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@nipunbatra
Created January 20, 2017 08:38
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We've all seen those weird looking mathematics equations that pop up when we hear about **Fourier transforms**. In this blog post, we'll programatically try and develop an intuitive understanding into the whole process. While I'll be using the scientific Python stack in this blog post, code in Matlab, R should not be that different. \n",
"\n",
"### Goal: Given a time series signal, we'll try and decompose it into various contituent freqencies."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, let us assume that we are doing some signal acquisition and we can sample at 100 Hz frequency (100 times per second). We collect data for 10 seconds. So, we have a total of 1000 samples. \n",
"\n",
"```python\n",
"Samples collection duration (T) = 10s\n",
"Sampling frequency (Fs) =100Hz\n",
"Number of samples (N) = Ts*Fs=1000\n",
"```\n",
"\n",
"It must be noted that Fs is the rate at which we are able to sample. Let us now create a signal composed of different frequencies. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code preliminaries"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I'll import a few packages necessary for the post. Numpy is a fundamental package in the scientific Python stack and provides array operations. We'll use matplotlib for the plots. I'm also importing the warnings module to suppress any warnings in the code."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Vendor: Continuum Analytics, Inc.\n",
"Package: mkl\n",
"Message: trial mode expires in 29 days\n"
]
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"plt.style.use('fivethirtyeight')\n",
"import warnings\n",
"warnings.filterwarnings('ignore')\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us create a simple function to generate sine and cosine waves given the time for which samples were collected, the frequency of sampling and the frequency of the desired sine wave. "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def create_sine(t, fs, frequency_of_sine):\n",
" return np.sin(2*np.pi*frequency_of_sine*np.arange(0, t, 1./fs))\n",
"def create_cosine(t, fs, frequency_of_cosine):\n",
" return np.cos(2*np.pi*frequency_of_cosine*np.arange(0, t, 1./fs))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us now plot a sample sine wave of 1 Hz where our instrument can sample at 100 Hz and we acquire the data for 10 seconds. "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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jHgBOK6VU7ggllOrCUOtIm5ShI+s6ZdfJKmBxYtvFCA2owbZKmEE56xqhNOal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\nKIqiKEHz/wPuvqg+mnOq4AAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1084a1610>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(8,4))\n",
"plt.plot(create_sine(10, 100, 1))\n",
"plt.xlabel(\"Samples\")\n",
"plt.ylabel(\"Amplitude\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Great! We can see 10 time periods of our sine wave in 10 seconds. Thus, our sine wave creation functin seems to be working correct :) Please ensure that you notice that the x-axis is the number of samples and not time. 1000 samples were collected in 10 seconds."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Creating the signal for processing"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will now create our dummy signal. It will be composed of four sinusoidal sine waves of different frequencies: 0 Hz (DC), 10 Hz, 2 Hz and 0.5 Hz. Did I introduce a new term here- DC. DC refers to direct current. Yes, the same direct current you might have heard in school. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"t = 10\n",
"fs = 100\n",
"N = t*fs\n",
"num_components = 4\n",
"\n",
"components = np.zeros((num_components, N))\n",
"components[0] = np.ones(N)\n",
"components[1] = create_sine(t, fs, 10)\n",
"components[2] = create_sine(t, fs, 2)\n",
