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Import.
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
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1
2
3 <p>
4 <ul>
5 <li><a href="#description">Description</a></li>
6 <li><a href="#call">Call</a></li>
7 <li><a href="#inputs">Inputs</a></li>
8 <li><a href="#outputs">Outputs</a></li>
9 <li><a href="#algorithm">Algorithm</a></li>
10 <li><a href="#parameters">Parameters</a></li>
11 </ul>
12 </p>
13
14 <h2><a name="description">Description</a></h2>
15
16 <p>
17 noisegen2D generates colored noise from withe noise with a
18 given cross spectrum. The coloring filter is constructed by a fitting procedure to the
19 models provided. If no model is provided an error is
20 prompted. The cross-spectral matrix is assumed to be
21 frequency by frequency of the type:
22 </p>
23 <div class="fragment"><pre>
24
25 / csd11(f) csd12(f) \
26 CSD(f) = | |
27 \ csd21(f) csd22(f) /
28
29 </pre></div>
30 <p>
31 Note: The function output colored noise data with one-sided
32 cross spectral density corresponding to the model provided.
33 </p>
34
35 <h2><a name="call">Call</a></h2>
36 <div class="fragment">
37 <pre>
38 b = noisegen2D(a, pl)
39 [b1,b2] = noisegen2D(a1, a2, pl)
40 [b1,b2,...,bn] = noisegen2D(a1,a2,...,an, pl);
41 </pre>
42 </div>
43 <p>
44 <ul>
45 <li> Note1: input AOs must come in couples.
46 <li> Note2: this method cannot be used as a modifier, the
47 call <tt> a.noisegen2D(pl) </tt> is forbidden.
48 </ul>
49 </p>
50
51
52 <h2><a name="inputs">Inputs</a></h2>
53
54 <p>
55 <ul>
56 <li> a is at least a couple of time series analysis objects
57 <li> pl is a parameter list, see the list of accepted parameters below
58 </ul>
59 </p>
60
61
62 <h2><a name="outputs">Outputs</a></h2>
63 <p>
64 <ul>
65 <li> b are a couple of colored time-series AOs. The coloring
66 filters used are stored in the objects procinfo field under
67 the parameters:
68 <ul>
69 <li> b(1): 'Filt11' and 'Filt12'
70 <li> b(2): 'Filt21' and 'Filt22'
71 </ul>
72 </ul>
73 </p>
74
75
76 <h2><a name="algorithm">Algorithm</a></h2>
77
78 <p>
79 <ol>
80 <li> Fit a set of partial fraction z-domain filters using
81 utils.math.psd2tf
82 <li> Convert to bank of mIIR filters
83 <li> Filter time-series in parallel
84 The filtering process is: <br/>
85 b(1) = Filt11(a(1)) + Filt12(a(2)) <br/>
86 b(2) = Filt21(a(1)) + Filt22(a(2))
87 </ol>
88 </p>
89
90
91
92 <h2><a name="parameters">Parameters</a></h2>
93
94 <p>
95 <ul>
96 <li> 'csd11' - a frequency-series AO describing the model csd11
97 <li> 'csd12' - a frequency-series AO describing the model csd12
98 <li> 'csd21' - a frequency-series AO describing the model csd21
99 <li> 'csd22' - a frequency-series AO describing the model csd22
100 <li> 'MaxIter' - Maximum number of iterations in fit routine
101 [default: 30]
102 <li> 'PoleType' - Choose the pole type for fitting:
103 <ul>
104 <li> 1 - use real starting poles.
105 <li> 2 - generates complex conjugate poles of the
106 type a.*exp(theta*pi*j)
107 with theta = linspace(0,pi,N/2+1).
108 <li> 3 - generates complex conjugate poles of the type
109 a.*exp(theta*pi*j)
110 with theta = linspace(0,pi,N/2+2) [default].
111 </ul>
112 </li>
113 <li> 'MinOrder' - Minimum order to fit with. [default: 2].
114 <li> 'MaxOrder' - Maximum order to fit with. [default: 25]
115 <li> 'Weights' - choose weighting for the fit: [default: 2]
116 <ul>
117 <li> 1 - equal weights for each point.
118 <li> 2 - weight with 1/abs(model).
119 <li> 3 - weight with 1/abs(model).^2.
120 <li> 4 - weight with inverse of the square mean spread of the model.
121 </ul>
122 </li>
123 <li> 'Plot' - plot results of each fitting step. [default: false]
124 <li> 'Disp' - Display the progress of the fitting iteration.
125 [default: false]
126 <li> 'FitTolerance' - Log Residuals difference check if the minimum
127 of the logarithmic difference between data and
128 residuals is larger than a specified value.
129 ie. if the conditioning value is 2, the
130 function ensures that the difference between
131 data and residuals is at lest 2 order of
132 magnitude lower than data itsleves. [default: 2].
133 <li> 'RMSEVar' - Root Mean Squared Error Variation - Check if the
134 variation of the RMS error is smaller than 10^(-b),
135 where b is the value given to the variable. This
136 option is useful for finding the minimum of Chi
137 squared. [default: 7].
138 <li> 'UseSym' - Use symbolic calculation in eigendecomposition. [default: 0]
139 <ul>
140 <li> 0 - perform double-precision calculation in the
141 eigendecomposition procedure to identify 2dim
142 systems and for poles stabilization
143 <li> 1 - uses symbolic math toolbox variable precision
144 arithmetic in the eigendecomposition for 2dim
145 system identification and double-precison for
146 poles stabilization
147 <li> 2 - uses symbolic math toolbox variable precision
148 arithmetic in the eigendecomposition for 2dim
149 system identification and for poles
150 stabilization
151 </ul>
152 </li>
153 </ul>
154 </p>