Mercurial > hg > ltpda

annotate m-toolbox/classes/@ao/welch.m @ 21:8be9deffe989 database-connection-manager

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Update ltpda_uo.update
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +0100
parents f0afece42f48
children
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0
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Daniele Nicolodi <nicolodi@science.unitn.it>
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1 % WELCH Welch spectral estimation method.
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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2 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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3 % [pxx, f, info] = welch(x,type,pl)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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4 % [pxx, f, info] = welch(x,y,type,pl)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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5 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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6 % INPUTS: x - input analysis objects
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Daniele Nicolodi <nicolodi@science.unitn.it>
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7 % y - input analysis objects
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Daniele Nicolodi <nicolodi@science.unitn.it>
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8 % type - type of spectrum:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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9 % 'psd' - compute Power Spectral Denstiy (PSD)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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10 % 'ms' - compute Mean-square (Power) Spectrum (MS)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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11 % 'cpsd' - compute cross-spectral density
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Daniele Nicolodi <nicolodi@science.unitn.it>
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12 % 'tfe' - estimate transfer function between inputs
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Daniele Nicolodi <nicolodi@science.unitn.it>
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13 % 'mscohere' - estimate magnitude-squared cross-coherence
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Daniele Nicolodi <nicolodi@science.unitn.it>
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14 % 'cohere' - estimate complex cross-coherence
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Daniele Nicolodi <nicolodi@science.unitn.it>
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15 % pl - input parameter list
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Daniele Nicolodi <nicolodi@science.unitn.it>
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16 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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17 % PARAMETERS: 'Win' - a specwin window object [default: Kaiser -200dB psll]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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18 % 'Olap' - segment percent overlap [default: taken from window function]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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19 % 'Nfft' - number of samples in each fft [default: length of input data]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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20 % 'Scale' - one of
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Daniele Nicolodi <nicolodi@science.unitn.it>
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21 % 'ASD' - amplitude spectral density
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Daniele Nicolodi <nicolodi@science.unitn.it>
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22 % 'PSD' - power spectral density [default]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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23 % 'AS' - amplitude spectrum
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Daniele Nicolodi <nicolodi@science.unitn.it>
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24 % 'PS' - power spectrum
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Daniele Nicolodi <nicolodi@science.unitn.it>
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25 % * applies only to spectrum 'Type' 'psd'
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Daniele Nicolodi <nicolodi@science.unitn.it>
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26 % 'Order' - order of segment detrending
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Daniele Nicolodi <nicolodi@science.unitn.it>
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27 % -1 - no detrending
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Daniele Nicolodi <nicolodi@science.unitn.it>
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28 % 0 - subtract mean [default]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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29 % 1 - subtract linear fit
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Daniele Nicolodi <nicolodi@science.unitn.it>
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30 % N - subtract fit of polynomial, order N
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Daniele Nicolodi <nicolodi@science.unitn.it>
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31 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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32 % Copied directly from MATLAB and extended to do segment-wise detrending,
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Daniele Nicolodi <nicolodi@science.unitn.it>
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33 % compute transfer function variance and to take a plist input
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Daniele Nicolodi <nicolodi@science.unitn.it>
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34 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 % M Hewitson 08-05-08
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Daniele Nicolodi <nicolodi@science.unitn.it>
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36 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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37 % $Id: welch.m,v 1.34 2011/03/14 16:06:05 mauro Exp $
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Daniele Nicolodi <nicolodi@science.unitn.it>
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38 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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39
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Daniele Nicolodi <nicolodi@science.unitn.it>
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40 % Author(s): P. Pacheco
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Daniele Nicolodi <nicolodi@science.unitn.it>
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41 % Copyright 1988-2006 The MathWorks, Inc.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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42 % $Revision: 1.34 $ $Date: 2011/03/14 16:06:05 $
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Daniele Nicolodi <nicolodi@science.unitn.it>
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43
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Daniele Nicolodi <nicolodi@science.unitn.it>
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44 % References:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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45 % [1] Petre Stoica and Randolph Moses, Introduction To Spectral
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Daniele Nicolodi <nicolodi@science.unitn.it>
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46 % Analysis, Prentice-Hall, 1997, pg. 15
