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<p id="example-plot-fft-py"><strong>Python source code:</strong> <a class="reference download internal" href="../_downloads/plot_fft.py"><tt class="xref download docutils literal"><span class="pre">plot_fft.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">100</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="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mf">1.07</span><span class="p">]</span>
<div class="newline"></div>
<div class="newline"></div>
<div class="newline"></div><span class="n">t</span><span class="p">,</span> <span class="n">theta_0</span><span class="p">,</span> <span class="n">theta_dot_0</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_factors</span><span class="p">[</span><span class="mi">0</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>
<div class="newline"></div><span class="n">t</span><span class="p">,</span> <span class="n">theta_1</span><span class="p">,</span> <span class="n">theta_dot_1</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_factors</span><span class="p">[</span><span class="mi">1</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>
<div class="newline"></div><span class="n">time_mask</span> <span class="o">=</span> <span class="n">t</span> <span class="o">></span> <span class="mi">400</span>
<div class="newline"></div>
<div class="newline"></div><span class="n">theta_0</span> <span class="o">=</span> <span class="n">theta_0</span><span class="p">[</span><span class="n">time_mask</span><span class="p">]</span>
<div class="newline"></div><span class="n">theta_1</span> <span class="o">=</span> <span class="n">theta_1</span><span class="p">[</span><span class="n">time_mask</span><span class="p">]</span>
<div class="newline"></div>
<div class="newline"></div><span class="n">theta_0</span> <span class="o">-=</span> <span class="n">theta_0</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span>
<div class="newline"></div><span class="n">theta_1</span> <span class="o">-=</span> <span class="n">theta_1</span><span class="o">.</span><span class="n">mean</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="nb">len</span><span class="p">(</span><span class="n">theta_0</span><span class="p">))</span>
<div class="newline"></div><span class="n">theta_0</span> <span class="o">*=</span> <span class="n">hann</span>
<div class="newline"></div><span class="n">theta_1</span> <span class="o">*=</span> <span class="n">hann</span>
<div class="newline"></div>
<div class="newline"></div><span class="n">fft_theta_0</span> <span class="o">=</span> <span class="n">fftpack</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">theta_0</span><span class="p">)</span>
<div class="newline"></div><span class="n">freq</span> <span class="o">=</span> <span class="n">fftpack</span><span class="o">.</span><span class="n">fftfreq</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">theta_0</span><span class="p">),</span> <span class="n">dt</span><span class="p">)</span>
<div class="newline"></div>
<div class="newline"></div><span class="n">fft_theta_1</span> <span class="o">=</span> <span class="n">fftpack</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">theta_1</span><span class="p">)</span>
<div class="newline"></div>
<div class="newline"></div><span class="n">f_driving</span> <span class="o">=</span> <span class="mf">2.</span><span class="o">/</span> <span class="mi">3</span> <span class="o">*</span> <span class="mf">1.</span><span class="o">/</span> <span class="p">(</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="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>
<div class="newline"></div><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">211</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">freq</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">fft_theta_0</span><span class="p">),</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<div class="newline"></div><span class="n">plt</span><span class="o">.</span><span class="n">axvline</span><span class="p">(</span><span class="n">f_driving</span><span class="p">,</span> <span class="n">ls</span><span class="o">=</span><span class="s">'--'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">'k'</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</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="o">-</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</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="mi">0</span><span class="p">,</span> <span class="mi">5000</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'$\hat{</span><span class="se">\\</span><span class="s">theta}$'</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">subplot</span><span class="p">(</span><span class="mi">212</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">freq</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">fft_theta_1</span><span class="p">),</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<div class="newline"></div><span class="n">plt</span><span class="o">.</span><span class="n">axvline</span><span class="p">(</span><span class="n">f_driving</span> <span class="o">/</span> <span class="mi">2</span><span class="p">,</span> <span class="n">ls</span><span class="o">=</span><span class="s">'--'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">'k'</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</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="o">-</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</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="mi">0</span><span class="p">,</span> <span class="mi">5000</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'$f$ (Hz)'</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'$\hat{</span><span class="se">\\</span><span class="s">theta}$'</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>
<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">show</span><span class="p">()</span>
<div class="newline"></div></pre></div>
</div>
<img alt="../_images/plot_fft_1.png" class="align-center" src="../_images/plot_fft_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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