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<p id="example-cascade-py"><strong>Python source code:</strong> <a class="reference download internal" href="../_downloads/cascade.py"><tt class="xref download docutils literal"><span class="pre">cascade.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>
<div class="newline"></div><span class="n">fft_sig</span> <span class="o">=</span> <span class="p">[]</span>
<div class="newline"></div>
<div class="newline"></div><span class="n">t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">tf</span><span class="p">,</span> <span class="n">dt</span><span class="p">)</span>
<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">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">mask</span><span class="o">.</span><span class="n">sum</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="k">print</span> <span class="n">i</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">theta</span> <span class="o">=</span> <span class="n">theta</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
<div class="newline"></div> <span class="n">theta</span> <span class="o">-=</span> <span class="n">theta</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span>
<div class="newline"></div> <span class="n">theta</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</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>
<div class="newline"></div> <span class="n">theta</span> <span class="o">*=</span> <span class="n">hann</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">theta</span><span class="p">))</span>
<div class="newline"></div>
<div class="newline"></div>
<div class="newline"></div><span class="n">fft_sig</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">fft_sig</span><span class="p">)</span>
<div class="newline"></div>
<div class="newline"></div><span class="n">np</span><span class="o">.</span><span class="n">save</span><span class="p">(</span><span class="s">'fft_sig.npy'</span><span class="p">,</span> <span class="n">fft_sig</span><span class="p">)</span>
<div class="newline"></div></pre></div>
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