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Fix. Default password should be [] not an empty string
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 07 Dec 2011 17:29:47 +0100
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Daniele Nicolodi <nicolodi@science.unitn.it>
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1 <p>
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2 Multivariate power spectral density is performed by the Welch's averaged, modified periodogram method.
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3 <tt>ao/cpsd</tt> estimates the cross-spectral density of time-series
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4 signals, included in the input <tt>ao</tt>s. Data are windowed prior to the estimation of the spectra, by multiplying
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5 it with a <a href="specwin.html">spectral window object</a>, and can be detrended by polinomial of time in order to reduce the impact
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6 of the border discontinuities. The window length is adjustable to shorter lenghts to reduce the spectral
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7 density uncertainties, and the percentage of subsequent window overlap can be adjusted as well.
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8 <br>
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9 <br>
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10 <b>Syntaxis</b>
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11 </p>
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12 <div class="fragment"><pre>
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13 b = cpsd(a1,a2,pl)
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14 </pre>
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15 </div>
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16 <p>
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17 <tt>a1</tt> and <tt>a2</tt> are the 2 <tt>ao</tt>s containing the input time series to be evaluated; <tt>b</tt> is the output object.
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18 The parameter list <tt>pl</tt> includes the following parameters:</p>
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19 <ul>
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20 <li> <tt>'Nfft'</tt> - number of samples in each fft [default: length of input data]
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21 A string value containing the variable 'fs' can
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22 also be used, e.g., plist('Nfft', '2*fs') </li>
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23 <li> <tt>'Win'</tt> - the window to be applied to the data to remove the
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24 discontinuities at edges of segments. [default: taken from user prefs]
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25 Only the design parameters of the window object are used. Enter either:
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26 <ul>
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27 <li>a specwin window object OR</li>
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28 <li>a string value containing the window name e.g., plist('Win', 'Kaiser', 'psll', 200)</li></ul>
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29 </li>
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30 <li> <tt>'Olap'</tt> - segment percent overlap [default: -1, (taken from window function)] </li>
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31 <li> <tt>'Order'</tt> - order of segment detrending <ul>
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32 <li> -1 - no detrending </li>
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33 <li> 0 - subtract mean [default] </li>
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34 <li> 1 - subtract linear fit </li>
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35 <li> N - subtract fit of polynomial, order N </li> </ul> </li>
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36 <li><tt>'Navs'</tt> - number of averages. If set, and if Nfft was set to 0 or -1, the number of points for each window will be calculated to match the request. [default: -1, not set] </li>
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37 </ul>
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38 <p>
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39 The length of the window is set by the value of the parameter <tt>'Nfft'</tt>, so that the window
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40 is actually rebuilt using only the key features of the window, i.e. the name and, for Keiser windows, the PSLL.
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41 </p>
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42 <p>As an alternative, the user can input, as a value for the <tt>'Win'</tt> key, a string corresponding to the name of the window. In the case of Kaiser window, it's necessary to specify the additional parameter <tt>'psll'</tt>.</p>
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43 <p>As an alternative to setting the number of points <tt>'Nfft'</tt> in each window, it's possible to ask for a given number of CPSD estimates by setting the <tt>'Navs'</tt> parameter, and the algorithm takes care of calculating the correct window length, according to the amount of overlap between subsequent segments.</p>
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44 <p>
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45 <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1">
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46 <tr width="90%">
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47 <td>
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48 If the user doesn't specify the value of a given parameter, the default value is used.
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49 </td>
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50 </tr>
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51 </table>
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52 </p>
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53
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54 <p>
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55 The function makes CPSD estimates between the 2 input <tt>ao</tt>s. The input argument
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56 list must contain 2 analysis objects, and the output will contain the CPSD estimate.
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57 If passing two identical objects <tt>ai</tt>, the output will be equivalent to the output of <tt>psd(ai)</tt>.
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58 </p>
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59 </pre> </div>
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60 </p>
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61 <p>
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62 <b>Example</b>
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63 </p>
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64 <p>
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65 Evaluation of the CPSD of two time-series represented by: a low frequency sinewave signal superimposed to
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66 white noise, and a low frequency sinewave signal at the same frequency, phase shifted and with different
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67 amplitude, superimposed to white noise.
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68 </p>
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69 <div class="fragment"><pre>
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70 nsecs = 1000;
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71 x = ao(plist(<span class="string">'waveform'</span>,<span class="string">'sine wave'</span>,<span class="string">'f'</span>,0.1,<span class="string">'A'</span>,1,<span class="string">'nsecs'</span>,nsecs,<span class="string">'fs'</span>,10)) + ...
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72 ao(plist(<span class="string">'waveform'</span>,<span class="string">'noise'</span>,<span class="string">'type'</span>,<span class="string">'normal'</span>,<span class="string">'nsecs'</span>,nsecs,<span class="string">'fs'</span>,10));
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73 x.setYunits(<span class="string">'m'</span>);
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74 y = ao(plist(<span class="string">'waveform'</span>,<span class="string">'sine wave'</span>,<span class="string">'f</span>',0.1,<span class="string">'A'</span>,2,<span class="string">'nsecs'</span>,nsecs,<span class="string">'fs'</span>,10,<span class="string">'phi'</span>,90)) + ...
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75 4*ao(plist(<span class="string">'waveform'</span>,<span class="string">'noise'</span>,<span class="string">'type'</span>,<span class="string">'normal'</span>,<span class="string">'nsecs'</span>,nsecs,<span class="string">'fs'</span>,10));
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76 y.setYunits(<span class="string">'V'</span>);
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77 z = cpsd(x,y,plist(<span class="string">'nfft'</span>,1000));
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78 iplot(z);
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79 </pre>
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80 </div>
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81
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82 <img src="images/cpsd_2.png" alt="" border="3">
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83 <br>