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function [AF,BF]=wpfbtbounds(wt,varargin)
%-*- texinfo -*-
%@deftypefn {Function} wpfbtbounds
%@verbatim
%WPFBTBOUNDS Frame bounds of WPFBT
% Usage: fcond=wpfbtbounds(wt,L);
% [A,B]=wpfbtbounds(wt,L);
% [...]=wpfbtbounds(wt);
%
% WPFBTBOUNDS(wt,L) calculates the ratio B/A of the frame bounds
% of the wavelet packet filterbank specified by wt for a system of length
% L. The ratio is a measure of the stability of the system.
%
% WPFBTBOUNDS(wt) does the same, except L is chosen to be the next
% compatible length bigger than the longest filter from the identical
% filterbank.
%
% [A,B]=WPFBTBOUNDS(...) returns the lower and upper frame bounds
% explicitly.
%
% See WFBT for explanation of parameter wt.
%
% Additionally, the function accepts the following flags:
%
% 'intsqrt'(default),'intnoscale', 'intscale'
% The filters in the filterbank tree are scaled to reflect the
% behavior of WPFBT and IWPFBT with the same flags.
%
% 'scaling_notset'(default),'noscale','scale','sqrt'
% Support for scaling flags as described in UWPFBT. By default,
% the bounds are caltulated for WPFBT, passing any of the non-default
% flags results in bounds for UWPFBT.
%
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/wavelets/wpfbtbounds.html}
%@seealso{wpfbt, filterbankbounds}
%@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/>.
% AUTHOR: Zdenek Prusa
complainif_notenoughargs(nargin,1,'WPFBTBOUNDS');
definput.keyvals.L = [];
definput.flags.interscaling = {'intsqrt', 'intscale', 'intnoscale'};
definput.import = {'uwfbtcommon'};
definput.importdefaults = {'scaling_notset'};
[flags,~,L]=ltfatarghelper({'L'},definput,varargin);
wt = wfbtinit({'strict',wt},'nat');
if ~isempty(L) && flags.do_scaling_notset
if L~=wfbtlength(L,wt)
error(['%s: Specified length L is incompatible with the length of ' ...
'the time shifts.'],upper(mfilename));
end;
end
for ii=1:numel(wt.nodes)
a = wt.nodes{ii}.a;
assert(all(a==a(1)),sprintf(['%s: One of the basic wavelet ',...
'filterbanks is not uniform.'],...
upper(mfilename)));
end
% Do the equivalent filterbank using multirate identity property
[gmultid,amultid] = wpfbt2filterbank(wt,flags.interscaling,flags.scaling);
if isempty(L)
L = wfbtlength(max(cellfun(@(gEl) numel(gEl.h),gmultid)),wt);
end
% Do the equivalent uniform filterbank
if any(amultid~=amultid(1))
[gu,au] = nonu2ufilterbank(gmultid,amultid);
else
[gu,au] = deal(gmultid,amultid);
end
if nargout<2
AF = filterbankbounds(gu,au,L);
elseif nargout == 2
[AF, BF] = filterbankbounds(gu,au,L);
end
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