function [g,info] = wilwin(g,M,L,callfun);
%WILWIN Compute a Wilson/WMDCT window from text or cell array
% Usage: [g,info] = wilwin(g,M,L);
%
% [g,info]=WILWIN(g,M,L) computes a window that fits well with the
% specified number of channels M and transform length L. The window itself
% is specified by a text description or a cell array containing additional
% parameters.
%
% The window can be specified directly as a vector of numerical
% values. In this case, WILWIN only checks assumptions about transform
% sizes etc.
%
% [g,info]=WILWIN(g,M) does the same, but the window must be a FIR
% window, as the transform length is unspecified.
%
% The window can be specified as one of the following text strings:
%
% 'gauss' Gaussian window with optimal concentration
%
% 'dualgauss' Riesz dual of Gaussian window with optimal concentration.
%
% 'tight' Window generating an orthonormal basis
%
% In these cases, a long window is generated with a length of L.
%
% It is also possible to specify one of the window names from FIRWIN. In
% such a case, WILWIN generates the specified FIR window with a length
% of M.
%
% The window can also be specified as cell array. The possibilities are:
%
% {'gauss',...}
% Additional parameters are passed to PGAUSS
%
% {'dual',...}
% Dual window of whatever follows. See the examples below.
%
% {'tight',...}
% Orthonormal window of whatever follows.
%
% It is also possible to specify one of the window names from FIRWIN as
% the first field in the cell array. In this case, the remaining
% entries of the cell array are passed directly to FIRWIN.
%
% Some examples:
%
% g=wilwin('gauss',M,L);
%
% This computes a Gaussian window of length L fitted for a system with
% M channels. :
%
% g=wilwin({'gauss',1},M,L);
%
% This computes a Gaussian window with equal time and frequency support
% irrespective of M. :
%
% gd=wilwin('gaussdual',M,L);
%
% This computes the dual of a Gaussian window fitted for a system with M*
% channels. :
%
% gd=wilwin({'tight','gauss'},M,L);
%
% This computes the orthonormal window of the Gaussian window fitted for
% the system. :
%
% g=wilwin({'dual',{'hann',20}},M,L);
%
% This computes the dual of a Hann window of length 20.
%
% The structure info provides some information about the computed
% window:
%
% info.gauss
% True if the window is a Gaussian.
%
% info.tfr
% Time/frequency support ratio of the window. Set whenever it makes sense.
%
% info.wasrow
% Input was a row window
%
% info.isfir
% Input is an FIR window
%
% info.isdual
% Output is the dual window of the auxiliary window.
%
% info.istight
% Output is known to be a tight window.
%
% info.auxinfo
% Info about auxiliary window.
%
% info.gl
% Length of window.
%
% See also: pgauss, firwin, gabwin
%
% Url: http://ltfat.github.io/doc/gabor/wilwin.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/>.
% Assert correct input.
complainif_argnonotinrange(nargin,2,4,mfilename);
if nargin==2
L=[];
end;
% Basic discovery: Some windows depend on L, and some windows help define
% L, so the calculation of L is window dependant.
% Default values.
info.gauss=0;
info.wasrow=0;
info.isfir=0;
info.istight=0;
info.isdual=0;
% Manually get the list of window names
definput=arg_firwin(struct);
firwinnames = definput.flags.wintype;
% Create window if string was given as input.
if ischar(g)
winname=lower(g);
switch(winname)
case {'pgauss','gauss'}
complain_L(L,callfun);
g=comp_pgauss(L,2*M*M/L,0,0);
info.gauss=1;
info.tfr=2*M*M/L;
case {'psech','sech'}
complain_L(L,callfun);
g=psech(L,2*M*M/L);
info.tfr=a*M/L;
case {'dualgauss','gaussdual'}
complain_L(L,callfun);
g=comp_pgauss(L,2*M*M/L,0,0);
g=wildual(g,M);
info.isdual=1;
info.tfr=a*M/L;
case {'tight'}
complain_L(L,callfun);
g=wilorth(M,L);
info.tfr=2*M*M/L;
info.istight=1;
case firwinnames
[g,firinfo]=firwin(winname,2*M,'2');
info.isfir=1;
if firinfo.issqpu
info.istight=1;
end;
otherwise
error('%s: Unknown window type: %s',callfun,winname);
end;
end;
if iscell(g)
if isempty(g) || ~ischar(g{1})
error('First element of window cell array must be a character string.');
end;
winname=lower(g{1});
switch(winname)
case {'pgauss','gauss'}
complain_L(L,callfun);
[g,info.tfr]=pgauss(L,g{2:end});
info.gauss=1;
case {'psech','sech'}
complain_L(L,callfun);
[g,info.tfr]=psech(L,g{2:end});
case {'dual'}
gorig = g{2};
[g,info.auxinfo] = wilwin(gorig,M,L,callfun);
g = wildual(g,M,L);
% gorig can be string or cell array
if info.auxinfo.isfir && test_isfir(gorig,M)
info.isfir = 1;
end
info.isdual=1;
case {'tight'}
gorig = g{2};
[g,info.auxinfo] = wilwin(g{2},M,L,callfun);
g = wilorth(g,M,L);
% gorig can be string or cell array
if info.auxinfo.isfir && test_isfir(gorig,M)
info.isfir = 1;
end
info.istight=1;
case firwinnames
g=firwin(winname,g{2},'energy',g{3:end});
info.isfir=1;
otherwise
error('Unsupported window type.');
end;
end;
if isnumeric(g)
if size(g,2)>1
if size(g,1)==1
% g was a row vector.
g=g(:);
info.wasrow=1;
end;
end;
end;
if rem(length(g),2*M)~=0
% Zero-extend the window to a multiple of 2*M
g=fir2long(g,ceil(length(g)/(2*M))*2*M);
end;
% Information to be determined post creation.
info.wasreal = isreal(g);
info.gl = length(g);
if (~isempty(L) && (info.gl<L))
info.isfir=1;
end;
function complain_L(L,callfun)
if isempty(L)
error(['%s: You must specify a length L if a window is represented as a ' ...
'text string or cell array.'],callfun);
end;
function isfir=test_isfir(gorig,M)
% Original window is FIR, dual window is FIR if length of the original
% window is <= M. This is true if the length was not explicitly
% defined (gorig{2}).
if iscell(gorig) && numel(gorig)>1 && isnumeric(gorig{2}) && gorig{2}<=2*M...
|| ischar(gorig)
isfir = 1;
else
isfir = 0;
end