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Daniele Nicolodi <nicolodi@science.unitn.it>
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47 % [2] Monson Hayes, Statistical Digital Signal Processing and
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Daniele Nicolodi <nicolodi@science.unitn.it>
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48 % Modeling, John Wiley & Sons, 1996.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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49 % [3] JS Bendat and AG Piersol, Engineering applications of correlation
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Daniele Nicolodi <nicolodi@science.unitn.it>
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50 % and spectral analysis, John Wiley & Sons, 1993.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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51
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Daniele Nicolodi <nicolodi@science.unitn.it>
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52
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Daniele Nicolodi <nicolodi@science.unitn.it>
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53 % Compute the periodogram power spectrum of each segment and average always
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Daniele Nicolodi <nicolodi@science.unitn.it>
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54 % compute the whole power spectrum, we force Fs = 1 to get a PS not a PSD.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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55
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Daniele Nicolodi <nicolodi@science.unitn.it>
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56 function varargout = welch(varargin)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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57
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Daniele Nicolodi <nicolodi@science.unitn.it>
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58 if nargin == 3
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Daniele Nicolodi <nicolodi@science.unitn.it>
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59 a = varargin{1};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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60 esttype = varargin{2};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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61 pl = varargin{3};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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62 x = a.data.y;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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63 inunits = a.data.yunits;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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64 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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65 a = varargin{1};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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66 b = varargin{2};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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67 esttype = varargin{3};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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68 pl = varargin{4};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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69 if a.data.fs ~= b.data.fs
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Daniele Nicolodi <nicolodi@science.unitn.it>
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70 error('### Two time-series have different sample rates.');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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71 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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72 inunits = b.data.yunits / a.data.yunits;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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73 x = {a.data.y, b.data.y};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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74 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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75
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Daniele Nicolodi <nicolodi@science.unitn.it>
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76 % Parse inputs
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Daniele Nicolodi <nicolodi@science.unitn.it>
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77 win = find(pl, 'Win');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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78 nfft = find(pl, 'Nfft');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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79 olap = find(pl, 'Olap')/100;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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80 scale = find(pl, 'scale');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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81 Xolap = round(olap*nfft);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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82 fs = a.data.fs;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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83 order = find(pl, 'order');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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84
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Daniele Nicolodi <nicolodi@science.unitn.it>
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85 [x,M,isreal_x,y,Ly,win,winName,winParam,noverlap,k,L,options] = ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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86 ao.welchparse(x,esttype,win.win, Xolap, nfft, fs);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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87
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Daniele Nicolodi <nicolodi@science.unitn.it>
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88 % Initialize
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Daniele Nicolodi <nicolodi@science.unitn.it>
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89 Sxx = zeros(options.nfft,1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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90
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Daniele Nicolodi <nicolodi@science.unitn.it>
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91 % Frequency vector was specified, return and plot two-sided PSD
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Daniele Nicolodi <nicolodi@science.unitn.it>
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92 freqVectorSpecified = false; nrow = 1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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93 if length(options.nfft) > 1,
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Daniele Nicolodi <nicolodi@science.unitn.it>
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94 freqVectorSpecified = true;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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95 [ncol,nrow] = size(options.nfft);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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96 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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97
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Daniele Nicolodi <nicolodi@science.unitn.it>
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98 % Compute the periodogram power spectrum of each segment and average always
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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99 % compute the whole power spectrum, we force Fs = 1 to get a PS not a PSD.
