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annotate m-toolbox/classes/+utils/@math/overlapCorr.m @ 0:f0afece42f48

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Import.
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
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Daniele Nicolodi <nicolodi@science.unitn.it>
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1 % OVERLAPCORR Compute correlation introduced by segment overlapping
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Daniele Nicolodi <nicolodi@science.unitn.it>
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2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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3 % OVERLAPCORR Compute correlation introduced by segment overlapping in WOSA
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Daniele Nicolodi <nicolodi@science.unitn.it>
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4 % spectral estimations. It estimates the term contributing to the variance
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Daniele Nicolodi <nicolodi@science.unitn.it>
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5 % because of segment overlapping.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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6 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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7 % CALL
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8 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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9 % R = utils.math.overlapCorr(w,N,T)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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10 % [R,n] = utils.math.overlapCorr(w,N,T)
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11 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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12 % INPUT
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13 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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14 % - w, window samples, Nsx1 double, Ns must be the effective length of the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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15 % segments used for spectral estimation. E.g. For a periodogram Ns is equal
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Daniele Nicolodi <nicolodi@science.unitn.it>
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16 % to the length of the data series. For a WOSA estimation Ns is the length
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Daniele Nicolodi <nicolodi@science.unitn.it>
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17 % of each averaging segment.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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18 % - N total length of data series, 1x1 double
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Daniele Nicolodi <nicolodi@science.unitn.it>
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19 % - navs, number of averages, 1x1 double
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20 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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21 % REFERENCES
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Daniele Nicolodi <nicolodi@science.unitn.it>
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22 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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23 % D. B. Percival and A. T. Walden, Spectral Analysis for Physical
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Daniele Nicolodi <nicolodi@science.unitn.it>
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24 % Applications (Cambridge University Press, Cambridge, 1993) p 292.
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25 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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26 % L Ferraioli 09-03-2011
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27 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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28 % $Id: overlapCorr.m,v 1.1 2011/03/28 16:37:23 luigi Exp $
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29 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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30 function varargout = overlapCorr(w,N,navs)
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31
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32 Ns = numel(w);
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33 % willing to work with columns
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34 [nn,mm] = size(w);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 if nn<mm
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Daniele Nicolodi <nicolodi@science.unitn.it>
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36 w = w.';
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37 end
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38
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39 % make suaqre integrable
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Daniele Nicolodi <nicolodi@science.unitn.it>
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40 a = sqrt(sum(w.^2));
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41 w = w./a;
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42
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43 n = floor((N-Ns)/(navs-1));
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44 win = [w; zeros((navs-1)*n,1)];
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45
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46 R = 0;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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47 for kk=1:navs-1
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48 ew = zeros(size(win));
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49 ew(kk*n+1:kk*n+Ns) = win(1:Ns);
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50
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51 R = R + (navs-kk)*abs(win.'*ew)^2;
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52 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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53 R = R./navs^2;
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54
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Daniele Nicolodi <nicolodi@science.unitn.it>
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55 if nargout == 1
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56 varargout{1} = R;
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57 else
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58 varargout{1} = R;
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59 varargout{2} = n;
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60 end
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61
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62
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63 end