Now uses Centroid calculation, retained the old calculation

notebooks/spectral_features.ipynb

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  "metadata": {
   "name": "",
-  "signature": "sha256:620336a15b319b335fbc26f830d5f6b5507392500835305cf3d7fd579934ff6e"
+  "signature": "sha256:b4779de8997f272445c84c210f3048f03d085c9dd003e7005e82662dc0906c79"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -211,11 +211,12 @@
      "cell_type": "code",
      "collapsed": false,
      "input": [
-      "from essentia.standard import ZeroCrossingRate, CentralMoments, Spectrum, Windowing\n",
+      "from essentia.standard import ZeroCrossingRate, CentralMoments, Spectrum, Windowing, Centroid\n",
       "zcr = ZeroCrossingRate()\n",
       "hamming_window = Windowing(type = 'hamming') # we need to window the frame to avoid FFT artifacts.\n",
       "spectrum = Spectrum()\n",
       "central_moments = CentralMoments()\n",
+      "spectral_centroid = Centroid()\n",
       "\n",
       "frame_size = 0.100 * sample_rate   # 100ms\n",
       "file_index = 0 # to process a single file, this will be your file loop iteration\n",
@@ -223,15 +224,65 @@
       "current_frame = audio[0 : frame_size]\n",
       "features_snare[file_index, 0] = zcr(current_frame)\n",
       "spectral_magnitude = spectrum(hamming_window(current_frame))\n",
+      "centroid = spectral_centroid(spectral_magnitude)\n",
       "\n",
+      "# Spectral centroid in normalised bandwidth (i.e fraction of Nyquist frequency).\n",
+      "centroid"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 41,
+       "text": [
+        "0.22001729905605316"
+       ]
+      }
+     ],
+     "prompt_number": 41
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "# Centroid in spectral coefficient indices.\n",
+      "centroid * spectral_magnitude.shape[0]"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 42,
+       "text": [
+        "485.3581617176533"
+       ]
+      }
+     ],
+     "prompt_number": 42
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Essentia can make things seem a little magical, here is how the centroid would be calculated:"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
       "# Normalize the spectral magnitude\n",
-      "norm_spectral_mag = spectral_magnitude / np.sum(spectral_magnitude);\n",
+      "norm_spectral_mag = spectral_magnitude / np.sum(spectral_magnitude)\n",
       "# Make index vector\n",
-      "indices = np.arange(spectral_magnitude.shape[0])\n",
+      "indices = np.arange(norm_spectral_mag.shape[0])\n",
       "\n",
       "# Centroid, in spectral coefficient indices.\n",
-      "centroid = np.sum(norm_spectral_mag * indices)\n",
-      "centroid"
+      "my_centroid = np.sum(norm_spectral_mag * indices)\n",
+      "my_centroid"
      ],
      "language": "python",
      "metadata": {},
@@ -239,13 +290,13 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 23,
+       "prompt_number": 50,
        "text": [
         "485.13728477961195"
        ]
       }
      ],
-     "prompt_number": 23
+     "prompt_number": 50
     },
     {
      "cell_type": "code",
@@ -266,13 +317,13 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 32,
+       "prompt_number": 51,
        "text": [
         "array([ 1.        ,  0.        ,  0.04079479,  0.00723291,  0.00497805], dtype=float32)"
        ]
       }
      ],
-     "prompt_number": 32
+     "prompt_number": 51
     },
     {
      "cell_type": "code",
@@ -289,14 +340,13 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 34,
+       "prompt_number": 52,
        "text": [
-        "array([  1.29251704e-01,   4.85137285e+02,   4.07947935e-02,\n",
-        "         7.23291235e-03,   4.97804629e-03])"
+        "array([ 0.1292517 ,  0.2200173 ,  0.04079479,  0.00723291,  0.00497805])"
        ]
       }
      ],
-     "prompt_number": 34
+     "prompt_number": 52
     },
     {
      "cell_type": "markdown",