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−% OVERLAPCORR Compute correlation introduced by segment overlapping
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−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−% OVERLAPCORR Compute correlation introduced by segment overlapping in WOSA
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−% spectral estimations. It estimates the term contributing to the variance
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−% because of segment overlapping.
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−% 
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−% CALL 
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−% 
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−% R = utils.math.overlapCorr(w,N,T)
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−% [R,n] = utils.math.overlapCorr(w,N,T)
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−% 
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−% INPUT
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−% 
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−% - w, window samples, Nsx1 double, Ns must be the effective length of the
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−% segments used for spectral estimation. E.g. For a periodogram Ns is equal
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−% to the length of the data series. For a WOSA estimation Ns is the length
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−% of each averaging segment.
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−% - N total length of data series, 1x1 double
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−% - navs, number of averages, 1x1 double
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−% 
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−% REFERENCES
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−% 
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−% D. B. Percival and A. T. Walden, Spectral Analysis for Physical
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−% Applications (Cambridge University Press, Cambridge, 1993) p 292.
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−% 
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−% L Ferraioli 09-03-2011
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−%
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−% $Id: overlapCorr.m,v 1.1 2011/03/28 16:37:23 luigi Exp $
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−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−function varargout = overlapCorr(w,N,navs)
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−  
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−  Ns = numel(w);
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−  % willing to work with columns
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−  [nn,mm] = size(w);
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−  if nn<mm
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−    w = w.';
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−  end
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−  
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−  % make suaqre integrable
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−  a = sqrt(sum(w.^2));
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−  w = w./a;
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−
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−  n = floor((N-Ns)/(navs-1));
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−  win = [w; zeros((navs-1)*n,1)];
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−  
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−  R = 0;
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−  for kk=1:navs-1
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−    ew = zeros(size(win));
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−    ew(kk*n+1:kk*n+Ns) = win(1:Ns);
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−      
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−    R = R + (navs-kk)*abs(win.'*ew)^2;   
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−  end
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−  R = R./navs^2;
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−  
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−  if nargout == 1
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−    varargout{1} = R;
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−  else
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−    varargout{1} = R;
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−    varargout{2} = n;
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−  end
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−  
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−
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−end