"components[3] = create_sine(t, fs, 0.5)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plotting these four components individually."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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VXxKRScDNIrJEVe/qb1kMwzAMwzAMwzCyRFSDchrPSiKvAxM0zsr9LYDIEpyxVi+LyI7A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B7Htg6J+KzJuFaA6rogccdXpN29su6swZv4Zp5jW5E8KErlyuW4LvFVvM+xrZ9FeZZ63o+Bs7Si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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x108570fd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(nrows=num_components, sharex=True, figsize=(12,6))\n",
"for i in range(num_components):\n",
" ax[i].plot(components[i])\n",
" ax[i].set_ylim((-1.1, 1.1))\n",
" ax[i].set_title('Component {}'.format(i))\n",
" ax[i].set_ylabel(\"Amplitude\")\n",
"ax[num_components-1].set_xlabel(\"Samples\")\n",
"plt.tight_layout()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let our signal be \n",
"\n",
"$$x = -0.5\\times x_0 + 0.1\\times x_1 + 0.2\\times x_2 -0.6\\times x_3 $$"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"x = -0.5*components[0]+0.1*components[1]+0.2*components[2]-0.6*components[3]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our dummy signal looks something like the following"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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PaWo89NsN8rzl9N3wvQBsmAwQkS2BuR3P0eCR1zLvyksXeM6LwBuIKvUkjZzK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\nA2BF+ABYET4AVgLLALAyCcFdqAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10a2e2390>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(x)\n",
"plt.xlabel(\"Samples\")\n",
"plt.ylabel(\"Amplitude\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"By looking at the data, we might be able to notice the presence of a signal which shows five periods in 10 seconds. Or, a signal of frequency 0.5 Hz. We can also guess the presence of high frequency signals."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Introducing DFT"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For finding the various frequency components in the signal, we'll be using the Discrete Fourier Transform (DFT). The key step in DFT is to find the `correlation` between cosine waves of different frequencies with the signal that we intend to process. A high amplitude of this `correlation` indicates the presence of this frequency in our signal. \n",
"\n",
"It must be noted that the definition of `correlation` is different from the definition we encounter in statistics. Here, `correlation` between two signals simply means the dot product between the two. Please note that the dot product is the sum of the element wise product between the two signals."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us see the `correlation` between a few pair of signals. \n",
"\n",
"#### Correlation between a sine and a cosine of 1 Hz "
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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Po4qE1D9/6O8G7AUwuzeEr6ZNB/jw0c++/t8/P/v6ICHE50KIzzGp7GDWxFqGjlvDsvFi\nNT4N5KaYtZW8kOuaQJwG8meDrU2QUfJb4CzL/DWwqQr9gvZWJ6BC/3MZJT/BXPcf5Hb9CJM9+HMV\n+lNKcc7hsLDXoMqSZtJavyKEuAYjQVeR0i5AzD986E5521StvwY2mDxdnwsco7VuuWnAPB39htWD\nF6uvMMKXD1u7NgRuGEydloySLSjWgE3AyCzZb3YdhQr9LzHZg3Zh90+B61ydlqPTEUIsK4Q4SAix\nSLY9EtMTsEKNIg3kXvZnp0zXk25574soW7O/BDhSCLFCdpwuIcSv6v8T1BYXsDKyLplbAGOtXQGm\nuHimn6ZklKwL3ETldZ6MWbOyg2NHkgWtTYEXrF2/wqjAOxydzHjMbM+TQoivMIHqOUwmIIDOZOb+\nYN2gxj346fh735gw5RMArXWMSW+/UQjRDTwPzLCGq9lwASuHF6uem+dL1q5dgCNm5lhZe5A7gHxh\n7HTgNyr0/zEYP9sNFfqfYdLbE2vXgTJK9ivBJYejKdBav6+13lprvajWes7s3z211l9pra+ZtuUq\nxwJ/BsSULVdhyTlmAZgIbPbBpKmB1vrY3LGu01p/X2vdpbVeTGv925J+rAHjApaFF6tPMcKQb1u7\nTk4D+Zv+HENGyXepLoOyhwr9ePBeth8q9D/EBC27Y/J5TjDX4SiSBnJ5jFLO8LwZ+KUXqyfK8aq+\nuIBVBS9W72KClq2IcXVWdNwrWYZbDNjposeq0L+8dl62Hyr036aoiCGAG2SUrFWOVw5H85EGcj7M\nDI7d92/XVtEFHAguYPWCF6tXMetXee3BWYDb0kAuXe0zWfPFKzFzznkuplgs7KiCCn2FWb/Kaw/O\nCsQySmyBYIej40gDORzT729Ja9fvvVi1pFh2f3EBqw+8WD2CWb/KMx8maFUrcD0Sk8GT515gv7Ja\nxLciWV3aHpZ5QeCvrkbL0clkyV9/ANa3dl0JnNF4jxqLC1gzwIvVdcAYy7wCZnrwm8QcGSW/oPgW\n9RKwtQr9aXV1sg1RoX8Fpho/zyjgsuxN1uHoRPbDdJjI8wiwlxertn8odgGrf5wAXG/ZfoF5o0JG\nyfKY1vZ5xtFGquslcTTwN8u2PXBQCb44HKWSBnI9TFfgPG8AW3mx6ogiexew+kH25LIbRf27Ez/8\nzQZbYeaT8zJO04CtVOi/3iAX2xIV+tMxAcruC3ZGppLhcHQEaSAXAm6msh3Rl8DmWWZzR+ACVj/x\nYjUB+DnfanABiDmnTrhh0a8+XN4avp8K/Yca5lwbkxUWbwnk31SHANfLKGkpHTSHYyCkgRyGCVYL\nWru282Jldz5oa1zAmgm8WL0FbI0pAAZgtnTysNOePJfh6Tdv5BFGBsVRI1Tovwr8hkqxz/mBG2WU\ndLwepqPtOY1KvU2Ak7xY3THQAwohXhBCrDfjkc2FC1gziRervwOH5m3LffEmBzwXgZE72cNlBNae\nLHPwWMv8A1y5gKONyWSXDrrh3c9Z86FXmOeO51jwrucnD7vt2dWEEH3WhPaF1nolrfUjNXS1IbiA\nNQDW2+Kaax5eaNTEvO3Xb9zLlQ8efZkK/Qll+dUBnALcZ9kOl1GyWRnOOBz1JA3kUsBV5772MQe/\n8B5HLrsg749e6d3H119mMQ0XYbRPOwo3nTKTyCgRDJvtimNX32e2Pz9wGItO+PibfSuPe/XkNJB3\nebF6o0QX2xYV+tNllGwPKCr7+Fwro0Sq0G+pdt+O1iENZMWsiQTSKv2oesOL1UyVYmTrVtd3T03n\nOv7lD7lq1cXYcqF5pgK/9O/478fatOW5UwgxC0bUtkd5/WbgcK31FCHE/MDVwLqYZYwXtdbrAQgh\n3gJ20Vr/QwgxBlOqMxGzTv8/YEet9TPZ2IWBC4EfYlRoztVaXzgzP0+tcG9YM88eQPD1sNk5Yq0D\nmSoqOmDMDdyUBnKWclxrf7Lmj7+hUgljBEa+yT2AOdqFE4A1Hh/3NZOmTydYqAvgIC9WT1rjjgLW\nAFbOvtbAlIOAUXR/B7PeuwCVAt52sN0cuAHoAm7HFCcjhBiCKS1RmMaRGwIHCCE2rsHPONO4gDUT\nyChZCTinZ/uleZfiyuW3skVyRwEnN9SxDiPrI3akZV6HmVTUdziakTSQGwKHA4ybMo35hw9liBC3\nYaYBbbYFTtBaf6q1/hQ4HgizfVOAhYDFtdap1rqvZrH/1Frfo7XWwHWY4AewOjC/1vokrfU0rfWb\nwBWYh8aG4wJWP8kkgW6ksl3I+GuW2XJDjNhtnoPSQP64Yc51JmcBtsjncU4k19HKpIH8DibTWACM\nGD6UT6dM44NJU3/bi5LFwlR2lvhfZgPTT+414D4hxOtCiMP7OPVHue8nALNmb1ffAxYWQnze84V5\nMFxgID/fYHFTKP3nbGBFy7bnUzut8HoaswuwKrBYZhfANWkgv+/F6otGOtkpZOtZu2Ca2fX88XiY\nTsVShf748rxztBv2GtTYsWP1qFGjaioRlkm9XYV5KwJg7RFzaK2ZPPLeF9fXRqDA5n1gcb7t4bdY\nZkNr/RVwCHCIEGJF4B9CiKe01g/OhFvvAG9qrZeZ6R+oDrg3rH4go2RTYE/LHKnQ/zOAF6vPgR2o\nnBceSfVXeEeNUKH/EbCzZV4KOL8EdxyOwbIb8LO8oWuYd3Jq1qkuEkJsKYSYXQgxTAixqRDidMy6\n09FCiPmzJItjMW9oCCF+JoRYWgghMKoYKbka0n7yFDBeCHGYEGI2IYQnhFhJCDFqkD/rgHABawbI\nKBmBUULO8zqwd97gxephzDRVnm372/TRMTBU6N9F8cFgZxklvyzDH4djIKSBXJLc+njG48DxWutz\nMPqZRwMfY6b99gL+iqlDHIuZaXgu+76nNnFp4H5gPPAv4CKt9cNVTq8pJmFoAK11igmiq2B0Cz8B\nLqPYh6shuCnBGXMhuVd0zBPK9r1MOR2Dafy4cs52cRrIx7xYvVNHHzudQ4ENgLxE1qUySh693BbN\ncjiajDSQQzDp53PkzF8D23uxmgagtb6eogB3D/tnXxVorc8Dzqv2Aa31Ernvj7f2vUVOs1Br/QEm\nuaN03BtWH2RP6fZ/1Gkq9Ku2n/ZiNRkj1jo5Z54H04rEXes6oUJ/Iub/Kd9scwRwsXaaI47m5wBM\njVOeg1w9ZxF3E+0FGSULUtQE/A8mbbRXvFi9QDG9egPgd7XzzmGjQv9Zvq0/6SF46sthZbjjcPSL\nNJArYBRc8twNXF6CO02PC1hVyBoEXobpLtzDVGAHFfr96TtzPvB3y3ZGGsjv1chFR3XOBioKK6//\ncFZklCzUy3iHozQyNYtrgLzQwOdAbynsHY8LWNXZnqJO13Eq9J/rz4e9WE0HdsHImPQwJ3B5vkux\no7ao0E+BnchNyU6YPgTgEtel2NGEHI4RGsizjxer98twphVwAcsimwq006KfwBTh9RsvVv/DUnUH\nfgLsOnDvHDNChf7LFKcGtwC2K8EdR2vQ8PtgNhVodx+4BZOm3srU9Vq6gFXkAmDe3PYkYEcV+tMG\ncKzLALtI7+w0kIsO1DlHvzgXkxKc5wIZJQtXG+zoeN7q7u7eqbu7uyFv4WkgPYy8UX6B9WNgr1ad\nCuzu7hbd3d07A2/V8zwurT2HjJItgF9b5mOzBoIzjRer6Wkgf4vpkzV7Zp4buCwN5Gat+svZ7KjQ\nT2WU7Aw8y7dSWvNiHkZcfZajgq6urqu6u7vXAU7q7u6eRj9U2EeMGEF3d/eYgZzPO/DUNYa8+cra\nedv05VZ+JF1e7k13d28fa2YEJpbc2dXV9a+6nkg3Qd5vd3f3N050dXWVstYgo6QL+C/f6nABPAOs\nNcC3q29IA7kv5maZZ0cvVtcO5Hj1kIVpR2SUHEyxmDtQoX9bGf40O+73qv8M9FqlgVwMeBGzpt3D\n7UDQrg+wtby/uynBbzmdymCVAr8dbLDKuAh41LKdkwZy/hoc29E75y0+a+G/7yIZJaVU6Ts6myzh\n6hIqg9WXtPBUYKNxAQuQUbI+xTqpM7LankGTyxqclDPPR/Hp31FDVOinOyw0ESp7Zy2Ca//iKIdt\ngU0t22FerN4rw5lWZNABSwgxWgjxshAiqSZfL4T4kRCiWwihsi87g6tUsrYhdpHeq5gGajXDi1VS\n5Zg7ujYk9WXkrNOh+GCwt2tD4mgkWdsQO/v4EVyB8EwxqIAlhPAwnSlHY1osbyOEqKbe9rDWWmZf\nJ1XZXyZHAb5l202F/qRqgwfJ2Zj56zyXpIGctdpgR804ASPc2YMALpdR4mQwHI3ibCqFCCYDu2Wz\nL45+Mtg3rDWA17TWb2mtp2IaHG5ZZVxTLuTKKFkWOMwyX6pC/5F6nM+L1RSKU4/L4Drl1hUV+hMo\nXveVML2CHI66kgZyfb7tAtzD8V6sBpR93MkMNmAtgmnw1cO7mS2PBtYRQvxHCHGXEGKFQZ6zJmTK\nB3+kshbiQ7LW1PXCi9VjwKWW+Yg0kMvV87ydjgr9BwA7K/M4GSVLl+GPozNIAzkcuNgyP49bvx4Q\ng0prF0JsBYzWWu+WbW8PrKm13jc3Zi4g1VpPEEJsCpxvd6/Mpz0mSTJgf2aGJ7uHccX7s1fYdlt4\nAmt0Te3lE7XDm/g1y19yLMO+/vIb2/jFluG18BAQTfky2haMnyY49o05+Sr99jltpTmmst/ICe6y\nO+rCgo/dzcIP/qXC9uqOh/P1yM55TvL9b1dcBpvWPtiAtRYwRms9Ots+ApiutT69j8+8CaymtR7X\nY2t0HVZWc/UKsGDO/ACwsQr9hqSXpoHcGjOFmmcXL1Z/mtFnXb1M/7GvlYySkOKb1i9U6P+1sZ41\nH+73qv/051plYtcvAbPlzFd5seooebZmqsMaC/hCiMWFEMOBrTFFcN8ghFgwa9GMEGINTJAcVzxU\nQzmJymA1Bdi7UcEq42bgHst2ehrIeasNdtSM6zDZWXnOl1EyR7XBDscguIDKYDWOOi85tDuDClha\n62nAPsC9GJWIm7TWLwkhfieE6Fnk/iXwvBDiWUz3y1JbxssoWQ3TXjrP6QOVXxooWaHgXlTWZn2H\nGqfTOyrJHkr2prI2ayQmW9ThqAlpILeg2PHhMC9Wn5bhT7sw6DosrfXdWutltdZLa61PzWyXaq0v\nzb6/SGu9ktZ6Fa31Olrrqt16G4GMEg+zAJr/ud8ATi3DHy9Wb1Y5915pIFcpw59OQYX+CxRbhx8i\no8QlvjgGTRrIOShKsT0OzHC639E3naZ0sRuwumXbJ2uxXhZnUFkjNAT4g+ubVXeOB/J9h4YBf3B9\nsxw14Cgg36w1BfZwNVeDp2MCloyS+Si2or5Vhf7dZfjTgxerScD+lnldTBNJR51QoT8eOMgybwj8\nqgR3HG1CGkifYn3fBV6s+tX81dE3HROwgBOp7HP1NXBASb5U4MXqDuAOy3xmGsiuMvzpIG4G/m7Z\nzpVRMlcZzjjagnOprO18HziuJF/ajo4IWDJKVqaodHCSCv13y/CnFw4g19odk8U4phxXOoMsAWMf\nIF98tzBwTDkeOVqZNJA/BTazzId4sRpfhj/tSNsHrGxN4gIqf9bXMU9CTYMXq9cx61l59k0D+X9l\n+NMpqNB/GaPzlucAGSW2vqTD0SuZooWdyPMoxVpLxyBo+4CFWZNYz7IdoEJ/crXBJXMa8HZu28Ml\nYDSCkzCyYj0MoxjEHI6+2J9KEW0N7Of6XNWWtg5YMkpmp6jZdQ9wZwnuzBAvVhMorquth2vrXldU\n6H9NUQR5cxklm5Thj6O1SAO5EHCsZb7Mi5Uqw592pq0DFqaqfGRuexrm7aqZn3puo6iAcWYayNmq\nDXbUjBuBxyzbua4FiaMfnEplF+EvgKbq+9cutG3AklGyBEUZlPNV6L9Shj/9JZtCOBATXHv4XmZz\n1InsIWZ/zFROD8sDe5bjkaMVSAO5JrCjZT7WKVrUh7YNWJipwFly2x/RIrJHXqxeBi6yzEdmUw+O\nOqFC/xmKagTHyyiZvwx/HM1NGsghwIWW+UWK7UQcNaItA5aMkg2BX1jmI1Tof1ltfJNyPEYss4c5\nKBY+O2rPUUA+DXkeWuRBx9FwdqSonLO/F6tp1QY7Bk/bBaxML9BOL30auKYEdwaMF6vPKS7k7pQG\ncrUy/OlQ/GMNAAAgAElEQVQUVOh/iCkyz/M7GSXfL8MfR3MyZPIkKOqA3urFyi5Ed9SQtgtYwC6Y\n9ud59lWh34o6XpdiVPDznM8gepg5+sUFwGu57SHAeU5n0NHDgv+6GypbFE2iKMnkqDFtFbAySR37\n6fg6FfpPluHPYMmmFuxki3XneWlsGe50DFmNnq0z+GOK08yODiQN5MgFnrzfNp/txeqtEtzpKNoq\nYGGyAu2nniNL8qUmeLG6D6tubOG/34pLc687dwD3WbYzZJQML8MZR1NxypBpeTUvPgJ67bLuqB1t\nE7BklIwEDrbMZ6vQf6cMf2rMweTS3Gfp/gyKbwCOGpKluR9IZaPHJTHNHx0dShrI1Sl2Ujja6QU2\nhrYJWJgMullz223z1OPF6hXgD5b5iDSQC5fhT6egQv+/wGWW+RgZJSPK8MdRLplEmi3Z9TyuMWPD\naIuAJaNkFMWnnmOynkftwgnAZ7ntOTAaeI76MobKNPd5cSoGncrPgR9atoO9WKXVBjtqT8sHrCxz\n6xzL/DxwVQnu1I0+0txdunUdUaH/McX6t31klCxVhj+OcsjU2O1uCnd5sSpkXzjqR8sHLCCg+NRz\niAr9dnzquQx4ObctKP4ROWrP+cD/ctvDMMr6js5hb+CbhxQthgAcWpo3HUpLB6wsY8u+Yd+tQt/O\n7moLsjR3W1V8kzSQG5fhT6egQn8ixWzTX8ooWbcMfxyNJQ3kfFizG5+uuh5erOwaSUedaemABewF\nLJ3bnk77P/XcMX6xZWzbmWkgvTKc6SBuAOwCuLNdMXFHcAxGoquHLz9cb/OyfOloWjZgZZlahR40\nKvRfLMOfRuHFSr+30a9s8/eBsAR3OoZMKcUum1gT+HUJ7jgaRBrIZSiWMpw8bY65y3Cn42nZgIV5\n6pk3tz0eOK4kXxrKxIUXB7jeMp+UBnL2xnvTOajQfwSILfNpMkpmqTbe0RacDgzNbb+Nke5ylEBL\nBiwZJUtTfOo5Jcvo6hSOAqbktheh2K3YUXsOp7JX2eLAvuW44qgnaSB/gEnqynO4F6tJZfjjaNGA\nBZyMydTq4X8UFdrbmky3zH7S+30ayAVKcKdjUKH/KsV+R0fLKJmvDH8c9SErErYTup4Abi7BHUdG\nywUsGSWrU1w3OEKFfic+9ZxCZc+sueiQadGSOQHozm13UVxPdbQ2WwJrW7ZDs47gjpJoqYCVZWTZ\nckv/Bm4swZ3SyYqJC72b0kAuW4Y/nYIK/U8xb/l59pRRsmQZ/jhqSxrIoRR7Xd3uxerRMvxxfEtL\nBSxgE0ybhzyHt2ivq1rxR+CN3LZHm2goNjkXYhbgexiGk8pqF3YGlsttT6fFuz60Cy0TsLJOwvaN\n+H4V+g+U4U+z4MVqCvB7y7xlGkhb/cNRQ7IpaFtTcBsZJa4jdAuTZdoeb5mv9mLV1uUyrULLBCxg\nW0y9UZ7Dy3CkCbkFsyCc56xs4dhRP64H/mPZnGRTa7M/sFBuexJuXbhpaImAJaNkVorTLder0Fdl\n+NNsZAvBdnvuNYCtSnCnY8imou2Hpo1klDiprBYkDeT8FGcrzvdi9W4Z/jiKtETAwkgwLZbbnopr\n8VCBF6vHgL9a5lPSQA6rNt5RM+4D/m7ZTpdR0ip/W45vORLIS1h8jlsPbiqa/o9KRsk8mCLZPH9U\nof9mGf40OUdQ2SHXB3YtyZeOIOtMbL9lrQJsU4I7jgGSBnJxqogRZJm4jiah6QMW5maQ7/A6nmJK\nsYNvOhNfaZnHpIGcswx/OgUV+s9QLK04yUk2tRQnAsNz2+9Q7PLtKJmmDlgyShalKDd0ugr9T8rw\np0U4HpiY214QJ9nUCI7CTFX3sDiwZzmuOGaGNJCrANtZ5mOcBFPz0dQBC9OefNbc9gd0mATTzOLF\n6n3gXMt8WBrI75ThT6egQv8N4BLLfLSMkq4y/HHMFKdimqH28DxwXUm+OPqgaQOWjJIVMAV8ecao\n0P+6DH9ajDMoSjbZ64CO2nMiZsq6h/koNtx0NBFpIDcARlvm33uxaseO5S1P0wYszFNP3r9XgKtK\n8qWl8GLVTXGdb680kEuU4U+nkE1V24KpB8ooWaQMfxx9kwZyCMX/r4eBu0twx9EPmjJgySj5AbCF\nZT5Chf60auMdVfkjRsW+h2EY0VZHfTkX+DC3PRuu8LRZ+SVgK5Mc7gRum5emC1iZwG01WX+7cZ6j\nD7IF42Ms83bZArOjTmRT1mMs864ySpYvwR1HL6SBHI7pdpDnFi9WT5bhj6N/NF3AwjRMs2X9D8vq\nXRwzx58xC8g9CIoq1I7acxXwam57CO66Nxu7AUvltlPcOm/T04wBy/7D/psK/X+W4kmLky0c21Iz\no7OFZkedUKE/FVPEnWdLGSXrluGPo5I0kHNR7F92uRerV6uNdzQPzRiw8r2cplP8w3fMHHdjFpLz\nnO6EcevOXykKEp+RTXk7yuVgIN+ZewJufbclaMaAledqFfpO1n8QZAvItnTQKMyCs6NOZFPYdkr7\nOphOto6SSAO5IEWh6LO9WH1Qhj+OmaOZA5aT9a8R2ULyrZbZCePWmWwq+2+W+VQZJUPL8McBmESk\nOXLbnwJnleSLYyZp5oB1vgp9J+tfO46iUhh3aeC3JfnSSRyBmdruYTlgp3Jc6WzSQPrA7yzziV6s\nvizDH8fMM+iAJYQYLYR4WQiRCCGqNlQUQlyQ7f+PEEL247BO1r/G9CKMe5wTxq0v2ZT21Zb5eBkl\ns5fgTqdzEpB/u32TopyWo4kZVMASQngYRePRwArANkKI5a0xPwWW1lr7wO7Axf049Mkq9J2sf+1x\nwrjlMAYzxd3DwsB+5bjSmaSBXB34tWU+yovVlDL8cQyMwb5hrQG8prV+S2s9FdNiwV5U3gK4BkBr\n/SQwjxBiwT6O+T/gokH65aiCE8YtBxX67wAXWObfyyiZrwx/Oo0sI9aesfk3cFMJ7jgGwWAD1iKY\nvjE9vJvZZjRm0T6OeYwKfSfrXz+cMG45nIaZ6u6hC9Ph1lF/NgF+bNkO92I1vdpgR22oRwmH0Hrg\nAhJCiK2A0Vrr3bLt7YE1tdb75sb8DThNa/1Ytv0AcJjW+t89Y7q7u79x4pVXE4a4SpW68p0n72fR\n+2/+Znv6EI+X9jyRKfO6F616cu9nw7nl49m+2R4qNCctNZ75hjkRl7qhp7Pc5Scy28ff5m99ucQK\nvL7dgSU61f5M03D6W3Ow6lxT2W/t731j7+rqGtTdfbABay1gjNZ6dLZ9BDBda316bswlwENa6xuz\n7ZeB9bXWH/WMyQeswf5AncDYsWP1qFGjBnyd0kDOglG//17OfL0XK7uJXcsz2GtVS2SUzIqRbBqZ\nM0cq9HcoyaUKmula1Yo0kCFwrWVezYvVv6uN7y/teK1qiYySvciWdh7a4tsa7cHe3wc7JTgW8IUQ\niwshhgNbA7dbY24HdoBvAtwX+WDlaDxerCZTlKbZNg1kfzI4HQMkm+q2r/v2MkpWLsOfdicN5KyY\nzMA8Nww2WDn6RkbJnBR/z2vCoAKW1noasA9wL/Bf4Cat9UtCiN8JIX6XjbkLeEMI8RpwKbDXIH12\n1IY/A89ZttPKcKTDiIAXcttOkLh+7AksltueChxdki+dxAGYDOSaM+g6LK313VrrZbXWS2utT81s\nl2qtL82N2Sfbv3J+7cpRHr0I426cBnKjMvzpFFToV7vum8oosZMCHIMgDWQXxeB0sRerN8rwp1OQ\nUTI/deyy3cxKF476cw/wkGU7I+vE6qgfdwGPWDYnjFtbDgdG5LbHU5wedNSeozGZxz2M623gQHA3\npg4mE8a1n4YkZi3SUScyYVwnSFwn0kAuQrEg/kwvVp+U4U+nIKNkCYpLPnaTzEHhAlaH48XqaeBm\ny3xylknoqBMq9J+giiCxjBInSDx4xgCz5bY/BM4px5WO4iQg//tbcxEIF7AcYAqHp+W2l6AoEuqo\nPdUEiXcryZe2IA3kCsAulnmMF6uvy/CnU5BRIoFtLfPRtRaBcAHLgRerngzOPMekgZy7DH86BRX6\nrwBXWObjsrRgx8A4hcr72qvAVSX50knY0lfPAdfX+iQuYDl6OBH4Krc9P3BoSb50EsdjOt72sABw\nUEm+tDRpINelqGV6hBerqWX40ynIKPkJ8BPLfHiWEVtTXMByAODF6iOKjewOSgO5UBn+dAoq9D+g\nuL5yqIySBaqNd1QnE7g9wzI/Afy1BHc6BhklQyi+XT2Iqc2tOS5gOfKcA3yc254d1/W5EZwJfJbb\nnhPTGdfRf7YE1rFsh2eZsI768RtMZnGew7NM2JrjApbjG7xYjcdMUeX5bRrIZcvwp1NQof8lZko2\nzx4ySpYqw59WIw3kUIpqIXd4sbJr3Rw1REbJLMDJlvlmFfpP1+ucLmA5bC4HXsttezjpoEZwCaYD\nbg9DKd4MHNXZGVgutz0dOKIkXzqJPYDFc9vTqHOrIhewHBVkC9R2n6afp4Fcuwx/OgUV+pMpSglt\nLaNkVBn+tAppIOegOCtwjRerF6qNd9QGGSVdFKetL1Wh/1q18bXCBSxHNW4BnrJsZ2QL2476cSPw\nrGU73Uk29cn+QD4xaBJu3bURHArkO2Z/BZxQ75O6gOUokC1U29JBPwB+VoI7HYMK/ekUr/sGFFOG\nHUAayPkpXq8LvFi9U228ozbIKFmYYunFWSr0P642vpa4gOWoiherhzAirXlOyxa4HXVChf59wAOW\n+fQsfdhRyVFAvrj9c1yLnEZwHJXSVx8BZzfixO6PwNEXRwD59NQVyJpxOuqK3X5kFWCbMhxpVtJA\nLgHsbZlP9mL1eRn+dAoySpYDdrXMx6vQ/6ra+FrjApajV7xYPUexvfgJaSBnL8OfTkGF/jOY9aw8\nJ2VpxA7DidRZaNVRlVMwmcM9JBTlxeqGC1iOGXEsMDm3vQiwb0m+dBJHYTrk9rA4poNux5MGUgLb\nWeZjvFjVVGjVUYmMknWAn1vmI1XoN0z6ygUsR594sfofcKFlPiIN5HzVxjtqgwr9NzC1WXmOztKJ\nOx1bCuh54M9lONIpZJmq9nV/imKLnLriApajP5wKfJHb7qJYq+WoPSdRKUg8Hx0uSJwGchOqCK16\nsaq50KqjggCTKZznsHpJMPWGC1iOGeLFahxFtYt90kAuXoI7HUOWJnymZT4oSyvuONJAehQFmh8C\n7mm8N52DjJLhFIWF71Kh/3CjfXEBy9FfLgTezW0Px7wBOOrLOZi04R5mw3TU7UR2BlaybIc4gdu6\nswemuWgP04HDynDEBSxHv/BiNRGTgJFnuzSQa5ThT6eQpQvb0kO7yiixb9xtTRrIOSkKBF/nxeqZ\nMvzpFGSUzENROeQKFfovluGPC1iOmeFaTCfRPOc4yaa6cwUmfbiHIRSnCtudQ4Hv5rYnUWehVQdg\nrvGI3PZXlCh95QKWo99kC9sHW+Z1gV+U4E7HkKUN28kWo2WUjC7Dn0aTBnIRij//uVkGq6NOyChZ\nAtjPMp+uQv/DMvwBF7AcM4kXqweAOy3zGWkgXVFrfbkdsBe5z5JR0glSWSdSKQX0MU6CqRGcilmr\n7uE9it2xG4oLWI6BcCiQTyNekqJMjqOGZOnDB1EplbUiRZmctiIN5MrATpb5OC9WX5bgTscgo2Qt\nYGvLfKQK/Qll+NODC1iOmcaL1UvApZb5GFdMXF9U6P+bKlJZMkrmrja+1cnWRs8C8mukL9FAKaBO\nJCsStsVsFXBdCe5U4AKWY6CMAfJPufNQzCJ01J6jgIm57QUoiuW2C6OBjSzboV6sppXhTAfxC2Ad\ny3Zw1v6mVFzAcgwIL1afUGzhvlcayGXL8KdTUKH/HtWLib9Xhj/1ImtjYxcJ/51iyxtHDcmKhG0J\npr+p0H+wDH9sXMByDIYLgLdy20MpVsQ7as+ZwAe57VkwKtrtxC6YdjY9aFyRcCPYC1gqt51SUpFw\nNVzAcgyYTB3bno7aIg3kj8vwp1PIiontGqRtZZSsWYY/tSYN5FwU261f48Xq2TL86RRklIygOK1/\nqQr9l8vwpxouYDkGy83AE5bt7DSQ7nervlwL/MeynZMtmLc6RwEL5rYnAkeX5EsnMQaYN7c9niaT\nAXM3FcegyKZoDrTMEghLcKdjUKFfrYh7HWCrEtypGWkgl6b4+3SWF6v3yvCnU5BRsiJmOjDPKSr0\nPynDn95wAcsxaLxYPQHcZJlPyfTfHHVChf7fgb9Z5jNklMxahj814iyKxap2EoCjhmRv5edS2Un4\nDeC8cjzqHRewHLXi91R2Jl4Y1zOrERwK5NO8l6D45tUSpIH8CbClZT7Mi9XXZfjTQWxOscfYwSr0\nm66DswtYjprgxeotzFNanoPTQC5VZbijRqjQfwX4o2U+UkbJomX4M1CyNHb7if5fwA0luNMxyCiZ\nhaLc0t+B20pwZ4a4gOWoJadQmW49nGLFvKP2jAE+y23PTuuVF+xBZRo7wP4ujb3u7E9lGvt04IBG\ndxLuLy5gOWqGF6vxwOGWecs0kBuX4U+noEL/c4pp7tvIKLFbmjclmaSXncb+Jy9WY8vwp1OQUfJd\n4BjLfLEK/RfK8Kc/uIDlqDV/Bh63bOengRxWhjMdxBWAXad0oYwSr9rgJuN4KtOpv8KtfzaCU4B8\nYtTnlNjrqj+4gOWoKV6spmN66OSnFJYD9inHo84gS3Pf1zKvAvy2BHf6TRrI/wP2tMwnerEqredS\nJyCjZHVgZ8t8rAr9z6qNbxZcwHLUnGwq5yrLPCYN5AJl+NMpqNB/lGKSwskySuatNr5sMjX286i8\nD70OnF+OR51BlsZuX+MXgUtKcGemcAHLUS+OpFLNfW7aT++uGTkMyPcsmg8z5daM/ALYwLId5MVq\ncrXBjpqxPbC2ZTtAhX7Tq+C7gOWoC16sPqYo67JLGshRJbjTMajQf5fig8FeMkpWKsOf3siKyu00\n9vspFkI7aoiMknkoquDfpkL/gTL8mVlcwHLUkz9gGu71IIALnc5g3TkbeDO37QEXNJnO4NFAvlZs\nGnCAS2OvOydgeqj1MJkWKjR3Nw5H3fBiNRU4wDKvRXGx11FDMoWCgyzzj4HflOBOgTSQy1O8SZ7j\nxeq/ZfjTKcgokcDelvlUFfqvl+HPQHABy1FXvFjdR7Fq/ow0kPOX4U8HcRtmii3POTJKuspwpocs\n0eIiTO+0Ht4FTizHo85ARskQjCJK/p7/Bi1WYO4ClqMRHEBlW/cRwGkl+dIRZEoF+wBTcubvUn5g\n2BrztpfnQC9WX5XhTAexE2Z2I89+KvQnVhnbtAw4YAkhRggh7hdCvCqEuE8IMU8v494SQjwnhFBC\niKcG7qqjVcl0Bm0lg13TQK5bgjsdgwr9Vykqne8to2TVMvxJAzk3Rd26+4FbS3CnY8gaM9q/B7ep\n0L+zDH8Gw2DesH4P3K+1XgYjlmh3nu1BAz/SWkut9RqDOJ+jtTmHygQMgIsz0VNH/TgVM/XTwxDg\nkpIUMI4DFsptTwX2cYkWdedkID