+
−<p>
+
−  Spectral windows are typically used in spectral analysis algorithms. In all LTPDA spectral analysis 
+
−  functions, spectral windows are specified as parameters in an input parameter list. The following
+
−  example shows the use of <tt>ao/psd</tt> to estimate an Amplitude Spectral Density of
+
−  the time-series captured in the input AO, <tt>a</tt>. The help for <a href="matlab:doc('ao/ao/psd')">ao/lpsd</a>
+
−  reveals that the required parameter for setting the window function is <tt>'Win'</tt>.
+
−</p>	
+
−<div class="fragment"><pre>
+
−    <br>    <span class="comment">% Parameters</span> 
+
−    nsecs = 1000;
+
−    fs = 10;
+
−    
+
−    <span class="comment">% Create input AOs</span>
+
−    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));
+
−    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));
+
−       
+
−    <span class="comment">% Add both</span>
+
−    x = x1 + x2;
+
−    
+
−    <span class="comment">% Compute psd with Blackman-Harris window</span>
+
−    z = psd(x,plist(<span class="string">'win'</span>,<span class="string">'BH92'</span>));
+
−        
+
−    <span class="comment">% Plot</span>
+
−    iplot(z);
+
−</pre></div>
+
−<p>
+
−  In this case, the size of the spectral window (number of samples) may not match the length
+
−  of the segments in the spectral estimation. The <tt>psd</tt> algorithm then 
+
−  recomputes the window using the input design but for the correct length of window function.
+
−</p>
+
−
+
−<img src="images/specwin_using1.png" >
+
−
+
−<h2>Selecting the Peak Side-Lobe level (psll) with Kaiser's window</h2>
+
−<p>
+
−  The <a href="specwin_description.html">table</a> in the previous section shows how each standard spectral window is defined by the 
+
−  Peak Side-Lobe level (<tt>psll</tt>). However, Kaiser's window allows the user to define the <tt>psll</tt> of the window.
+
−</p> 
+
−<p>
+
−  The following example shows the importance of selecting a suitable <tt>psll</tt> according to each application. The example creates 
+
−  1/f noise (in fact, noise generated 
+
−  by a pole-zero model with a pole at low frequencies) and computes the Amplitude Spectrum Density (ASD) with three different <tt>psll</tt> 
+
−  values. The ASD with the lowest value shows a bias at high frequencies compared with the response of the pzmodel used to generate 
+
−  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
+
−  <tt>psll</tt> adds a feature at low frequencies because the main lobe of the window is too wide. Only the 
+
−  middle value gives an estimation of the ASD without adding window related features.   
+
−</p> 
+
−
+
−<div class="fragment"><pre>
+
−    <br>    <span class="comment">% Parameters</span>
+
−    nsecs = 10000;
+
−    fs = 1;
+
−    
+
−    <span class="comment">% Create pzmodel with a low frequency pole</span>
+
−    pzm = pzmodel(1e5,[1e-7,0.1],[]);
+
−    
+
−    <span class="comment">% Build (nearly) 1/f noise</span>
+
−    x = ao(plist(<span class="string">'pzmodel'</span>,pzm, <span class="string">'nsecs'</span>,nsecs, <span class="string">'fs'</span>,fs));
+
−    
+
−    <span class="comment">% Compute psd with Blackman-Harris window</span>
+
−    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));
+
−    z1.setName(<span class="string">'psll = 50'</span>);
+
−    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));
+
−    z2.setName(<span class="string">'psll = 100'</span>);
+
−    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));
+
−    z3.setName(<span class="string">'psll = 1000'</span>);
+
−    
+
−    <span class="comment">% Plot</span>
+
−    r = resp(pzm,plist(<span class="string">'f1'</span>,1e-4,<span class="string">'f2'</span>,1));
+
−    r.setName(<span class="string">'response'</span>)
+
−    r.setPlotinfo(plist(<span class="string">'color'</span>,<span class="string">'k'</span>))
+
−    iplot(z1,z2,z3,abs(r));
+
−</pre></div>
+
−
+
−<img src="images/specwin_using2.png" >
+
−
+
−
+
−