WFBTBOUNDS - Frame bounds of WFBT

function [AF,BF]=wfbtbounds(wt,varargin)
%WFBTBOUNDS Frame bounds of WFBT
%   Usage: fcond=wfbtbounds(wt,L);
%          [A,B]=wfbtbounds(wt,L);
%          [...]=wfbtbounds(wt);
%
%   WFBTBOUNDS(wt,L) calculates the ratio B/A of the frame bounds
%   of the filterbank tree specified by wt for a system of length
%   L. The ratio is a measure of the stability of the system.
%
%   WFBTBOUNDS({w,J,'dwt'},L) calculates the ratio B/A of the frame
%   bounds of the DWT (|FWT|) filterbank specified by w and J for a
%   system of length L.
%
%   WFBTBOUNDS(wt) does the same thing, but L is assumed to be the
%   next compatible length bigger than the longest filter in the identical
%   filterbank.
%
%   [A,B]=WFBTBOUNDS(...) returns the lower and upper frame bounds
%   explicitly.
%
%   See WFBT for explanation of parameter wt and FWT for explanation
%   of parameters w and J.
%
%   The function supports the following flag groups:
%
%   'scaling_notset'(default),'noscale','scale','sqrt'
%     Support for scaling flags as described in UWFBT. By default,
%     the bounds are computed for WFBT, passing any of the non-default
%     flags results in framebounds for UWFBT.
%
%   See also: wfbt, fwt, filterbankbounds
%
%   Url: http://ltfat.github.io/doc/wavelets/wfbtbounds.html

% Copyright (C) 2005-2023 Peter L. Soendergaard <peter@sonderport.dk> and others.
% This file is part of LTFAT version 2.6.0
%
% 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: Zdenek Prusa

complainif_notenoughargs(nargin,1,'WFBTBOUNDS');

% Frequency or natural ordering should not make a difference
wt = wfbtinit({'strict',wt},'nat');

definput.keyvals.L = [];
definput.import = {'uwfbtcommon'};
definput.importdefaults = {'scaling_notset'};
[flags,~,L]=ltfatarghelper({'L'},definput,varargin);

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

% Do the equivalent filterbank using multirate identity property
[gmultid,amultid] = wfbt2filterbank(wt,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