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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
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1 <!--
2 <p>
3 <ul>
4 <li><a href="#description">Description</a></li>
5 <li><a href="#call">Call</a></li>
6 <li><a href="#inputs">Inputs</a></li>
7 <li><a href="#outputs">Outputs</a></li>
8 <li><a href="#algorithm">Algorithm</a></li>
9 <li><a href="#parameters">Parameters</a></li>
10 </ul>
11 </p>
12 -->
13 <h2><a name="description">Description</a></h2>
14
15 <p>
16 whiten2D whitens cross-correlated time-series. Whitening filters are constructed
17 by a fitting procedure to the corss-spectrum models provided.
18 Note: The function assumes that the input model corresponds
19 to the one-sided csd of the data to be whitened.
20 </p>
21
22 <h2><a name="call">Call</a></h2>
23 <div class="fragment">
24 <pre>
25 b = whiten2D(a, pl)
26 [b1,b2] = whiten2D(a1, a2, pl)
27 [b1,b2,...,bn] = whiten2D(a1,a2,...,an, pl);
28 </pre>
29 </div>
30 <p>
31 <ul>
32 <li> Note1: input AOs must come in couples.
33 <li> Note2: this method cannot be used as a modifier, the
34 call <tt> a.whiten2D(pl) </tt> is forbidden.
35 </ul>
36 </p>
37
38
39 <h2><a name="inputs">Inputs</a></h2>
40
41 <p>
42 <ul>
43 <li> a is at least a couple of time series analysis objects
44 <li> pl is a parameter list, see the list of accepted parameters below
45 </ul>
46 </p>
47
48
49 <h2><a name="outputs">Outputs</a></h2>
50 <p>
51 <ul>
52 <li> b is at least a couple of "whitened" time-series AOs. The whitening
53 filters used are stored in the objects procinfo field as.
54 <ul>
55 <li> b(1): 'Filt11' and 'Filt12'
56 <li> b(2): 'Filt21' and 'Filt22'
57 </ul>
58 </ul>
59 </p>
60
61
62 <h2><a name="algorithm">Algorithm</a></h2>
63
64 <p>
65 <ol>
66 <li> Fit a set of partial fraction z-domain filters using
67 utils.math.psd2wf
68 <li> Convert to bank of mIIR filters
69 <li> Filter time-series in parallel
70 The filtering process is: <br/>
71 b(1) = Filt11(a(1)) + Filt12(a(2)) <br/>
72 b(2) = Filt21(a(1)) + Filt22(a(2))
73 </ol>
74 </p>
75
76
77
78 <h2><a name="parameters">Parameters</a></h2>
79
80 <p>
81 <ul>
82 <li> 'csd11' - a frequency-series AO describing the model csd11
83 <li> 'csd12' - a frequency-series AO describing the model csd12
84 <li> 'csd21' - a frequency-series AO describing the model csd21
85 <li> 'csd22' - a frequency-series AO describing the model csd22
86 <li> 'MaxIter' - Maximum number of iterations in fit routine
87 [default: 30]
88 <li> 'PoleType' - Choose the pole type for fitting:
89 <ul>
90 <li> 1 - use real starting poles.
91 <li> 2 - generates complex conjugate poles of the
92 type a.*exp(theta*pi*j)
93 with theta = linspace(0,pi,N/2+1).
94 <li> 3 - generates complex conjugate poles of the type
95 a.*exp(theta*pi*j)
96 with theta = linspace(0,pi,N/2+2) [default].
97 </ul>
98 </li>
99 <li> 'MinOrder' - Minimum order to fit with. [default: 2].
100 <li> 'MaxOrder' - Maximum order to fit with. [default: 25]
101 <li> 'Weights' - choose weighting for the fit: [default: 2]
102 <ul>
103 <li> 1 - equal weights for each point.
104 <li> 2 - weight with 1/abs(model).
105 <li> 3 - weight with 1/abs(model).^2.
106 <li> 4 - weight with inverse of the square mean spread of the model.
107 </ul>
108 </li>
109 <li> 'Plot' - plot results of each fitting step. [default: false]
110 <li> 'Disp' - Display the progress of the fitting iteration.
111 [default: false]
112 <li> 'FitTolerance' - Log Residuals difference check if the minimum
113 of the logarithmic difference between data and
114 residuals is larger than a specified value.
115 ie. if the conditioning value is 2, the
116 function ensures that the difference between
117 data and residuals is at lest 2 order of
118 magnitude lower than data itsleves. [default: 2].
119 <li> 'RMSEVar' - Root Mean Squared Error Variation - Check if the
120 variation of the RMS error is smaller than 10^(-b),
121 where b is the value given to the variable. This
122 option is useful for finding the minimum of Chi
123 squared. [default: 7].
124 <li> 'UseSym' - Use symbolic calculation in eigendecomposition. [default: 0]
125 <ul>
126 <li> 0 - perform double-precision calculation in the
127 eigendecomposition procedure to identify 2dim
128 systems and for poles stabilization
129 <li> 1 - uses symbolic math toolbox variable precision
130 arithmetic in the eigendecomposition for 2dim
131 system identification and double-precison for
132 poles stabilization
133 <li> 2 - uses symbolic math toolbox variable precision
134 arithmetic in the eigendecomposition for 2dim
135 system identification and for poles
136 stabilization
137 </ul>
138 </li>
139 </ul>
140 </p>
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