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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100
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Daniele Nicolodi <nicolodi@science.unitn.it>
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101 % Initialize
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Daniele Nicolodi <nicolodi@science.unitn.it>
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102 Mnxx = 0; Mn2xx = 0;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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103 if freqVectorSpecified,
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Daniele Nicolodi <nicolodi@science.unitn.it>
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104 Sxx = zeros(length(options.nfft),1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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105 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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106 Sxx = zeros(options.nfft,1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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107 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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108 range = options.range;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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109
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Daniele Nicolodi <nicolodi@science.unitn.it>
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110 LminusOverlap = L-noverlap;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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111 xStart = 1:LminusOverlap:k*LminusOverlap;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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112 xEnd = xStart+L-1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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113 switch lower(esttype)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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114 case {'ms','psd'}
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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115 for ii = 1:k,
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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116 if order < 0
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Daniele Nicolodi <nicolodi@science.unitn.it>
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117 seg = x(xStart(ii):xEnd(ii));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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118 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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119 [seg,coeffs] = ltpda_polyreg(x(xStart(ii):xEnd(ii)), order);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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120 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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121 [Sxxk,w] = ao.computeperiodogram(seg,win,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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122 options.nfft,esttype,options.Fs);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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123 % Welford's algorithm for updating mean and variance
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Daniele Nicolodi <nicolodi@science.unitn.it>
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124 if ii == 1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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125 Mnxx = Sxxk;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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126 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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127 Qxx = Sxxk - Mnxx;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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128 Mnxx = Mnxx + Qxx/ii;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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129 Mn2xx = Mn2xx + Qxx.*(Sxxk - Mnxx);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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130 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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131 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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132 Sxx = Mnxx;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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133 if k == 1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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134 Svxx = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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135 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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136 Svxx = Mn2xx/(k-1)/k;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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137 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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138 case 'cpsd'
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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139 for ii = 1:k,
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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140 if order < 0
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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141 xseg = x(xStart(ii):xEnd(ii));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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142 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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143 [xseg,coeffs] = ltpda_polyreg(x(xStart(ii):xEnd(ii)), order);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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144 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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145 if order < 0
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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146 yseg = y(xStart(ii):xEnd(ii));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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147 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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148 [yseg,coeffs] = ltpda_polyreg(y(xStart(ii):xEnd(ii)), order);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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149 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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150 [Sxxk,w] = ao.computeperiodogram({xseg,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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151 yseg},win,options.nfft,esttype,options.Fs);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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152 % Welford's algorithm to update mean and variance
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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153 Qxx = Sxxk - Mnxx;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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154 Mnxx = Mnxx +Qxx/ii;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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155 Mn2xx = Mn2xx + abs(Qxx.*conj(Sxxk - Mnxx));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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156 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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157 Sxx = Mnxx;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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158 if k ==1
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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159 Svxx = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
160 else
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
161 Svxx = Mn2xx/(k-1)/k;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
162 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
163 case 'tfe'
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
164 % compute transfer function
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
165 Sxy = zeros(options.nfft,1); % Initialize
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
166 Syy = zeros(options.nfft,1); % Initialize
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
167 for ii = 1:k,
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
168 if order < 0
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
169 xseg = x(xStart(ii):xEnd(ii));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
170 else
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
171 [xseg,coeffs] = ltpda_polyreg(x(xStart(ii):xEnd(ii)), order);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
172 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
173 if order < 0
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
174 yseg = y(xStart(ii):xEnd(ii));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
175 else
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
176 [yseg,coeffs] = ltpda_polyreg(y(xStart(ii):xEnd(ii)), order);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
177 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
178 [Sxxk,w] = ao.computeperiodogram(xseg,...
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
179 win,options.nfft,esttype,options.Fs);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
180 [Sxyk,w] = ao.computeperiodogram({yseg,...
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
181 xseg},win,options.nfft,esttype,options.Fs);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
182 [Syyk,w] = ao.computeperiodogram(yseg,...
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
183 win,options.nfft,esttype,options.Fs);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
184 Sxx = Sxx + Sxxk;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
185 Sxy = Sxy + Sxyk;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
186 Syy = Syy + Syyk;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
187 % don't need to be divided by k because only rations are used here
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
188 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
189 case {'mscohere','cohere'}
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
190 % Note: (Sxy1+Sxy2)/(Sxx1+Sxx2) ~= (Sxy1/Sxy2) + (Sxx1/Sxx2)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
191 % ie, we can't push the computation of Cxy into computeperiodogram.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
192 Sxy = zeros(options.nfft,1); % Initialize
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
193 Syy = zeros(options.nfft,1); % Initialize
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
194 for ii = 1:k,
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
195 if order < 0
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
196 xseg = x(xStart(ii):xEnd(ii));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
197 else
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
198 [xseg,coeffs] = ltpda_polyreg(x(xStart(ii):xEnd(ii)), order);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
199 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
200 if order < 0
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
201 yseg = y(xStart(ii):xEnd(ii));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
202 else
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
203 [yseg,coeffs] = ltpda_polyreg(y(xStart(ii):xEnd(ii)), order);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
204 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
205 [Sxxk,w] = ao.computeperiodogram(xseg,...
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
206 win,options.nfft,esttype,options.Fs);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
207 [Syyk,w] = ao.computeperiodogram(yseg,...
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
208 win,options.nfft,esttype,options.Fs);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
209 [Sxyk,w] = ao.computeperiodogram({xseg,...
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
210 yseg},win,options.nfft,esttype,options.Fs);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
211 Sxx = Sxx + Sxxk;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
212 Sxy = Sxy + Sxyk;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
213 Syy = Syy + Syyk;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
214 % don't need to be divided by k because only rations are used here
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
215 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
216 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
217 % Generate the freq vector directly in Hz to avoid roundoff errors due to
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
218 % conversions later.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
219 if ~freqVectorSpecified,
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
220 w = psdfreqvec('npts',options.nfft, 'Fs',options.Fs);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
221 else
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
222 if strcmpi(options.range,'onesided')
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
223 warning(generatemsgid('InconsistentRangeOption'),...
