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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 <p>
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2 Spectral windows are typically used in spectral analysis algorithms. In all LTPDA spectral analysis
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3 functions, spectral windows are specified as parameters in an input parameter list. The following
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4 example shows the use of <tt>ao/psd</tt> to estimate an Amplitude Spectral Density of
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5 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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6 reveals that the required parameter for setting the window function is <tt>'Win'</tt>.
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7 </p>
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8 <div class="fragment"><pre>
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9 <br> <span class="comment">% Parameters</span>
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10 nsecs = 1000;
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11 fs = 10;
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12
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13 <span class="comment">% Create input AOs</span>
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14 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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15 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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16
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17 <span class="comment">% Add both</span>
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18 x = x1 + x2;
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19
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20 <span class="comment">% Compute psd with Blackman-Harris window</span>
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21 z = psd(x,plist(<span class="string">'win'</span>,<span class="string">'BH92'</span>));
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22
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23 <span class="comment">% Plot</span>
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24 iplot(z);
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25 </pre></div>
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26 <p>
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27 In this case, the size of the spectral window (number of samples) may not match the length
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28 of the segments in the spectral estimation. The <tt>psd</tt> algorithm then
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29 recomputes the window using the input design but for the correct length of window function.
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30 </p>
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31
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32 <img src="images/specwin_using1.png" >
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33
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34 <h2>Selecting the Peak Side-Lobe level (psll) with Kaiser's window</h2>
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35 <p>
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36 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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Daniele Nicolodi <nicolodi@science.unitn.it>
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37 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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38 </p>
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39 <p>
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40 The following example shows the importance of selecting a suitable <tt>psll</tt> according to each application. The example creates
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41 1/f noise (in fact, noise generated
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42 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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43 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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44 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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45 <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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46 middle value gives an estimation of the ASD without adding window related features.
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47 </p>
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48
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49 <div class="fragment"><pre>
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50 <br> <span class="comment">% Parameters</span>
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51 nsecs = 10000;
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52 fs = 1;
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53
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54 <span class="comment">% Create pzmodel with a low frequency pole</span>
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55 pzm = pzmodel(1e5,[1e-7,0.1],[]);
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56
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57 <span class="comment">% Build (nearly) 1/f noise</span>
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58 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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59
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60 <span class="comment">% Compute psd with Blackman-Harris window</span>
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61 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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62 z1.setName(<span class="string">'psll = 50'</span>);
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63 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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64 z2.setName(<span class="string">'psll = 100'</span>);
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65 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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66 z3.setName(<span class="string">'psll = 1000'</span>);
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67
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68 <span class="comment">% Plot</span>
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69 r = resp(pzm,plist(<span class="string">'f1'</span>,1e-4,<span class="string">'f2'</span>,1));
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70 r.setName(<span class="string">'response'</span>)
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71 r.setPlotinfo(plist(<span class="string">'color'</span>,<span class="string">'k'</span>))
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72 iplot(z1,z2,z3,abs(r));
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73 </pre></div>
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74
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75 <img src="images/specwin_using2.png" >
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76
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