Mercurial > hg > ltpda
diff m-toolbox/html_help/help/ug/whiten2D_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/whiten2D_content.html Wed Nov 23 19:22:13 2011 +0100 @@ -0,0 +1,154 @@ +<!-- +<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> + + + + + + + + + + + + + +