Mercurial > hg > ltpda

annotate m-toolbox/html_help/help/ug/whiten2D_content.html @ 4:e3c5468b1bfe database-connection-manager

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Integrate with LTPDAPreferences
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +0100
parents f0afece42f48
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
0
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
1 <!--
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
2 <p>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
3 <ul>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
4 <li><a href="#description">Description</a></li>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
5 <li><a href="#call">Call</a></li>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
6 <li><a href="#inputs">Inputs</a></li>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
7 <li><a href="#outputs">Outputs</a></li>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
8 <li><a href="#algorithm">Algorithm</a></li>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
9 <li><a href="#parameters">Parameters</a></li>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
10 </ul>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
11 </p>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
12 -->
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
13 <h2><a name="description">Description</a></h2>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
14
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
15 <p>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
16 whiten2D whitens cross-correlated time-series. Whitening filters are constructed
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
17 by a fitting procedure to the corss-spectrum models provided.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
18 Note: The function assumes that the input model corresponds
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
19 to the one-sided csd of the data to be whitened.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
20 </p>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
21
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
22 <h2><a name="call">Call</a></h2>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
23 <div class="fragment">
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
24 <pre>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
25 b = whiten2D(a, pl)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
26 [b1,b2] = whiten2D(a1, a2, pl)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
27 [b1,b2,...,bn] = whiten2D(a1,a2,...,an, pl);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
28 </pre>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
29 </div>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
30 <p>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
31 <ul>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
32 <li> Note1: input AOs must come in couples.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
33 <li> Note2: this method cannot be used as a modifier, the
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
34 call <tt> a.whiten2D(pl) </tt> is forbidden.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
35 </ul>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
36 </p>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
37
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
38
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
39 <h2><a name="inputs">Inputs</a></h2>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
40
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
41 <p>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
42 <ul>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
43 <li> a is at least a couple of time series analysis objects
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
44 <li> pl is a parameter list, see the list of accepted parameters below
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
45 </ul>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
46 </p>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
47
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
48
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
49 <h2><a name="outputs">Outputs</a></h2>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
50 <p>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
51 <ul>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
52 <li> b is at least a couple of "whitened" time-series AOs. The whitening
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
53 filters used are stored in the objects procinfo field as.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
54 <ul>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
55 <li> b(1): 'Filt11' and 'Filt12'
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
56 <li> b(2): 'Filt21' and 'Filt22'
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
57 </ul>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
58 </ul>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
59 </p>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
60
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
61
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
62 <h2><a name="algorithm">Algorithm</a></h2>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
63
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
64 <p>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
65 <ol>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
66 <li> Fit a set of partial fraction z-domain filters using
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
67 utils.math.psd2wf
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
68 <li> Convert to bank of mIIR filters
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
69 <li> Filter time-series in parallel
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
70 The filtering process is: <br/>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
71 b(1) = Filt11(a(1)) + Filt12(a(2)) <br/>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
72 b(2) = Filt21(a(1)) + Filt22(a(2))
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
73 </ol>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
74 </p>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
75
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
76
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
77
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
78 <h2><a name="parameters">Parameters</a></h2>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
79
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
80 <p>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
81 <ul>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
82 <li> 'csd11' - a frequency-series AO describing the model csd11
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
83 <li> 'csd12' - a frequency-series AO describing the model csd12
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
84 <li> 'csd21' - a frequency-series AO describing the model csd21
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
85 <li> 'csd22' - a frequency-series AO describing the model csd22
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
86 <li> 'MaxIter' - Maximum number of iterations in fit routine
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
87 [default: 30]
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
88 <li> 'PoleType' - Choose the pole type for fitting:
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
89 <ul>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
90 <li> 1 - use real starting poles.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
91 <li> 2 - generates complex conjugate poles of the
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
92 type a.*exp(theta*pi*j)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
93 with theta = linspace(0,pi,N/2+1).
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
94 <li> 3 - generates complex conjugate poles of the type
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
95 a.*exp(theta*pi*j)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
96 with theta = linspace(0,pi,N/2+2) [default].
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
97 </ul>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
98 </li>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
99 <li> 'MinOrder' - Minimum order to fit with. [default: 2].
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
100 <li> 'MaxOrder' - Maximum order to fit with. [default: 25]
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
101 <li> 'Weights' - choose weighting for the fit: [default: 2]
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
102 <ul>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
103 <li> 1 - equal weights for each point.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
104 <li> 2 - weight with 1/abs(model).
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
105 <li> 3 - weight with 1/abs(model).^2.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
106 <li> 4 - weight with inverse of the square mean spread of the model.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
107 </ul>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
108 </li>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
109 <li> 'Plot' - plot results of each fitting step. [default: false]
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
110 <li> 'Disp' - Display the progress of the fitting iteration.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
111 [default: false]
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
112 <li> 'FitTolerance' - Log Residuals difference check if the minimum
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
113 of the logarithmic difference between data and
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
114 residuals is larger than a specified value.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
115 ie. if the conditioning value is 2, the
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
116 function ensures that the difference between
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
117 data and residuals is at lest 2 order of
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
118 magnitude lower than data itsleves. [default: 2].
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
119 <li> 'RMSEVar' - Root Mean Squared Error Variation - Check if the
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
120 variation of the RMS error is smaller than 10^(-b),
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
121 where b is the value given to the variable. This
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
122 option is useful for finding the minimum of Chi
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
123 squared. [default: 7].
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
124 <li> 'UseSym' - Use symbolic calculation in eigendecomposition. [default: 0]
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
125 <ul>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
126 <li> 0 - perform double-precision calculation in the
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
127 eigendecomposition procedure to identify 2dim
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
128 systems and for poles stabilization
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
129 <li> 1 - uses symbolic math toolbox variable precision
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
130 arithmetic in the eigendecomposition for 2dim
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
131 system identification and double-precison for
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
132 poles stabilization
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
133 <li> 2 - uses symbolic math toolbox variable precision
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
134 arithmetic in the eigendecomposition for 2dim
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
135 system identification and for poles
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
136 stabilization
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
137 </ul>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
138 </li>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
139 </ul>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
140 </p>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
141
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
142
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
143
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
144
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
145
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
146
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
147
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
148
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
149
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
150
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
151
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
152
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
153
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
154