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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +0100
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1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
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2 "http://www.w3.org/TR/1999/REC-html401-19991224/loose.dtd">
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3
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4 <html lang="en">
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5 <head>
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6 <meta name="generator" content=
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7 "HTML Tidy for Mac OS X (vers 1st December 2004), see www.w3.org">
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8 <meta http-equiv="Content-Type" content=
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9 "text/html; charset=us-ascii">
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10
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11 <title>Using spectral windows (LTPDA Toolbox)</title>
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12 <link rel="stylesheet" href="docstyle.css" type="text/css">
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13 <meta name="generator" content="DocBook XSL Stylesheets V1.52.2">
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14 <meta name="description" content=
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15 "Presents an overview of the features, system requirements, and starting the toolbox.">
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16 </head>
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17
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18 <body>
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19 <a name="top_of_page" id="top_of_page"></a>
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20
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21 <p style="font-size:1px;">&nbsp;</p>
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22
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23 <table class="nav" summary="Navigation aid" border="0" width=
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24 "100%" cellpadding="0" cellspacing="0">
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25 <tr>
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26 <td valign="baseline"><b>LTPDA Toolbox</b></td><td><a href="../helptoc.html">contents</a></td>
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27
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28 <td valign="baseline" align="right"><a href=
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29 "specwin_description.html"><img src="b_prev.gif" border="0" align=
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30 "bottom" alt="What are LTPDA spectral windows?"></a>&nbsp;&nbsp;&nbsp;<a href=
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31 "sigproc_methods.html"><img src="b_next.gif" border="0" align=
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32 "bottom" alt="Spectral Estimation Methods"></a></td>
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33 </tr>
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34 </table>
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35
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36 <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Using spectral windows</h1>
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37 <hr>
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38
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39 <p>
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40 <p>
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41 Spectral windows are typically used in spectral analysis algorithms. In all LTPDA spectral analysis
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42 functions, spectral windows are specified as parameters in an input parameter list. The following
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43 example shows the use of <tt>ao/psd</tt> to estimate an Amplitude Spectral Density of
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44 the time-series captured in the input AO, <tt>a</tt>. The help for <a href="matlab:doc('ao/ao/psd')">ao/lpsd</a>
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45 reveals that the required parameter for setting the window function is <tt>'Win'</tt>.
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46 </p>
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47 <div class="fragment"><pre>
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48 <br> <span class="comment">% Parameters</span>
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49 nsecs = 1000;
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50 fs = 10;
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51
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52 <span class="comment">% Create input AOs</span>
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53 x1 = ao(plist( <span class="string">'waveform'</span>, <span class="string">'sine wave'</span>, <span class="string">'f'</span>,0.1, <span class="string">'A'</span>,1, <span class="string">'nsecs'</span>,nsecs, <span class="string">'fs'</span>,fs));
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54 x2 = ao(plist( <span class="string">'waveform'</span>, <span class="string">'noise'</span>, <span class="string">'type'</span>, <span class="string">'normal'</span>, <span class="string">'nsecs'</span>,nsecs, <span class="string">'fs'</span>,fs));
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55
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56 <span class="comment">% Add both</span>
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57 x = x1 + x2;
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58
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59 <span class="comment">% Compute psd with Blackman-Harris window</span>
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60 z = psd(x,plist(<span class="string">'win'</span>,<span class="string">'BH92'</span>));
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61
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62 <span class="comment">% Plot</span>
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63 iplot(z);
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64 </pre></div>
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65 <p>
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66 In this case, the size of the spectral window (number of samples) may not match the length
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67 of the segments in the spectral estimation. The <tt>psd</tt> algorithm then
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68 recomputes the window using the input design but for the correct length of window function.
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69 </p>
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70
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71 <img src="images/specwin_using1.png" >
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72
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73 <h2>Selecting the Peak Side-Lobe level (psll) with Kaiser's window</h2>
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74 <p>
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75 The <a href="specwin_description.html">table</a> in the previous section shows how each standard spectral window is defined by the
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76 Peak Side-Lobe level (<tt>psll</tt>). However, Kaiser's window allows the user to define the <tt>psll</tt> of the window.
