function [c,newphase,usedmask,tgrad,fgrad]=constructphase(s,g,a,varargin)
%CONSTRUCTPHASE Construct phase for DGT
% Usage: c=constructphase(s,g,a);
% c=constructphase(s,g,a,tol);
% c=constructphase(c,g,a,tol,mask);
% c=constructphase(c,g,a,tol,mask,usephase);
% [c,newphase,usedmask,tgrad,fgrad] = constructphase(...);
%
% Input parameters:
% s : Initial coefficients.
% g : Analysis Gabor window.
% a : Hop factor.
% tol : Relative tolerance.
% mask : Mask for selecting known phase.
% usephase : Explicit known phase.
% Output parameters:
% c : Coefficients with the constructed phase.
% newphase : Just the (unwrapped) phase.
% usedmask : Mask for selecting coefficients with the new phase.
% tgrad : Relative time phase derivative.
% fgrad : Relative frequency phase derivative.
%
% CONSTRUCTPHASE(s,g,a) will construct a suitable phase for the postive
% valued coefficients s.
%
% If s is the absolute values of the Gabor coefficients of a signal
% obtained using the window g and time-shift a, i.e.:
%
% c=dgt(f,g,a,M);
% s=abs(c);
%
% then constuctphase(s,g,a) will attempt to reconstruct c.
%
% The window g must be Gaussian, i.e. g must have the value 'gauss'
% or be a cell array {'gauss',tfr}.
%
% CONSTRUCTPHASE(s,g,a,tol) does as above, but sets the phase of
% coefficients less than tol to random values.
% By default, tol has the value 1e-10.
%
% CONSTRUCTPHASE(c,g,a,M,tol,mask) accepts real or complex valued
% c and real valued mask of the same size. Values in mask which can
% be converted to logical true (anything other than 0) determine
% coefficients with known phase which is used in the output. Only the
% phase of remaining coefficients (for which mask==0) is computed.
%
% CONSTRUCTPHASEreal(c,g,a,M,tol,mask,usephase) does the same as before
% but uses the known phase values from usephase rather than from c.
%
% In addition, tol can be a vector containing decreasing values. In
% that case, the algorithm is run numel(tol) times, initialized with
% the result from the previous step in the 2nd and the further steps.
%
% Further, the function accepts the following flags:
%
% 'freqinv' The constructed phase complies with the frequency
% invariant phase convention such that it can be directly
% used in IDGTREAL.
% This is the default.
%
% 'timeinv' The constructed phase complies with the time-invariant
% phase convention. The same flag must be used in the other
% functions e.g. IDGTREAL
%
% This function requires a computational subroutine that is only
% available in C. Use LTFATMEX to compile it.
%
% See also: dgt, gabphasegrad, ltfatmex
%
% References:
% Z. Průša, P. Balazs, and P. L. Søndergaard. A Non-iterative Method for
% STFT Phase (Re)Construction. IEEE/ACM Transactions on Audio, Speech,
% and Language Processing, 2016. In preparation. Preprint will be
% available at http://ltfat.github.io/notes/ltfatnote040.pdf.
%
%
%
% Url: http://ltfat.github.io/doc/gabor/constructphase.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: Peter L. Søndergaard, Zdenek Prusa
thismfilename = upper(mfilename);
complainif_notposint(a,'a',thismfilename);
definput.keyvals.tol=[1e-1 1e-10];
definput.keyvals.mask=[];
definput.keyvals.usephase=[];
definput.flags.phase={'freqinv','timeinv'};
[flags,~,tol,mask,usephase]=ltfatarghelper({'tol','mask','usephase'},definput,varargin);
if ~isnumeric(s)
error('%s: *s* must be numeric.',thismfilename);
end
if ~isempty(usephase) && isempty(mask)
error('%s: Both mask and usephase must be used at the same time.',...
thismfilename);
end
if isempty(mask)
if ~isreal(s) || any(s(:)<0)
error('%s: *s* must be real and positive when no mask is used.',...
thismfilename);
end
else
if any(size(mask) ~= size(s)) || ~isreal(mask)
error(['%s: s and mask must have the same size and mask must',...
' be real.'],thismfilename)
end
% Sanitize mask (anything other than 0 is true)
mask = cast(mask,'double');
mask(mask~=0) = 1;
end
if ~isempty(usephase)
if any(size(mask) ~= size(s)) || ~isreal(usephase)
error(['%s: s and usephase must have the same size and usephase must',...
' be real.'],thismfilename)
end
else
usephase = angle(s);
end
if ~isnumeric(tol) || ~isequal(tol,sort(tol,'descend'))
error(['%s: *tol* must be a scalar or a vector sorted in a ',...
'descending manner.'],thismfilename);
end
abss = abs(s);
% Compute phase gradient, check parameteres
[tgrad,fgrad] = gabphasegrad('abs',abss,g,a,2);
absthr = max(abss(:))*tol;
if isempty(mask)
usedmask = zeros(size(s));
else
usedmask = mask;
end
if isempty(mask)
% Build the phase (calling a MEX file)
newphase=comp_heapint(abss,tgrad,fgrad,a,tol(1),flags.do_timeinv);
% Set phase of the coefficients below tol to random values
bigenoughidx = abss>absthr(1);
usedmask(bigenoughidx) = 1;
else
newphase=comp_maskedheapint(abss,tgrad,fgrad,mask,a,tol(1),...
flags.do_timeinv,usephase);
% Set phase of small coefficient to random values
% but just in the missing part
% Find all small coefficients in the unknown phase area
missingidx = find(usedmask==0);
bigenoughidx = abss(missingidx)>absthr(1);
usedmask(missingidx(bigenoughidx)) = 1;
end
% Do further tol
for ii=2:numel(tol)
newphase=comp_maskedheapint(abss,tgrad,fgrad,usedmask,a,tol(ii),...
flags.do_timeinv,newphase);
missingidx = find(usedmask==0);
bigenoughidx = abss(missingidx)>absthr(ii);
usedmask(missingidx(bigenoughidx)) = 1;
end
% Convert the mask so it can be used directly for indexing
usedmask = logical(usedmask);
% Assign random values to coefficients below tolerance
zerono = numel(find(~usedmask));
newphase(~usedmask) = rand(zerono,1)*2*pi;
% Combine the magnitude and phase
c=abss.*exp(1i*newphase);