diff m-toolbox/html_help/help/ug/whiten2D_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>
+  <ul>
+    <li><a href="#description">Description</a></li>
+    <li><a href="#call">Call</a></li>
+    <li><a href="#inputs">Inputs</a></li>
+    <li><a href="#outputs">Outputs</a></li>
+    <li><a href="#algorithm">Algorithm</a></li>
+    <li><a href="#parameters">Parameters</a></li>
+  </ul>
+</p>
+-->
+<h2><a name="description">Description</a></h2>
+
+<p>
+  whiten2D whitens cross-correlated time-series. Whitening filters are constructed
+  by a fitting procedure to the corss-spectrum models provided.
+  Note: The function assumes that the input model corresponds
+  to the one-sided csd of the data to be whitened.
+</p>
+
+<h2><a name="call">Call</a></h2>
+<div class="fragment">
+  <pre>
+    b = whiten2D(a, pl)
+    [b1,b2] = whiten2D(a1, a2, pl)
+    [b1,b2,...,bn] = whiten2D(a1,a2,...,an, pl);
+  </pre>
+</div>
+<p>
+  <ul>
+    <li> Note1: input AOs must come in couples. 
+    <li> Note2: this method cannot be used as a modifier, the
+    call <tt> a.whiten2D(pl) </tt> is forbidden.
+  </ul>
+</p>
+
+
+<h2><a name="inputs">Inputs</a></h2>
+
+<p>
+  <ul>
+    <li> a is at least a couple of time series analysis objects
+    <li> pl is a parameter list, see the list of accepted parameters below
+  </ul>
+</p>
+
+
+<h2><a name="outputs">Outputs</a></h2>
+<p>
+  <ul>
+    <li> b is at least a couple of "whitened" time-series AOs. The whitening
+    filters used are stored in the objects procinfo field as.
+    <ul>
+      <li> b(1): 'Filt11' and 'Filt12'
+      <li> b(2): 'Filt21' and 'Filt22'
+    </ul>
+  </ul>
+</p>
+
+
+<h2><a name="algorithm">Algorithm</a></h2>
+
+<p>
+  <ol>
+    <li> Fit a set of partial fraction z-domain filters using
+    utils.math.psd2wf
+    <li> Convert to bank of mIIR filters
+    <li> Filter time-series in parallel
+    The filtering process is: <br/>
+    b(1) = Filt11(a(1)) + Filt12(a(2)) <br/>
+    b(2) = Filt21(a(1)) + Filt22(a(2))
+  </ol>
+</p>
+
+
+
+<h2><a name="parameters">Parameters</a></h2>
+
+<p>
+  <ul>
+    <li> 'csd11' - a frequency-series AO describing the model csd11
+    <li> 'csd12' - a frequency-series AO describing the model csd12
+    <li> 'csd21' - a frequency-series AO describing the model csd21
+    <li> 'csd22' - a frequency-series AO describing the model csd22
+    <li> 'MaxIter' - Maximum number of iterations in fit routine
+    [default: 30]
+    <li> 'PoleType' - Choose the pole type for fitting:
+      <ul>
+        <li> 1 - use real starting poles.
+        <li> 2  - generates complex conjugate poles of the
+        type a.*exp(theta*pi*j)
+        with theta = linspace(0,pi,N/2+1).
+        <li> 3  - generates complex conjugate poles of the type
+        a.*exp(theta*pi*j)
+        with theta = linspace(0,pi,N/2+2) [default].
+      </ul>
+    </li>
+    <li> 'MinOrder' - Minimum order to fit with. [default: 2].
+    <li> 'MaxOrder' - Maximum order to fit with. [default: 25]
+    <li> 'Weights'  - choose weighting for the fit: [default: 2]
+      <ul>
+        <li> 1 - equal weights for each point.
+        <li> 2  - weight with 1/abs(model).
+        <li> 3  - weight with 1/abs(model).^2.
+        <li> 4  - weight with inverse of the square mean spread of the model.
+      </ul>
+    </li>
+    <li> 'Plot' - plot results of each fitting step. [default: false]
+    <li> 'Disp' - Display the progress of the fitting iteration.
+    [default: false]
+    <li> 'FitTolerance' - Log Residuals difference check if the minimum
+    of the logarithmic difference between data and
+    residuals is  larger than a specified value.
+    ie. if the conditioning value is 2, the
+    function ensures that the difference between
+    data and residuals is at lest 2 order of
+    magnitude lower than data itsleves. [default: 2].
+    <li> 'RMSEVar'  - Root Mean Squared Error Variation - Check if the
+    variation of the RMS error is smaller than 10^(-b),
+    where b is the value given to the variable. This
+    option is useful for finding the minimum of Chi
+    squared. [default: 7].
+    <li> 'UseSym'   - Use symbolic calculation in eigendecomposition. [default: 0]
+      <ul>
+        <li> 0 - perform double-precision calculation in the
+        eigendecomposition procedure to identify 2dim
+        systems and for poles stabilization
+        <li> 1 - uses symbolic math toolbox variable precision
+        arithmetic in the eigendecomposition for 2dim
+        system identification and double-precison for
+        poles stabilization
+        <li> 2 - uses symbolic math toolbox variable precision
+        arithmetic in the eigendecomposition for 2dim
+        system identification and for poles
+        stabilization
+      </ul>
+    </li>
+  </ul>
+</p>
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