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<p id="example-plot-spectra-py"><strong>Python source code:</strong> <a class="reference download internal" href="../_downloads/plot_spectra.py"><tt class="xref download docutils literal"><span class="pre">plot_spectra.py</span></tt></a></p>
<div class="highlight-python"><div class="highlight"><pre><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<div class="newline"></div><span class="kn">from</span> <span class="nn">scipy</span> <span class="kn">import</span> <span class="n">fftpack</span>
<div class="newline"></div><span class="kn">from</span> <span class="nn">scipy</span> <span class="kn">import</span> <span class="n">signal</span>
<div class="newline"></div>
<div class="newline"></div><span class="kn">from</span> <span class="nn">dyna</span> <span class="kn">import</span> <span class="n">forced_pendulum</span>
<div class="newline"></div>
<div class="newline"></div><span class="n">omega</span> <span class="o">=</span> <span class="mf">2.</span><span class="o">/</span><span class="mi">3</span>
<div class="newline"></div>
<div class="newline"></div><span class="n">dt</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">/</span> <span class="n">omega</span> <span class="o">/</span> <span class="mi">25</span>
<div class="newline"></div>
<div class="newline"></div><span class="n">tf</span> <span class="o">=</span> <span class="mi">1000</span>
<div class="newline"></div>
<div class="newline"></div><span class="n">acc_factors</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mf">1.5</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
<div class="newline"></div><span class="n">acc_factors</span> <span class="o">=</span> <span class="n">acc_factors</span><span class="p">[[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">15</span><span class="p">,</span> <span class="mi">34</span><span class="p">]]</span>
<div class="newline"></div>
<div class="newline"></div><span class="n">all_theta_signals</span> <span class="o">=</span> <span class="p">[]</span>
<div class="newline"></div>
<div class="newline"></div><span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">acc</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">acc_factors</span><span class="p">):</span>
<div class="newline"></div> <span class="n">t</span><span class="p">,</span> <span class="n">theta</span><span class="p">,</span> <span class="n">theta_dot</span> <span class="o">=</span> <span class="n">forced_pendulum</span><span class="p">(</span><span class="n">tf</span><span class="p">,</span> <span class="n">dt</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">3</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span>
<div class="newline"></div> <span class="n">q</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">acc</span><span class="o">=</span><span class="n">acc</span><span class="p">,</span> <span class="n">omega</span><span class="o">=</span><span class="n">omega</span><span class="p">)</span>
<div class="newline"></div> <span class="n">all_theta_signals</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
<div class="newline"></div>
<div class="newline"></div><span class="n">all_theta_signals</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">all_theta_signals</span><span class="p">)</span>
<div class="newline"></div>
<div class="newline"></div><span class="n">mask</span> <span class="o">=</span> <span class="n">t</span> <span class="o">></span> <span class="mi">400</span>
<div class="newline"></div><span class="n">theta_signals</span> <span class="o">=</span> <span class="n">all_theta_signals</span><span class="p">[:,</span> <span class="n">mask</span><span class="p">]</span>
<div class="newline"></div><span class="n">theta_signals</span> <span class="o">-=</span> <span class="n">theta_signals</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)[:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">]</span>
<div class="newline"></div>
<div class="newline"></div><span class="n">theta_signals</span> <span class="o">/=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">((</span><span class="n">theta_signals</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">))[:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">]</span>
<div class="newline"></div>
<div class="newline"></div><span class="n">hann</span> <span class="o">=</span> <span class="n">signal</span><span class="o">.</span><span class="n">hanning</span><span class="p">(</span><span class="n">theta_signals</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
<div class="newline"></div><span class="n">theta_signals</span> <span class="o">*=</span> <span class="n">hann</span>
<div class="newline"></div>
<div class="newline"></div><span class="n">fft_sig</span> <span class="o">=</span> <span class="p">[]</span>
<div class="newline"></div><span class="k">for</span> <span class="n">sig</span> <span class="ow">in</span> <span class="n">theta_signals</span><span class="p">:</span>
<div class="newline"></div> <span class="n">fft_sig</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">fftpack</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">sig</span><span class="p">))</span>
<div class="newline"></div>
<div class="newline"></div><span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<div class="newline"></div><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">all_theta_signals</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s">u'$A=1$'</span><span class="p">)</span>
<div class="newline"></div><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">all_theta_signals</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s">u'$A=1.08$'</span><span class="p">)</span>
<div class="newline"></div><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">all_theta_signals</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s">u'$A=1.17$'</span><span class="p">)</span>
<div class="newline"></div><span class="n">plt</span><span class="o">.</span><span class="n">xlim</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">550</span><span class="p">)</span>
<div class="newline"></div><span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">(</span><span class="o">-</span><span class="mi">22</span><span class="p">,</span> <span class="mi">22</span><span class="p">)</span>
<div class="newline"></div><span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
<div class="newline"></div><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s">u'$t$'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">24</span><span class="p">)</span>
<div class="newline"></div><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s">u'$</span><span class="se">\\</span><span class="s">theta$'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">24</span><span class="p">)</span>
<div class="newline"></div><span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">()</span>
<div class="newline"></div><span class="n">plt</span><span class="o">.</span><span class="n">gca</span><span class="p">()</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="s">'both'</span><span class="p">,</span> <span class="n">which</span><span class="o">=</span><span class="s">'major'</span><span class="p">,</span> <span class="n">labelsize</span><span class="o">=</span><span class="mi">18</span><span class="p">)</span>
<div class="newline"></div>
<div class="newline"></div><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
<div class="newline"></div>
<div class="newline"></div><span class="n">plt</span><span class="o">.</span><span class="n">axes</span><span class="p">([</span><span class="mf">0.63</span><span class="p">,</span> <span class="mf">0.65</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">,</span> <span class="mf">0.28</span><span class="p">])</span>
<div class="newline"></div><span class="n">mask</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">logical_and</span><span class="p">(</span><span class="n">t</span> <span class="o">></span> <span class="mi">400</span><span class="p">,</span> <span class="n">t</span> <span class="o"><</span> <span class="mi">430</span><span class="p">)</span>
<div class="newline"></div><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">[</span><span class="n">mask</span><span class="p">],</span> <span class="n">all_theta_signals</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">mask</span><span class="p">],</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s">u'$A=1$'</span><span class="p">)</span>
<div class="newline"></div><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">[</span><span class="n">mask</span><span class="p">],</span> <span class="n">all_theta_signals</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="n">mask</span><span class="p">],</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s">u'$A=1.08$'</span><span class="p">)</span>
<div class="newline"></div><span class="n">plt</span><span class="o">.</span><span class="n">xticks</span><span class="p">([])</span>
<div class="newline"></div><span class="n">plt</span><span class="o">.</span><span class="n">yticks</span><span class="p">([])</span>
<div class="newline"></div>
<div class="newline"></div>
<div class="newline"></div><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<div class="newline"></div></pre></div>
</div>
<img alt="../_images/plot_spectra_1.png" class="align-center" src="../_images/plot_spectra_1.png" />
<p><strong>Total running time of the example:</strong> 0.00 seconds</p>
<p><div style="clear: both"></div></p>
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