8FP5Hi2nJLMJiAtQVwTfb9NUDQx9hmyk5ylIAXqykUG8T9H0YV\nw1EnsikfW2VkdWC3RvqRKVrsb5nP9GL1aiP96DQyRYvfWeaTVei/VYI7g2YwAWtBrfVH2fcfUdnS\nOo8GHhBCjBVCNPSPxNFceLF6CIgs8/FpIFuqFUaroUL/borTbqfKKOntb7amZGUMl1HZIPB/mCd/\nR52QUTIUc93zLwwJxTqslkFo3fvbuBDifsxCrc1RwDVa63lzY8dprUdUOcZCWusPhBDfwcxX76u1\n/md+THd39zdOJEky8z+Fo2UY+tWXLH/JMQyd9K0Yw+fLr8ZbW+1Rolftz7ipgmNfn4vJ+tt719pd\nU9hl4fqvuc8/9kFG3nN9he2NX+1F97Ky7ufuZO79bDi3fDxbhW3/kV+z0pyNFbTwff+b77u6ugY1\n29ZnwOrzg0K8jFmb+lAIsRDwoNZ6uRl85jjgK611RY+kfMAa7A/UCYwdO1aPGjWqZa9TGsg9KTYd\n/JkXq5ovArf6taolMkoOpvh0vaEK/X9Afa5VGshFMGuXc+XMtwE/b+W1q2b/vZJRsgRGHzAfsW5Q\nob9to32p5f19MFOCtwM7Zt/vCMT2ACHE7EKIubLv5wA2Bp4fxDkd7cFlwNOW7ZIsi8xRPy6g+Pd3\nuYyS2et4zj9QGay+wiVa1JVM0eQSKoPV58CB5XhUOwYTsE4DfiKEeBUjYHkagBBiYSFEz5Pyd4F/\nCiGeBZ4E7tBa3zcYhx2tjxerFLMQnObMi2Iy2hx1QoX+VMx1zweLJamTOG4ayJ9TTMY6wovVu/U4\nn+MbtsW8HOQ5RIX+R9UGtxIDDlha63Fa64201storTfWWn+R2d/XWm+Wff+G1nqV7GslrbW7ITkA\n8GKlMJp3efZKA9kSXXJbFRX6j2OUJvIcJKOkpqLEaSC7MG9XeZ4ELq7leRyVyCiZj6Ko8EPAnxrv\nTe1xSheOMhkDvGbZrkgDOWsJvnQSRwLv5LaHAFdOq+0k3SnAwrntacBu2du1o36cRWXN1WTgd5ny\nScvjApajNLxYTaRYD7QsRsnbUSdU6I+nWJvz/Xs/m6Umx88UTOwuwmd4sXLr13VERslGGAmmPCdm\niidtgQtYjlLJarMut8yHp4H8fgnudAxZbdaf87Y7Pp0FGSXLDua4aSBnB66msvbnNeCkwRzX0Tcy\nSuYGrrTMLwBnluBO3XABy9EMHAZ8kNseClzpZJvqzoHAZz0b00yN1uWZsvdAORlY2rLtnr1NO+rH\nmcBiuW0N7K5Cf0ov41sSF7AcpePF6guKsk2jMIHMUSdU6H9CUS7phwxQLisN5A+rHO9iL1YPDuR4\njv4ho2RjYHfLfE6WYNNWuIDlaAq8WMXALZZ5TBrIlcvwp4O4Hrjbsp0qo6RPEQCbbCrwKiqnAt/C\nPXTUlay/2RWW+RXgmBLcqTsuYDmaib2BT3Pbw4Br00DWJhvAUSDLHtsd6M6ZZwWuzbTo+sspFKcC\nd3F9rurOWcDI3PZ0YOdW63PVX1zAcjQNXqw+pkr2GqYthaNOqNB/F9jXMq9O7y2DKsimAu1pxD+6\nqcD6IqNkE+C3lrktpwJ7cAHL0VR4sfoLVvYaJmvQ7pbqqC3Xybmm2rbjZJSs0teHMjmtq6mcCnwT\nOLym3jkqyJoy2lmBrwDHluBOw3ABy9GM7Au8n9seAlyTrZM46oAKfb39dycCfJIzDwUiGSV9Tcle\ngJF3yuOmAutIphV4KbBIzjwd2KldpwJ7cAHL0XR4sfoc2NUyL0Ob1ZQ0G3MP1VCckl2JXmqo0kD+\nmm8FsHu4MKutc9SPHYFfWrYzVeg/UYYzjcQFLEdT4sXqHsxTZJ690kBuWYY/nYIK/b9SbLJ5SJY6\n/Q1pIEdS/P95ETcVWFdklCwFXGiZ/02bTwX24AKWo5k5BHjDsl2V9Vhy1I/9AFtR/VoZJQsApIH0\ngGuBeXL7pwDbuQLh+iGjZBhmfXfOnHkisF27FQj3hgtYjqYlWwfZBiOc2sMI4LrspumoAyr0vwC2\nw6yL9LAgcHWmgnEw8CPrY0d4sfpPYzzsWI4G1rRsB6nQf7kMZ8rABSxHU+PF6imKYrg/wk091RUV\n+o9QXLvadMs3/342Rn4pzwMUW1o4aoiMkh9T/Dv4G8Vp2bbGBSxHK3Am5qaY54Q0kGuX4UwHcSLw\nWM9G1+Tx7PbSLQdgsgd7GAfs6MVquv1hR22QUfJd4AYq79cfAbu2S9uQ/uIClqPpyW6GO1CpguEB\nN6WBnL/6pxyDRYX+NMzUYLfQ0zl+7B/47sTP7GG7eLF6v/hpRy2QUeJh5LMWzJk1sEOmBdlRuIDl\naAm8WH1AsdfPSOB6t55VP1Tovw3stsOrt/ODD1XFvumIc7xY3VaOZx3DccCPLdvJKvTvK8OZsnEB\ny9EyeLG6EzjXMv8EJ91UV8be+usP937hhoqpp/+MWIb1try28LrlqB1ZKYG9bvUgplN3R+IClqPV\nOBx41LIdkwZyszKcaXfSQC4E3DgE/Y300hfD5+TINQ9g0tBZTpRRsmGJ7rUtMkoWw6Sw5yWvPgK2\nVaGfluNV+biA5WgpvFhNBbbG/PHmuS4N5BIluNS2ZCr5twIL5+3HjdqHj2afH8z94wYZJYuW4F7b\nIqNkdiAG8uuz04FtVOh/WI5XzYELWI6WI1vk3xrIP2nOA/w1DeSc1T/lmBnSQArgIqAiE/OleZa4\n6bGFVs1PD34HuFVGyWyN9K9dyXQCrwCktes4Ffodr37vApajJfFi9TDF9hcrA1EaSPd7PXj2oqjn\neN/yX7y5HcU1lDWAK7ObrWNwHIopls8TY/qNdTzuD9vRypyNmbLKE9CLWKujf6SB/BHFQuDXgN94\nsUox1/cua/82wFH19659kVEyGjjNMr+ISWF3dW64gOVoYbxYaUyquy0JdEQayO0b71HrkwZyWcxD\nQL44+Ctgy0xFn+zmuS3wkvXxE2WUbNUQR9sMGSXfB26mMsniCyBQoT++HK+aDxewHC1Npje4BcUk\njCvTQK5Tgksty9CvvgS4G6PXmGc7L1b/zRtU6HcDm2OULvJEMkpWq5uTbUiWtHIXMFfOPB3YWoX+\na+V41Zy4gOVoebxY/Q8zFTg5Zx4O/G2WTz8ox6kWIw3kHEvefCGAnWl5tBer26t9RoX+68BWVIoT\nzwbclbXBcMwAGSVzA3dS2YwR4JBOLQ7uCxewHG2BF6snKCYJjFj6+vNIA+nSrvsgUwq5fo7337J3\nXckMFvtV6D8E7GmZFwDuk1GyYPETjh6ydiG3AN+3dl2IExOuigtYjrbBi9WfgePztuFfjgO4Jw3k\nvKU41eRk6et/xEyr5rkX2DNbJ+wTFfpXUOwGvSRwd/YG4bDI2rRchVFqyXMbcGCnidr2FxewHO3G\n8cBllm1F4G9pIGcvwZ+mJQtWZwO7W7v+A/w6K9LuL7+n2KlYAn+RUTLLwL1sP7L0/z8CdmLQU3S4\nktmbYicAAAvHSURBVMWMcAHL0VZkbwR7AX+1dq0L3JYG0hW4fssY4EDL9i6wmRerL2fmQFnm4K7A\nPdauDTGFxS5o8U2wOhP4nbXrDWBzFfoTGu9V6+AClqPtyGqFtgX+ae3aCKOGMWvjvWou0kAeChyb\nt02dfS6An3ixem8gx1ShPxX4FfC0tWsz4CYZJcMHctw24zhMx+Y87wMbqdD/uAR/WgoXsBxtiRer\nScAWExYcae/aBLg108nrSNJAHgWcYZm/eH27A/FiNah26yr0v8IEKLtGa0vgxizRoOOQUSJklJxM\nsbPAp5hg9WYJbrUcLmA52hYvVl+8tt2BAM9bu34K3J4Gco7Ge1UeaSBFGsiTKCqBfA1sOrEY3AdE\n1lhwA+AVa9fPgVtklHTUG242DXg2cKS1qxvYWIW+HdwdveAClqOtSc0014YYiZs8GwMPpIG0i2Tb\nkizB4kyK8kkTgJ9lZQE1I1MV3wBIrF1bAPd0SvZglg34B4prheOBTVXoq+KnHL3hApaj7fFi9Qkm\naNlPsmsBD6eBXLj4qfYhDeRw4FqKayfjgY29WD1Uj/Oq0H8f0y3XVmtYH3hQRskC9Thvs5Ap2N+E\nSQLK8zmwoQr9xxvvVWvjApajI/Bi9RHwI+Df1q6VgMfTQNrFm21BGsh5MJl7dgr1F8BGXqweq+f5\nVei/hwlQL1i7VgUek1GyXD3PXxYySuYHHgB+ae36FPixCn07McXRD1zAcnQMXqw+xjzxP2ztWgx4\nLA2kXTzb0qSBXBx4DPMz5/kU+LEXq6ca4Uf2prU+YE87Lg08kbWCbxtklPjAvwBby/IDYH0V+rZY\ns6OfuIDl6Ciy+qJNAVsfb04gTgN5eLbe09KkgdwEeAZYwdqVAGt7sXq2kf6o0B+HKSuw9fG6MIoY\n+7VDPy0ZJZtj0vp9a9d/gbVV6P+3+ClHf3EBy9FxeLGaiBFtvdjaJTD9iG5tVSmnNJBD0kAeTXXV\n9X8B63ixKkUBXIX+1xiF9z9Zu4YA5wPXt2oyhowST0bJiZgHoS5r94PAuir03268Z+2FC1iOjsSL\n1TQvVnsBewO2FM7PAZUGcq3GezZw0kAuglmvOpHKvkpgRFY38mL1acMdy6FCfwpGEeMQwNbL+w3w\n71ZrTyKj5HvA34Gjq+y+DhitQv+LxnrVnriA5ehovFj9ERiNSULI8z3g0TSQJ7VCkXEayF9j6s1s\nMdXpwBHA1tmbZemo0Ncq9M/GvG3ZzQmXAh6XUXJMsxcZZ8XAIfAcZo0uT4pJZd8hC9KOGuAClqPj\n8WL1ALAaMNbehalbUmkg1264Y/0gDeTINJC3YtKn7WnMz4BNvFid5sWq6Vqsq9C/E1gdc8PPMww4\nARjbrG9bn0wRYKb/rgXsacyPgA1U6J/nVNdriwtYDgfgxeoNjEDuuVV2L4/JIvxTs9RspYGcJdMD\nfBn4RZUhDwOrZsG4aVGh/wqmHs5eTwTTJ+opGSWXNktvLRkls8ooOfq4N+YC+FmVIfcDq6rQf6Sx\nnnUGLmA5HBlerKZ4sToIcyN639otgJ2AJA3kcVl9U8NJAzk0DeTOGNmjMwC7ZcoU4FBgg6wTc9Oj\nQn+iCv29MIHXFoAdgml/ksgoObKspAwZJcNklOyOybI8caouJDROAvbDrFfZvzuOGiG0Lv+Ntbu7\n+xsnurq6Wj61td6MHTtWjxo1yl2nfjDQa5UFpLModjHu4UvMW8G5WVFyXcnaomyPUatYtpdhTwG7\nebGyp9j6RTP8XskomQ/TbdcudO7hC0xH3gtU6Nc9gURGyRzADpjrvlQvwx4DdnOagNWp5f19wAFL\nCPErTD+d5YDVtda2gkDPuNGYX0APuEJrfbo9xgWsmaMZbiytwmCvVRrIjTAp13Y9Uw9TMV1irwLu\ny1qb1ISsHuz7mJv3zsB8vQz9HJNYcflg1qqa6fdKRsmmmPvGMr0MmYzpeXYl8I+sH1etzi0wzSd7\nrntvb9OfYt5mr63l+duNZglYy2EykC4FDq4WsIQQHmbqYiPgPUxB3TZa64onERewZo5murE0O7W4\nVmkghwK7YRIB5u9j6EfAHcCdwCNerD4bwLmGYxQSNsFk0a3Yx/CpmL+/EzMVj0HRbL9XWf+sPTEt\nOfqqi3ufb6/7P1Xofz6Ac82KWcPcGCPQ25dk1OSNRkye5YFxs8yvQn+m/487jaYIWN8cQIgH6T1g\nrQ0cp7UenW3/HkBrfVp+nAtYM0ez3ViamVpeqzSQXZi6rQPpO3D1kGC0C18DXsc8kX+JWe+YBZgN\nWABYFDPdJDHahjNqdJgC1wAneLGqWTFqs/5eySgZAeyLWSPqj7r+K3x73d/AXPfxVF73BTHXfWnM\ndV8Rk53YF9Mwb3QnXb589zvNeK2akVre34cO3p0+WQR4J7f9LrBmnc/pcNQFL1bdwClpIM8Dfgvs\nQ1GCJ48/g/0zy+fA5cBFrZJQUQsyWafjZZScjUnA2BtYso+PLEvv63wD4TPgEuDiTMyXsWPtCghH\nI+jzDUsIcT/w3Sq7jtRa/y0b09cb1lbAaK31btn29sCaWut98+PyEdjhcDgc7Uld37C01nbV/Mzy\nHpBvYzoS85blcDgcDsdMUas6rN6i5ljAF0IsLoQYDmxNUSXb4XA4HI4ZMpgswZ8DF2AWn7sBpbXe\nVAixMHC51nqzbFxPeqoHXKm1PrUmnjscDoejo2iKwmGHw+FwOGZE6dJMQojRQoiXhRCJEOLwsv0p\nGyHESCHEg0KIF4UQLwgh9svsI4QQ9wshXhVC3CeEmCf3mSOy6/eyEKKturf2ByGEJ4RQQoieRCB3\nraoghJhHCHGLEOIlIcR//3975/MiRxGG4eeVXYO6Em+auMIunuJFSWQTxSBIwB9I4jGXIPoPKB6i\n5i/wIv445KJENOgqqIQIHlS8CIIrmJUlMeiAQVfZVRQNejGB10PV7k4mPbOZHNIZ9n2gmeqaabr6\nYXq+6e76qiTtjKv+1OM/KWlB0juSNsVXQdIRScuSFrrqhnYjaUf1+4OkV9bdse3WFsptwg4wRcmB\nmAe2tdmmthdKr8y7anmCklOyjTJu3MFa/yzwQi3fUb2NV48d4Jq2j+MKO3sGeBs4XtfjqtnTm8CT\ntTxGmWgwrppdTVFyuDbV9feAx+Nr1c9uSv7aQlfdMG5W7u7NATO1/DGlV3nf/bZ9hTUDdGyfsX0O\neBfY13KbWsX2ku35Wv4H+I6Sz7aX8oNDfX2slvcBs7bP2T5D+TLMXNFGt4ikSeAR4HXWOv/EVQ+S\nNgO7bR8BsH3e9t/EVT/OUkYSuV7SGGWQ4V+JLwBsf0HJC+xmGDc7JW0BbrQ9Vz/3Vtc2jbQdsJoS\ni29tqS1XHZKmKP9ivgJutr0yyOoyJVMfYCsXpgpsNIcvUcZz6x7LLa4uZhr4XdIbkr6R9JqkG4ir\nRmz/CbwI/EQJVH/Z/pT4GsSwbnrrf2EdZ20HrPT46IOkCeAD4CnbF8zK6nL9PMjdhvAq6VHgN9sn\n6JNaEVerjAHbgcO2twP/As91fyCu1pB0O/A05RbWVmCiDnywSnz15xLcXBZtB6wkFjcgaZwSrI7a\nPlarlyXdUt/fwtq8Qb0OJ2vdRuBeYK+kH4FZ4AFJR4mrJhaBRdtf1/X3KQFsKa4auRv40vYfts8D\nHwL3EF+DGOa8W6z1kz31A521HbCSWNyDJFEG2Dxl++Wut45THvpSX4911e+XdK2kacrYdXNsAGwf\nsn2b7WlgP/C57QPE1UXYXgJ+lrQyXcce4CTwEXHVxGlgl6Tr6jm5BzhFfA1iqPOufifP1t6qAg50\nbdPMVdDb5GFKT7gO8Hzb7Wl7Ae6jPI+ZB07U5SHKKNWfAd8DnwA3dW1zqPo7DTzY9jG05O1+1noJ\nxlWzozspU/x8S7li2BxXA30dpAT1BUongvH4Wj3WWcqzvf8o/RCeuBw3wI7qtwO8ut5+kzgcQghh\nJGj7lmAIIYRwSSRghRBCGAkSsEIIIYwECVghhBBGggSsEEIII0ECVgghhJEgASuEEMJIkIAVQghh\nJPgfzHQJneNu4R8AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10af1f050>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"signal_1 = create_sine(10, 100,0.1)\n",
"signal_2 = create_cosine(10, 100,0.1 )\n",
"plt.plot(signal_1, label=\"Sine\")\n",
"plt.plot(signal_2, label=\"Cosine\")\n",
"plt.title(\"Correlation={}\".format(np.sum(signal_1*signal_2)))\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The correlation between the sine and the cosine wave is zero. Often, the two waves are on the other side of zero. Thus, they have a zero correlation."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Correlation between a sine and the same sine of 1 Hz "