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
224 'Ignoring ''onesided'' option. When a frequency vector is specified, a ''twosided'' PSD is computed');
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
225 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
226 options.range = 'twosided';
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
227 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
228
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
229 switch lower(esttype)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
230 case {'psd','cpsd'}
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
231 % Compute the 1-sided or 2-sided PSD [Power/freq] or mean-square [Power].
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
232 % Also, corresponding freq vector and freq units.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
233 % Here we use our own 'computepsd' to scale correctly the variance
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
234 if k == 1
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
235 [Pxx,w,units] = computepsd(Sxx,w,options.range,options.nfft,options.Fs,esttype);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
236 P = Pxx;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
237 dP = [];
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
238 else
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
239 [Pxx,Pvxx,w,units] = utils.math.computepsd(Sxx,Svxx,w,options.range,options.nfft,options.Fs,esttype);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
240 P = Pxx;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
241 % the 1/k factor should come after welchscale if we don't want to apply sqrt() to it.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
242 % we correct for that here. It is only needed for 'asd','as' in
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
243 % psd/cpsd, the other cases go always through 'PSD'.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
244 if (strcmpi(scale,'PSD') || strcmpi(scale,'PS'))
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
245 dP = Pvxx;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
246 elseif (strcmpi(scale,'ASD') || strcmpi(scale,'AS'))
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
247 dP = Pvxx/k;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
248 else
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
249 error('### Unknown scale')
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
250 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
251 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
252 case 'tfe'
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
253 % Compute the 1-sided or 2-sided PSD [Power/freq] or mean-square [Power].
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
254 % Also, corresponding freq vector and freq units.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
255 % In the Cross PSD, the frequency vector and xunits are not used.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
256 [Pxx,w,units] = computepsd(Sxx,w,options.range,options.nfft,options.Fs,esttype);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
257 [Pxy,w,units] = computepsd(Sxy,w,options.range,options.nfft,options.Fs,esttype);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
258 [Pyy,w,units] = computepsd(Syy,w,options.range,options.nfft,options.Fs,esttype);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
259 % mean and std
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
260 P = Pxy ./ Pxx; % Txy
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
261 if k == 1
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
262 dP =[];
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
263 else
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
264 dP = (k/(k-1)^2)*(Pyy./Pxx).*(1 - (abs(Pxy).^2)./(Pxx.*Pyy));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
265 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
266 case 'mscohere'
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
267 % Magnitude Square Coherence estimate.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
268 % Auto PSD for 2nd input vector. The freq vector & xunits are not
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
269 % used.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
270 [Pxx,w,units] = computepsd(Sxx,w,options.range,options.nfft,options.Fs,esttype);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
271 [Pxy,w,units] = computepsd(Sxy,w,options.range,options.nfft,options.Fs,esttype);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
272 [Pyy,w,units] = computepsd(Syy,w,options.range,options.nfft,options.Fs,esttype);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
273 % mean and std
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
274 P = (abs(Pxy).^2)./(Pxx.*Pyy); % Magnitude-squared coherence
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
275 dP = (2*P/k).*(1-P).^2;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
276 case 'cohere'
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
277 % Complex Coherence estimate.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
278 % Auto PSD for 2nd input vector. The freq vector & xunits are not
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
279 % used.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
280 [Pxx,w,units] = computepsd(Sxx,w,options.range,options.nfft,options.Fs,esttype);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
281 [Pxy,w,units] = computepsd(Sxy,w,options.range,options.nfft,options.Fs,esttype);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
282 [Pyy,w,units] = computepsd(Syy,w,options.range,options.nfft,options.Fs,esttype);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
283 P = Pxy./sqrt(Pxx.*Pyy); % Complex coherence
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
284 dP = (2*abs(P)/k).*(1-abs(P)).^2;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
285 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
286 % end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
287
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
288 % Scale to required units
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
289 [P, dP, info] = ao.welchscale(P, dP, win, fs, scale, inunits);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
290 info.navs = k;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
291
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
292 if k ==1
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
293 dev = [];
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
294 else
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
295 dev = sqrt(dP);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
296 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
297
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
298 varargout = {P, w, info, dev};
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
299
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
300 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
301