAMEBOUNDS(g,a,M,'lt',lt) does the same for a non-separable
% lattice specified by lt. Please see the help of MATRIX2LATTICETYPE
% for a precise description of the parameter lt.
%
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/gabor/gabframebounds.html}
%@seealso{gabrieszbounds, gabwin}
%@end deftypefn
% Copyright (C) 2005-2016 Peter L. Soendergaard <peter@sonderport.dk>.
% This file is part of LTFAT version 2.3.1
%
% 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/>.
%% ---------- Assert correct input.
if nargin<3
error('%s: Too few input parameters.',upper(mfilename));
end;
definput.keyvals.L=[];
definput.keyvals.lt=[0 1];
[flags,kv,L]=ltfatarghelper({'L'},definput,varargin);
%% ------ step 2: Verify a, M and L
if isempty(L)
if isnumeric(g)
% Use the window length
Ls=length(g);
else
% Use the smallest possible length
Ls=1;
end;
% ----- step 2b : Verify a, M and get L from the window length ----------
L=dgtlength(Ls,a,M,kv.lt);
else
% ----- step 2a : Verify a, M and get L
Luser=dgtlength(L,a,M,kv.lt);
if Luser~=L
error(['%s: Incorrect transform length L=%i specified. Next valid length ' ...
'is L=%i. See the help of DGTLENGTH for the requirements.'],...
upper(mfilename),L,Luser);
end;
end;
%% ----- step 3 : Determine the window
[g,info]=gabwin(g,a,M,L,kv.lt,'callfun',upper(mfilename));
if L<info.gl
error('%s: Window is too long.',upper(mfilename));
end;
%% ----- actual computation ------------
g=fir2long(g,L);
R=size(g,2);
if kv.lt(2)==1
% Rectangular case
% Get the factorization of the window.
gf=comp_wfac(g,a,M);
% Compute all eigenvalues.
lambdas=comp_gfeigs(gf,L,a,M);
s=size(lambdas,1);
else
% Convert to multi-window
mwin=comp_nonsepwin2multi(g,a,M,kv.lt,L);
% Get the factorization of the window.
gf=comp_wfac(mwin,a*kv.lt(2),M);
% Compute all eigenvalues.
lambdas=comp_gfeigs(gf,L,a*kv.lt(2),M);
s=size(lambdas,1);
end;
% Min and max eigenvalue.
if a>M*R
% This can is not a frame, so A is identically 0.
AF=0;
else
AF=lambdas(1);
end;
BF=lambdas(s);
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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