function phi = itd2angle(itd,lookup)
% ITD2ANGLE converts the given ITD to an angle using a lookup table
%   Usage: phi = itd2angle(itd,lookup)
%
%   Input parameters:
%       itd     : ITDs to convert to angles
%       lookup  : a struct containing the polinomial fitting entries p,MU,S.
%                 This struct can be generated by ITD2ANGLE_lookuptable
%
%   Output parameters:
%       phi     : angles for the corresponding ITD values / deg
%
%   ITD2ANGLE(itd,lookup) converts the given ITD values to azimuth angles phi.
%   Therefore a lookup table containing the polynomial fitting parameters is
%   used. This lookup table is created from a set of HRTFs with known azimuth
%   angles and stores the corresponding ITD values. itd2angle works with
%   DIETZ2011 and LINDEMANN1986. Corresponding lookup tables can be created
%   by ITD2ANGLE_LOOKUPTABLE.
%
%   Url: http://amtoolbox.org/amt-1.3.0/doc/common/itd2angle.php

%   #Author: Mathias Dietz
%   #Author: Hagen Wierstorf

% This file is licensed unter the GNU General Public License (GPL) either 
% version 3 of the license, or any later version as published by the Free Software 
% Foundation. Details of the GPLv3 can be found in the AMT directory "licences" and 
% at <https://www.gnu.org/licenses/gpl-3.0.html>. 
% You can redistribute this file and/or modify it under the terms of the GPLv3. 
% This file is distributed without any warranty; without even the implied warranty 
% of merchantability or fitness for a particular purpose. 


%% ===== Checking of input parameters ====================================
nargmin = 2;
nargmax = 2;
narginchk(nargmin,nargmax);


%% ===== Computation =====================================================
phi = zeros(size(itd));

for n = 1:size(itd,2)
    % by calling the output S and MU, phi is z-scored, thus improving the fitting
    phi(:,n)=polyval(lookup.p(:,n),itd(:,n),lookup.S{n},lookup.MU(:,n));
end
% neglect angles > 95°. Warning => maybe systematic underestimation for azi ~ 90°
phi(abs(phi)>95) = NaN;