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<!DOCTYPE html>
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<title>spectral_features_essentia</title>
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<div class=" highlight hl-ipython2"><pre><span class="kn">import</span> <span class="nn">numpy</span><span class="o">,</span> <span class="nn">scipy</span><span class="o">,</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span><span class="o">,</span> <span class="nn">IPython.display</span><span class="o">,</span> <span class="nn">sklearn</span>
<span class="kn">import</span> <span class="nn">essentia</span><span class="o">,</span> <span class="nn">essentia.standard</span> <span class="kn">as</span> <span class="nn">ess</span>
<span class="n">plt</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s">'figure.figsize'</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="mi">14</span><span class="p">,</span><span class="mi">5</span><span class="p">)</span>
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<h1 id="Spectral-Features-in-Essentia">Spectral Features in Essentia<a class="anchor-link" href="#Spectral-Features-in-Essentia">¶</a></h1>
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<p>For classification, we're going to be using new features in our arsenal: spectral moments (centroid, bandwidth, skewness, kurtosis) and other spectral statistics.</p>
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<p><a href="https://en.wikipedia.org/wiki/Moment_(mathematics"><em>Moments</em></a> is a term used in physics and statistics. There are raw moments and central moments.</p>
<p>You are probably already familiar with two examples of moments: mean and variance. The first raw moment is known as the mean. The second central moment is known as the variance.</p>
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<h2 id="essentia.standard.Centroid"><code>essentia.standard.Centroid</code><a class="anchor-link" href="#essentia.standard.Centroid">¶</a></h2>
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<p>To compute the spectral centroid in Essentia, we will use <a href="http://essentia.upf.edu/documentation/reference/std_Centroid.html"><code>essentia.standard.Centroid</code></a>:</p>
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<div class=" highlight hl-ipython2"><pre><span class="n">spectrum</span> <span class="o">=</span> <span class="n">ess</span><span class="o">.</span><span class="n">Spectrum</span><span class="p">()</span>
<span class="n">centroid</span> <span class="o">=</span> <span class="n">ess</span><span class="o">.</span><span class="n">Centroid</span><span class="p">()</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">essentia</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">scipy</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">1024</span><span class="p">))</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">spectrum</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="n">spectral_centroid</span> <span class="o">=</span> <span class="n">centroid</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="k">print</span> <span class="n">spectral_centroid</span>
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<pre>0.498104333878
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<p>This value is normalized between 0 and 1. If 0, then the centroid is at zero. If 1, then the centroid is all the way to the "right", i.e., equal to <code>fs/2</code>, the Nyquist frequency, or the highest frequency a digital signal can possibly have.</p>
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<p>Here is a sanity check:</p>
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<div class=" highlight hl-ipython2"><pre><span class="nb">sum</span><span class="p">((</span><span class="n">X</span><span class="o">/</span><span class="nb">sum</span><span class="p">(</span><span class="n">X</span><span class="p">))</span><span class="o">*</span><span class="n">numpy</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">X</span><span class="p">)))</span>
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<pre>0.49810430034108322</pre>
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<h2 id="essentia.standard.CentralMoments"><code>essentia.standard.CentralMoments</code><a class="anchor-link" href="#essentia.standard.CentralMoments">¶</a></h2>
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<p>The first step to computing the other three spectral moments (spread, skewness, and kurtosis) is to compute the central moments of a spectrum:</p>
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<div class=" highlight hl-ipython2"><pre><span class="n">central_moments</span> <span class="o">=</span> <span class="n">ess</span><span class="o">.</span><span class="n">CentralMoments</span><span class="p">()</span>
<span class="k">print</span> <span class="n">central_moments</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
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<pre>[ 1.00000000e+00 0.00000000e+00 8.12825486e-02 -3.57219629e-04
1.20308148e-02]
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<h2 id="essentia.standard.DistributionShape"><code>essentia.standard.DistributionShape</code><a class="anchor-link" href="#essentia.standard.DistributionShape">¶</a></h2>
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<p>To compute the spectral spread, skewness, and kurtosis, we use <a href="http://essentia.upf.edu/documentation/reference/std_DistributionShape.html"><code>essentia.standard.DistributionShape</code></a>:</p>
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<div class=" highlight hl-ipython2"><pre><span class="n">distributionshape</span> <span class="o">=</span> <span class="n">ess</span><span class="o">.</span><span class="n">DistributionShape</span><span class="p">()</span>
<span class="n">spectral_moments</span> <span class="o">=</span> <span class="n">distributionshape</span><span class="p">(</span><span class="n">central_moments</span><span class="p">(</span><span class="n">X</span><span class="p">))</span>
<span class="k">print</span> <span class="n">spectral_moments</span>
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<pre>(0.08128254860639572, -0.01541485171765089, -1.1790399551391602)
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