normalisation_gaussian.m

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function [Q, sigma_deg] = normalisation_gaussian(number_clusters, ...
						  power_lin, AS_deg, delta_phi_deg)
% [Q, sigma_deg] = normalisation_gaussian(number_clusters,
%                  power_lin, AS_deg, delta_phi_deg)
%
% Computes the variances sigma_k and the power normalising
% coefficients Q_k such that the Power Azimuth Spectrum (PAS) can
% be regarded as a probability distribution function (pdf), that is
% to say int_{-\pi}^{pi} PAS(\phi) d\phi = 1.
%
%
% STANDARD DISCLAIMER
%
% CSys is furnishing this item "as is". CSys does not provide any
% warranty of the item whatsoever, whether express, implied, or
% statutory, including, but not limited to, any warranty of
% merchantability or fitness for a particular purpose or any
% warranty that the contents of the item will be error-free.
%
% In no respect shall CSys incur any liability for any damages,
% including, but limited to, direct, indirect, special, or
% consequential damages arising out of, resulting from, or any way
% connected to the use of the item, whether or not based upon
% warranty, contract, tort, or otherwise; whether or not injury was
% sustained by persons or property or otherwise; and whether or not
% loss was sustained from, or arose out of, the results of, the
% item, or any services that may be provided by CSys.
%
% (c) Laurent Schumacher, AAU-TKN/IES/KOM/CPK/CSys - July 2001

%
% Computation of sigma
%
load AS2sigma_gaussian tmp;
for k=1:number_clusters
  if ((AS_deg(k) < min(tmp(:,1))) | (AS_deg(k) >= max(tmp(:,1))))
    disp('Look-up table AS -> sigma incomplete.');
    disp('Please regenerate with AS_vs_sigma_gaussian.m');
    break;
  end;
  pos          = find(tmp(:,1)>=AS_deg(k));
  sigma_deg(k) = ((tmp(pos(1),1)-AS_deg(k))*tmp(pos(1)-1,2) + ...
		  (AS_deg(k) - tmp(pos(1)-1,1))*tmp(pos(1),2))/ ...
      (tmp(pos(1),1)-tmp(pos(1)-1,1));
end;
% Conversion degree -> rad
AS_rad    = AS_deg.*(pi/180);
sigma_rad = sigma_deg.*(pi/180);
% Domain definition
delta_phi_rad = ((delta_phi_deg*pi)/180).*ones(1,number_clusters);
%
% Computation of Q
%
if (number_clusters == 1)
  Q = 1/erf(delta_phi_rad/(sqrt(2)*sigma_rad));
else
  A = zeros(number_clusters);
  A(1:number_clusters-1,1) = 1/(sigma_rad(1)*power_lin(1));
  for k=2:number_clusters
    A(k-1,k) = (-1)/(sigma_rad(k)*power_lin(k));
  end;
  A(number_clusters,:) = erf(delta_phi_rad./(sqrt(2).*sigma_rad));
  b = zeros(number_clusters,1);
  b(number_clusters,1) = 1;
  Q = (inv(A)*b).';
end;
%
% Validation
%
if ~(sum(erf(delta_phi_rad./(sqrt(2).*sigma_rad))*Q.')-1 < 1e-15)
  disp('Normalisation of gaussian distribution failed!');
  break;
end;