function [gd,relres,iter]=gabfirdual(Ldual,g,a,M,varargin)
%GABFIRDUAL Compute FIR dual window
% Usage: gd=gabfirdual(Ldual,g,a,M);
% gd=gabfirdual(Ldual,g,a,M, varagin);
%
% Input parameters:
% Ldual : Length of dual window
% g : Window function
% a : Time shift
% M : Number of Channels
% alpha1 : Weight of l^1-norm in the time domain
% alpha2 : Weight of l^1-norm in the freq. domain
%
% Output parameters:
% gd : Dual window
%
% GABFIRDUAL(Ldual,g,a,M) computes an FIR window gd which is an
% approximate dual window of the Gabor system defined by g, a and
% M. The FIR dual window will be supported on Ldual samples.
%
% This function solve a convex optimization problem that can be written
% as:
%
% gd = argmin_x || alpha x||_1 + || beta Fx||_1
%
% + || omega (x -g_l) ||_2^2 + delta || x ||_S0
%
% + gamma || nabla F x ||_2^2 + mu || nabla x ||_2^2
%
% such that x is a dual windows of g
%
% *Note**: This function require the unlocbox. You can download it at
% http://unlocbox.sourceforge.net
%
% The function uses an iterative algorithm to compute the approximate
% FIR dual. The algorithm can be controlled by the following flags:
%
% 'alpha',alpha Weight in time. If it is a scalar, it represent the
% weights of the entire L1 function in time. If it is a
% vector, it is the associated weight assotiated to each
% component of the L1 norm (length: Ldual).
% Default value is alpha=0.
% *Warning**: this value should not be too big in order to
% avoid the the L1 norm proximal operator kill the signal.
% No L1-time constraint: alpha=0
%
% 'beta',beta Weight in frequency. If it is a scalar, it represent the
% weights of the entire L1 function in frequency. If it is a
% vector, it is the associated weight assotiated to each
% component of the L1 norm in frequency. (length: Ldual).
% Default value is beta=0.
% *Warning**: this value should not be too big in order to
% avoid the the L1 norm proximal operator kill the signal.
% No L1-frequency constraint: beta=0
%
% 'omega',omega Weight in time of the L2-norm. If it is a scalar, it represent the
% weights of the entire L2 function in time. If it is a
% vector, it is the associated weight assotiated to each
% component of the L2 norm (length: Ldual).
% Default value is omega=0.
% No L2-time constraint: omega=0
%
% 'glike',g_l g_l is a windows in time. The algorithm try to shape
% the dual window like g_l. Normalization of g_l is done
% automatically. To use option omega should be different
% from 0. By default g_d=0.
%
% 'mu',mu Weight of the smooth constraint Default value is 1.
% No smooth constraint: mu=0
%
% 'gamma',gamma Weight of the smooth constraint in frequency. Default value is 1.
% No smooth constraint: gamma=0
%
% 'delta',delta Weight of the S0-norm. Default value is 0.
% No S0-norm: delta=0
%
% 'dual' Look for a dual windows (default)
%
% 'painless' Construct a starting guess using a painless-case
% approximation. This is the default
%
% 'zero' Choose a starting guess of zero.
%
% 'rand' Choose a random starting phase.
%
% 'tol',t Stop if relative residual error is less than the
% specified tolerance.
%
% 'maxit',n Do at most n iterations. default 200
%
% 'print' Display the progress.
%
% 'debug' Display all the progresses.
%
% 'quiet' Don't print anything, this is the default.
%
% 'fast' Fast algorithm, this is the default.
%
% 'slow' Safer algorithm, you can try this if the fast algorithm
% is not working. Before using this, try to iterate more.
%
% 'printstep',p If 'print' is specified, then print every p'th
% iteration. Default value is p=10;
%
% 'hardconstraint' Force the projection at the end (default)
%
% 'softconstaint' Do not force the projection at the end
%
% See also: gaboptdual, gabdual, gabtight, gabfirtight, gaboptdual
%
% Url: http://ltfat.github.io/doc/gabor/gabfirdual.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: Nathanael Perraudin
% Date : 18 Feb 2014
if nargin<4
error('%s: Too few input parameters.',upper(mfilename));
end;
% l=length(varargin);
% varargin(l+1)=cellstr('support');
% varargin(l+2)=num2cell(Ldual);
[gd,relres,iter]=gabconvexopt(g,a,M,varargin{:}, 'support',Ldual);