function [c,info] = ufwt(f,w,J,varargin)
%UFWT Undecimated Fast Wavelet Transform
% Usage: c = ufwt(f,w,J);
% [c,info] = ufwt(...);
%
% Input parameters:
% f : Input data.
% w : Wavelet Filterbank.
% J : Number of filterbank iterations.
%
% Output parameters:
% c : Coefficients stored in L x(J+1) matrix.
% info : Transform paramaters struct.
%
% UFWT(f,w,J) computes redundant time (or shift) invariant
% wavelet representation of the input signal f using wavelet filters
% defined by w in the "a-trous" algorithm.
%
% For all accepted formats of the parameter w see the FWTINIT function.
%
% [c,info]=UFWT(f,w,J) additionally returns the info struct.
% containing the transform parameters. It can be conviniently used for
% the inverse transform IUFWT e.g. fhat = iUFWT(c,info). It is also
% required by the PLOTWAVELETS function.
%
% The coefficents c are so called undecimated Discrete Wavelet transform
% of the input signal f, if w defines two-channel wavelet filterbank.
% Other names for this version of the wavelet transform are: the
% time-invariant wavelet transform, the stationary wavelet transform,
% maximal overlap discrete wavelet transform or even the "continuous"
% wavelet transform (as the time step is one sample). However, the
% function accepts any number filters (referred to as M) in the basic
% wavelet filterbank and the number of columns of c is then J(M-1)+1.
%
% For one-dimensional input f of length L, the coefficients c are
% stored as columns of a matrix. The columns are ordered with inceasing
% central frequency of the respective subbands.
%
% If the input f is L xW matrix, the transform is applied
% to each column and the outputs are stacked along third dimension in the
% L xJ(M-1)+1 xW data cube.
%
% Filter scaling
% --------------
%
% When compared to FWT, UFWT subbands are gradually more and more
% redundant with increasing level of the subband. If no scaling of the
% filters is introduced, the energy of subbands tends to grow with increasing
% level.
% There are 3 flags defining filter scaling:
%
% 'sqrt'
% Each filter is scaled by 1/sqrt(a), where 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' has to be used in IUFWT (and vice
% versa) in order to obtain a perfect reconstruction.
%
% Boundary handling:
% ------------------
%
% c=UFWT(f,w,J) uses periodic boundary extension. The extensions are
% done internally at each level of the transform, rather than doing the
% prior explicit padding.
%
% Examples:
% ---------
%
% A simple example of calling the UFWT function:
%
% [f,fs] = greasy;
% J = 8;
% [c,info] = ufwt(f,'db8',J);
% plotwavelets(c,info,fs,'dynrange',90);
%
% See also: iufwt, plotwavelets
%
% References:
% M. Holschneider, R. Kronland-Martinet, J. Morlet, and P. Tchamitchian.
% A real-time algorithm for signal analysis with the help of the wavelet
% transform. In Wavelets. Time-Frequency Methods and Phase Space,
% volume 1, page 286, 1989.
%
%
% Url: http://ltfat.github.io/doc/wavelets/ufwt.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,3,'UFWT');
complainif_notposint(J,'J');
definput.import = {'uwfbtcommon'};
[flags]=ltfatarghelper({},definput,varargin);
% Initialize the wavelet filters structure
w = fwtinit(w);
%% ----- step 1 : Verify f and determine its length -------
% Change f to correct shape.
[f,Ls]=comp_sigreshape_pre(f,upper(mfilename),0);
if(Ls<2)
error('%s: Input signal seems not to be a vector of length > 1.',upper(mfilename));
end
%% ----- step 2 : Run computation
c = comp_ufwt(f,w.h,w.a,J,flags.scaling);
%% ----- Optionally : Fill info struct ----
if nargout>1
info.fname = 'ufwt';
info.wt = w;
info.J = J;
info.scaling = flags.scaling;
end