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function f = iufwt(c,par,varargin)
%-*- texinfo -*-
%@deftypefn {Function} iufwt
%@verbatim
%IUFWT Inverse Undecimated Fast Wavelet Transform
% Usage: f = iufwt(c,info)
% f = iufwt(c,w,J);
%
% Input parameters:
% c : Coefficients stored in L xJ+1 matrix.
% info,w : Transform parameters struct/Wavelet filters definition.
% J : Number of filterbank iterations.
%
% Output parameters:
% f : Reconstructed data.
%
% f = IUFWT(c,info) reconstructs signal f from the wavelet
% coefficients c using parameters from info struct. both returned by
% UFWT function.
%
% f = IUFWT(c,w,J) reconstructs signal f from the wavelet
% coefficients c using the wavelet filterbank consisting of the J*
% levels of the basic synthesis filterbank defined by w using the "a-trous"
% algorithm. Node that the same flag as in the ufwt function have to be used.
%
% Please see the help on UFWT for a description of the parameters.
%
% Filter scaling
% --------------
%
% As in UFWT, 3 flags defining scaling of filters are recognized:
%
% 'sqrt'
% Each filter is scaled by 1/sqrt(a), there a is the hop
% factor associated with it. If the original filterbank is
% orthonormal, the overall undecimated transform is a tight
% frame.
% This is the default.
%
% 'noscale'
% Uses filters without scaling.
%
% 'scale'
% Each filter is scaled by 1/a.
%
% If 'noscale' is used, 'scale' must have been used in UFWT (and vice
% versa) in order to obtain a perfect reconstruction.
%
% Examples:
% ---------
%
% A simple example showing perfect reconstruction:
%
% f = gspi;
% J = 8;
% c = ufwt(f,'db8',J);
% fhat = iufwt(c,'db8',J);
% % The following should give (almost) zero
% norm(f-fhat)
%
%
% References:
% S. Mallat. A wavelet tour of signal processing. Academic Press, San
% Diego, CA, 1998.
%
%
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/wavelets/iufwt.html}
%@seealso{ufwt, plotwavelets}
%@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,2,'IUFWT');
if(isstruct(par)&&isfield(par,'fname'))
complainif_toomanyargs(nargin,2,'IUFWT');
if ~strcmpi(par.fname,'ufwt')
error(['%s: Wrong func name in info struct. ',...
' The info parameter was created by %s.'],...
upper(mfilename),par.fname);
end
% Ensure we are using the correct wavelet filters
w = fwtinit({'dual',par.wt});
J = par.J;
scaling = par.scaling;
% Use the "oposite" scaling
if strcmp(scaling,'scale')
scaling = 'noscale';
elseif strcmp(scaling,'noscale')
scaling = 'scale';
end
else
complainif_notenoughargs(nargin,3,'IUFWT');
definput.keyvals.J = [];
definput.import = {'uwfbtcommon'};
[flags, ~, J]=ltfatarghelper({'J'},definput,varargin);
complainif_notposint(J,'J');
% Initialize the wavelet filters
% It is up to user to use the correct ones.
w = fwtinit(par);
scaling = flags.scaling;
end
%% Run computation
f = comp_iufwt(c,w.g,w.a,J,scaling);
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