function gtout=filterbankrealtight(g,a,varargin)
%FILTERBANKREALTIGHT Tight filters of filterbank for real signals only
% Usage: gt=filterbankrealtight(g,a,L);
% gt=filterbankrealtight(g,a);
%
% filterabankrealtight(g,a,L) computes the canonical tight filters of
% g for a channel subsampling rate of a (hop-size) and a system
% length L. L must be compatible with subsampling rate a as
% L==filterbanklength(L,a). The tight filters work only for real-valued
% signals. Use this function on the common construction where the filters
% in g only covers the positive frequencies.
%
% filterabankrealtight(g,a) does the same, but the filters must be FIR
% filters, as the transform length is unspecified. L will be set to
% next suitable length equal or bigger than the longest impulse response.
%
% The format of the filters g are described in the help of FILTERBANK.
%
% In addition, the function recognizes a 'forcepainless' flag which
% forces treating the filterbank g and a as a painless case
% filterbank.
%
% REMARK: The resulting system is tight for length L. In some cases,
% using tight system calculated for shorter L might work but check the
% reconstruction error.
%
% See also: filterbank, ufilterbank, ifilterbank
%
% Url: http://ltfat.github.io/doc/filterbank/filterbankrealtight.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/>.
complainif_notenoughargs(nargin,2,'FILTERBANKREALTIGHT');
definput.import={'filterbankdual'};
definput.flags.outformat = {'fir','full','econ','asfreqfilter'};
definput.keyvals.efsuppthr = 10^(-5);
%definput.keyvals.bwthr = 10^(-3/10);
[flags,kv,L]=ltfatarghelper({'L'},definput,varargin,'filterbankrealtight');
[g,asan,info]=filterbankwin(g,a,L,'normal');
if isempty(L)
if info.isfir
% Pick shortest possible length for FIR filterbank
L = filterbanklength(info.longestfilter,asan);
else
% Just thow an error, nothing reasonable can be done without L
error(['%s: L must be specified when not working with FIR ',...'
'filterbanks.'], upper(mfilename));
end
end
M=info.M;
% Force usage of the painless algorithm
if flags.do_forcepainless
info.ispainless = 1;
end
% Check user defined L
if L~=filterbanklength(L,a)
error(['%s: Specified length L is incompatible with the length of ' ...
'the time shifts.'],upper(mfilename));
end;
% Prioritize painless over uniform algorithm
if info.isuniform && info.ispainless
info.isuniform = 0;
end
if info.isuniform
% Uniform filterbank, use polyphase representation
a=a(1);
% Transfer functions of individual filters as cols
G = filterbankfreqz(g,a,L);
thisclass = class(G);
N=L/a;
gt=zeros(M,N,thisclass);
for w=0:N-1
idx_a = mod(w-(0:a-1)*N,L)+1;
idx_b = mod((0:a-1)*N-w,L)+1;
Ha = G(idx_a,:);
Hb = conj(G(idx_b,:));
Ha=sqrtm(Ha*Ha'+Hb*Hb')\Ha;
gt(:,idx_a)=Ha.';
end;
% gt was created transposed because the indexing gt(:,idx_a)
% is much faster than gt(idx_a,:)
gt = gt.';
switch flags.outformat
case 'fir'
gt=ifft(gt)*sqrt(a);
% Matrix cols to cell elements + cast
gtout = cellfun(@(gtEl) cast(gtEl,thisclass), num2cell(gt,1),...
'UniformOutput',0);
% All filters in gdout will be treated as FIR of length L. Convert them
% to a struct with .h and .offset format.
gtout = filterbankwin(gtout,a);
case 'full'
gtout = gt*sqrt(a);
case 'econ'
% Shorten filters to essential support
gt = gt*sqrt(a);
gtout=economize_filters(gt,'efsuppthr',kv.efsuppthr);
case 'asfreqfilter'
gt = gt*sqrt(a);
% All filters in gdout will be treated as (numeric) freqfilter format.
% Manually convert them to a struct with .H and .foff.
template = struct('H',[],'foff',0,'realonly',0,'delay',0,'L',L);
gtout = cell(1,M);
gtout(:) = {template};
[H,foff,~]=economize_filters(gt,'efsuppthr',kv.efsuppthr);
for kk = 1:M
gtout{kk} = setfield(gtout{kk},'H',H{kk});
gtout{kk} = setfield(gtout{kk},'foff',foff(kk));
end
otherwise
error('%s: Unknown filter format.', upper(mfilename));
end
elseif info.ispainless
gtout = comp_painlessfilterbank(g,asan,L,'tight',1);
else
error(['%s: The canonical dual frame of this system is not a ' ...
'filterbank. You must call an iterative ' ...
'method to perform the desired inverstion. Please see ' ...
'FRANAITER or FRSYNITER.'],upper(mfilename));
end;