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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 <li><a href="#example">Example</a></li>
11 </ul>
12 </p>
13
14 <h2><a name="description">Description</a></h2>
15
16 <p>
17 noisegen1D is a coloring tool allowing the generation of colored noise from withe noise with a given spectrum.
18 The function constructs a coloring filter through a fitting procedure to the model provided.
19 If no model is provided an error is prompted. The colored noise provided has one-sided psd
20 corresponding to the input model.
21 </p>
22
23 <h2><a name="call">Call</a></h2>
24 <div class="fragment">
25 <pre>
26 b = noisegen1D(a, pl);
27 [b1,b2,...,bn] = noisegen1D(a1,a2,...,an, pl);
28 </pre>
29 </div>
30
31 <h2><a name="inputs">Inputs</a></h2>
32
33 <p>
34 <ul>
35 <li> a - is a tsdata analysis object or a vector of tsdata analysis objects
36 <li> pl - is a plist with the input parameters. See the list of function parameters below
37 </ul>
38 </p>
39
40 <h2><a name="outputs">Outputs</a></h2>
41
42 <p>
43 <ul>
44 <li> b - Colored time-series AOs. The coloring filters used
45 are stored in the objects procinfo field under the
46 parameter 'Filt'.
47 </ul>
48 </p>
49
50 <h2><a name="algorithm">Algorithm</a></h2>
51
52 <p>
53 <ol>
54 <li> Fit a set of partial fraction z-domain filters using utils.math.psd2tf.
55 <li> Convert to array of MIIR filters.
56 <li> Filter time-series in parallel.
57 </ol>
58 </p>
59
60 <h2><a name="parameters">Parameters</a></h2>
61 <p>
62 <ul>
63 <li> 'Model' - a frequency-series AO describing the model psd.
64 <li> 'MaxIter' - Maximum number of iterations in fit routine
65 [default: 30]
66 <li> 'PoleType' - Choose the pole type for fitting:
67 <ul>
68 <li> 1 - use real starting poles.
69 <li> 2 - generates complex conjugate poles of the
70 type a.*exp(theta*pi*j)
71 with theta = linspace(0,pi,N/2+1).
72 <li> 3 - generates complex conjugate poles of the type
73 a.*exp(theta*pi*j)
74 with theta = linspace(0,pi,N/2+2) [default].
75 </ul>
76 </li>
77 <li> 'MinOrder' - Minimum order to fit with. [default: 2].
78 <li> 'MaxOrder' - Maximum order to fit with. [default: 25]
79 <li> 'Weights' - choose weighting for the fit: [default: 2]
80 <ul>
81 <li> 1 - equal weights for each point.
82 <li> 2 - weight with 1/abs(model).
83 <li> 3 - weight with 1/abs(model).^2.
84 <li> 4 - weight with inverse of the square mean spread of the model.
85 </ul>
86 </li>
87 <li> 'Plot' - plot results of each fitting step. [default: false]
88 <li> 'Disp' - Display the progress of the fitting iteration.
89 [default: false]
90 <li> 'FitTolerance' - Log Residuals difference - Check if the minimum
91 of the logarithmic difference between data and
92 residuals is larger than a specified value.
93 ie. if the conditioning value is 2, the
94 function ensures that the difference between
95 data and residuals is at lest 2 order of
96 magnitude lower than data itsleves. [Default: 2].
97 <li> 'RMSEVar' - Root Mean Squared Error Variation - Check if the
98 variation of the RMS error is smaller than 10^(-b),
99 where b is the value given to the variable. This
100 option is useful for finding the minimum of Chi
101 squared. [default: 7].
102 </ul>
103 </p>
104
105 <h2><a name="example">Example</a></h2>
106
107 <div class="fragment">
108 <pre>
109 %% Noise generation from fsdata model object %%%%%%%%%%%%%%%%%%%%%%%%%%%
110
111 % Description:
112 % 1) Generate a fsdata object to be used as psd model
113 % 2) Generate a random series of data (white)
114 % 3) Generate colored noise with noisegen1D
115 % 4) calculated psd of generated data
116 % 5) check result by plotting
117
118 % 1)
119 fs = 10; % sampling frequency
120 pl_mod1 = plist('fsfcn', '0.01./(0.01+f)', 'f1', 1e-6, 'f2', 5, 'nf', 100);
121 mod1 = ao(pl_mod1); % fsdata model object
122
123 % 2)
124 % generating white noise
125 a1 = ao(plist('tsfcn', 'randn(size(t))', 'fs', fs, 'nsecs', 1000));
126
127 % 3) Noise generation
128
129 pl1 = plist(...
130 'model', mod1, ...
131 'MaxIter', 30, ...
132 'PoleType', 2, ...
133 'MinOrder', 10, ...
134 'MaxOrder', 20, ...
135 'Weights', 2, ...
136 'Plot', false,...
137 'Disp', false,...
138 'RMSEVar', 5,...
139 'FitTolerance', 2);
140
141 ac1 = noisegen1D(a1, pl1);
142
143 % 4)
144 acxx1 = ac1.psd;
145 % 5)
146 iplot(acxx1, mod1);
147 </pre>
148 </div>
149
150 <p>
151 <div align="center">
152 <IMG src="images/ng1D_1.png" width="800" height="600" align="center" border="0">
153 </div>
154 </p>
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