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77 </p>
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78 <p>
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79 The following example shows the importance of selecting a suitable <tt>psll</tt> according to each application. The example creates
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80 1/f noise (in fact, noise generated
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81 by a pole-zero model with a pole at low frequencies) and computes the Amplitude Spectrum Density (ASD) with three different <tt>psll</tt>
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82 values. The ASD with the lowest value shows a bias at high frequencies compared with the response of the pzmodel used to generate
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83 the data (in black). This effect is due to the power added by the high order lobes of the window. The ASD with the highet value of the
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84 <tt>psll</tt> adds a feature at low frequencies because the main lobe of the window is too wide. Only the
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85 middle value gives an estimation of the ASD without adding window related features.
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86 </p>
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87
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88 <div class="fragment"><pre>
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89 <br> <span class="comment">% Parameters</span>
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90 nsecs = 10000;
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91 fs = 1;
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92
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93 <span class="comment">% Create pzmodel with a low frequency pole</span>
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94 pzm = pzmodel(1e5,[1e-7,0.1],[]);
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95
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96 <span class="comment">% Build (nearly) 1/f noise</span>
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97 x = ao(plist(<span class="string">'pzmodel'</span>,pzm, <span class="string">'nsecs'</span>,nsecs, <span class="string">'fs'</span>,fs));
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98
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99 <span class="comment">% Compute psd with Blackman-Harris window</span>
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100 z1 = psd(x,plist(<span class="string">'scale'</span>,<span class="string">'ASD'</span>,<span class="string">'win'</span>,<span class="string">'Kaiser'</span>,<span class="string">'psll'</span>,50));
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101 z1.setName(<span class="string">'psll = 50'</span>);
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102 z2 = psd(x,plist('scale',<span class="string">'ASD'</span>,<span class="string">'win'</span>,<span class="string">'Kaiser'</span>,<span class="string">'psll'</span>,100));
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103 z2.setName(<span class="string">'psll = 100'</span>);
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104 z3 = psd(x,plist(<span class="string">'scale'</span>,<span class="string">'ASD'</span>,<span class="string">'win'</span>,<span class="string">'Kaiser'</span>,<span class="string">'psll'</span>,1000));
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105 z3.setName(<span class="string">'psll = 1000'</span>);
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106
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107 <span class="comment">% Plot</span>
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108 r = resp(pzm,plist(<span class="string">'f1'</span>,1e-4,<span class="string">'f2'</span>,1));
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109 r.setName(<span class="string">'response'</span>)
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110 r.setPlotinfo(plist(<span class="string">'color'</span>,<span class="string">'k'</span>))
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111 iplot(z1,z2,z3,abs(r));
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112 </pre></div>
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113
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114 <img src="images/specwin_using2.png" >
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115
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116
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117
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118
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119 </p>
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120
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121 <br>
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122 <br>
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123 <table class="nav" summary="Navigation aid" border="0" width=
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124 "100%" cellpadding="0" cellspacing="0">
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125 <tr valign="top">
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126 <td align="left" width="20"><a href="specwin_description.html"><img src=
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127 "b_prev.gif" border="0" align="bottom" alt=
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128 "What are LTPDA spectral windows?"></a>&nbsp;</td>
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129
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130 <td align="left">What are LTPDA spectral windows?</td>
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131
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132 <td>&nbsp;</td>
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133
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134 <td align="right">Spectral Estimation Methods</td>
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135
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136 <td align="right" width="20"><a href=
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137 "sigproc_methods.html"><img src="b_next.gif" border="0" align=
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138 "bottom" alt="Spectral Estimation Methods"></a></td>
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139 </tr>
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140 </table><br>
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141
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142 <p class="copy">&copy;LTP Team</p>
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143 </body>
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144 </html>