Mercurial > hg > ltpda
diff m-toolbox/html_help/help/ug/cpsd_content.html @ 0:f0afece42f48
Import.
author | Daniele Nicolodi <nicolodi@science.unitn.it> |
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date | Wed, 23 Nov 2011 19:22:13 +0100 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/m-toolbox/html_help/help/ug/cpsd_content.html Wed Nov 23 19:22:13 2011 +0100 @@ -0,0 +1,83 @@ +<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>