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Commit 7accef05 authored by Steve Tjoa's avatar Steve Tjoa
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removing all essentia

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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy, scipy, matplotlib.pyplot as plt, IPython.display, sklearn\n",
"import essentia, essentia.standard as ess\n",
"plt.rcParams['figure.figsize'] = (14,5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[← Back to Index](index.html)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Spectral Features in Essentia"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For classification, we're going to be using new features in our arsenal: spectral moments (centroid, bandwidth, skewness, kurtosis) and other spectral statistics."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[*Moments*](https://en.wikipedia.org/wiki/Moment_(mathematics) is a term used in physics and statistics. There are raw moments and central moments. \n",
"\n",
"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."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## `essentia.standard.Centroid`"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To compute the spectral centroid in Essentia, we will use [`essentia.standard.Centroid`](http://essentia.upf.edu/documentation/reference/std_Centroid.html):"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.498104333878\n"
]
}
],
"source": [
"spectrum = ess.Spectrum()\n",
"centroid = ess.Centroid()\n",
"x = essentia.array(scipy.randn(1024))\n",
"X = spectrum(x)\n",
"spectral_centroid = centroid(X)\n",
"print spectral_centroid"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"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 `fs/2`, the Nyquist frequency, or the highest frequency a digital signal can possibly have."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here is a sanity check:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.49810430034108322"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sum((X/sum(X))*numpy.linspace(0, 1, len(X)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## `essentia.standard.CentralMoments`"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The first step to computing the other three spectral moments (spread, skewness, and kurtosis) is to compute the central moments of a spectrum:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ 1.00000000e+00 0.00000000e+00 8.12825486e-02 -3.57219629e-04\n",
" 1.20308148e-02]\n"
]
}
],
"source": [
"central_moments = ess.CentralMoments()\n",
"print central_moments(X)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## `essentia.standard.DistributionShape`"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To compute the spectral spread, skewness, and kurtosis, we use [`essentia.standard.DistributionShape`](http://essentia.upf.edu/documentation/reference/std_DistributionShape.html):"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(0.08128254860639572, -0.01541485171765089, -1.1790399551391602)\n"
]
}
],
"source": [
"distributionshape = ess.DistributionShape()\n",
"spectral_moments = distributionshape(central_moments(X))\n",
"print spectral_moments"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[← Back to Index](index.html)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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