diff m-toolbox/html_help/help/ug/cpsd_content.html @ 0:f0afece42f48

Import.
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
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+<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>