line source
+ − <p>
+ − Multivariate power spectral density is performed by the Welch's averaged, modified periodogram method.
+ − <tt>ao/cpsd</tt> estimates the cross-spectral density of time-series
+ − signals, included in the input <tt>ao</tt>s. Data are windowed prior to the estimation of the spectra, by multiplying
+ − 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
+ − of the border discontinuities. The window length is adjustable to shorter lenghts to reduce the spectral
+ − density uncertainties, and the percentage of subsequent window overlap can be adjusted as well.
+ − <br>
+ − <br>
+ − <b>Syntaxis</b>
+ − </p>
+ − <div class="fragment"><pre>
+ − b = cpsd(a1,a2,pl)
+ − </pre>
+ − </div>
+ − <p>
+ − <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.
+ − The parameter list <tt>pl</tt> includes the following parameters:</p>
+ − <ul>
+ − <li> <tt>'Nfft'</tt> - number of samples in each fft [default: length of input data]
+ − A string value containing the variable 'fs' can
+ − also be used, e.g., plist('Nfft', '2*fs') </li>
+ − <li> <tt>'Win'</tt> - the window to be applied to the data to remove the
+ − discontinuities at edges of segments. [default: taken from user prefs]
+ − Only the design parameters of the window object are used. Enter either:
+ − <ul>
+ − <li>a specwin window object OR</li>
+ − <li>a string value containing the window name e.g., plist('Win', 'Kaiser', 'psll', 200)</li></ul>
+ − </li>
+ − <li> <tt>'Olap'</tt> - segment percent overlap [default: -1, (taken from window function)] </li>
+ − <li> <tt>'Order'</tt> - order of segment detrending <ul>
+ − <li> -1 - no detrending </li>
+ − <li> 0 - subtract mean [default] </li>
+ − <li> 1 - subtract linear fit </li>
+ − <li> N - subtract fit of polynomial, order N </li> </ul> </li>
+ − <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>
+ − </ul>
+ − <p>
+ − The length of the window is set by the value of the parameter <tt>'Nfft'</tt>, so that the window
+ − is actually rebuilt using only the key features of the window, i.e. the name and, for Keiser windows, the PSLL.
+ − </p>
+ − <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>
+ − <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>
+ − <p>
+ − <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1">
+ − <tr width="90%">
+ − <td>
+ − If the user doesn't specify the value of a given parameter, the default value is used.
+ − </td>
+ − </tr>
+ − </table>
+ − </p>
+ −
+ − <p>
+ − The function makes CPSD estimates between the 2 input <tt>ao</tt>s. The input argument
+ − list must contain 2 analysis objects, and the output will contain the CPSD estimate.
+ − If passing two identical objects <tt>ai</tt>, the output will be equivalent to the output of <tt>psd(ai)</tt>.
+ − </p>
+ − </pre> </div>
+ − </p>
+ − <p>
+ − <b>Example</b>
+ − </p>
+ − <p>
+ − Evaluation of the CPSD of two time-series represented by: a low frequency sinewave signal superimposed to
+ − white noise, and a low frequency sinewave signal at the same frequency, phase shifted and with different
+ − amplitude, superimposed to white noise.
+ − </p>
+ − <div class="fragment"><pre>
+ − nsecs = 1000;
+ − 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)) + ...
+ − 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));
+ − x.setYunits(<span class="string">'m'</span>);
+ − 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)) + ...
+ − 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));
+ − y.setYunits(<span class="string">'V'</span>);
+ − z = cpsd(x,y,plist(<span class="string">'nfft'</span>,1000));
+ − iplot(z);
+ − </pre>
+ − </div>
+ −
+ − <img src="images/cpsd_2.png" alt="" border="3">
+ − <br>