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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0kS4+BR4/gPaSU1WMbzn6wyFBE2NVzMRUcNGpStdoO+f0jGlbkYam0efWhvgF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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10af8b790>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"signal_1 = create_sine(10, 100,0.1)\n",
"signal_2 = create_sine(10, 100,0.1)\n",
"plt.plot(signal_1, label=\"Sine\")\n",
"plt.plot(signal_2, label=\"Sine 2\",linestyle='--')\n",
"plt.title(\"Correlation={}\".format(np.sum(signal_1*signal_2)))\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The correlation of a signal with itself is high. This is the key intuition behind DFT. We'll be trying to find out those frequencies which give us high correlation with our signal."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Thus, we will now try and see the `correlation` between our signal and a cosine wave of different frequencies. We also create small helper functions to create sine and cosine waves containing `k` periods in `N` sample points."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def create_cosine_k_N(k, N):\n",
" return np.cos((2*np.pi*k/N)*np.arange(N))\n",
"def create_sine_k_N(k, N):\n",
" return np.sin((2*np.pi*k/N)*np.arange(N))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We already know that our signal contains a 0.5 Hz component. This component would correspond to 5 time periods in 10 seconds (N=1000 sample points). Let us see the `correlation` between this cosine and our signal `x`. "
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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0FmGPhJIPeoKrK4FfuFzjWd8SkSdFZK6j2JPvUERmiMir9AxXdwLzXK5J4UpE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\n1AAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10b2e4050>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cos_5 = create_cosine_k_N(5,N)\n",
"plt.plot(x, label=\"x\")\n",
"plt.plot(cos_5, label=\"cosine (0.5Hz)\")\n",
"plt.plot(cos_5*x, label=\"cosine (0.5 Hz)*x\")\n",
"plt.title(\"Correlation={}\".format(np.sum(cos_5*x)))\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"No! This correlation is so very low! But, wait a minute, how about `correlation` with the sine of the same frequency?"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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5tPt7Op4qcfPBI3nOJDAXMYtxTth85mw7ESRqtxi5ajCO13vbAr2uNUeGoucq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\nr108+W99fX3/xqdv5Nivf4jYZD4XW8uTH7w2m+5zi+ctDc0XX8mRt12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Qw3aeQxiDRXUP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gnw0SD7Mrqcvx43WjI+qSXjHwfOGg3AVYba+Ww+RUvGbwCOCdKv0tTNZ/MpWjLerSXjJ4+zoKDg\nnufep2jJeK+WjJ8+Rb0z1b+C8fltPg2MOSOwLAi0Eo48bgAYCqRheQQszjME07Cona9OBDaMywUF\neZjn3qd5DMvmggvCCTmvvU8DY44KrEBaQySwgnIla8spc7+/YGRMNhZc5abnsfnUinEaC/Iwz71P\n8xincZ8u/afaSea192lgzEWBNRjEpXZK1r9QgWepdgwGcalNU1vJLNZVCS0ZzwYxc6Wp213omvmA\nUdlYUGuYpD4S7oBEDBYyzY/LBZE2GgBzUWAV1Bp0KRiQC30LRc4TDAX0qIy4IpiZK01dFCsDDMuW\ngmbkKVk3r/dGLShomp+UDfN6bzQo5qTAKvTjj9Isr77oPfPWQ8mCkSD7MhOyIdJGgTEaC3ppTcm6\nyPUYmKRhIC1jvtdMUR9powYKLrInqI88BANgTgqsQur1qGyMhBXBzVx75eKNFXicqseobCqoEaQj\nbRQAiRiapMH3mnS0j5zDUCHT/BT1kTYaAHNRYA0OyEW+F2SojTYwTQzJloL7CNdcdGnk+QYMyoUF\nnU8mZX0oZe73Aww24J/0Y0rWR5kbDAyOyGbfCyZl/XyOGw2MuSiwRl7UD/G9YAGTc/F7zQg2Zw+O\nPAADIkNdwcqt67NHPFGJZ5kDGNpXYOG4Wy79e4WepdoxNCRbfC8YlAvdqntHUDDnJnYtGc9ulSuG\nB+VCz2v+kDnpkQo+UlUjQ+3Qk/qRnufvT78mEmjTGPpV+p89Tz6WeRnff9ub522mCwVDd6Xf6Hly\nX7aV3syrflvB56lmDP0p0+57wfPZw+6u0LPMacw5gQWQJTZ40+TbGJMLGJML+PnUOeTiHHZml/Ln\nzImfneVHrCYM/mDyAvZlW0nLGPdMncGQaZ6YlHX8JfNPX53l56smDN4+dS5bs8vJSsGf0ifygn5o\n/uSDmVf/bBafrdow+Jv0aTylxwF4Wo/zcOa4/MnfZF779K/efup8ThRsxeAT+tH8Pn0SANuyB/Hr\n9Gn5k79Lnzz8h8wpf52lZ5tTmCsFHFUM/SFzMg9l1pJFkKaee9JncGzsmU3r9KO+/cDbX/2n2X7A\nKsLQM9kj+fex/6aeNOM08qOpTk6ofWzzBn31fVtk2/Wz/YBVhKHd8gDePXYtLYwyQgsNTHJSbd8L\nW7Irn0hlV783ku55DE1Rz5Xjn2UhwwyzkBp0jo+t2ztJ/VNP6/F3fWS2n7B6MASC6ybfy3cn384I\nxoLx/vRrWCwG1z2uH/MBM/dghAKYswILwOqltEcuve76i95xxaw9UfViCECnlnHz5x6h5dfXXXTJ\n2bP6VNUJ00FFMIKx5zBJw+brL3rH6ll8pmpF3plnGMM8nyXGI/pxq7RkPHLRtiPPVa5fATybPaJd\nS8YjzaoIzEmTIODmURPFfLgj4io4Iq6Cw42rKSyl4SPk4eUBGPWtIjFXBZZbtoHILdQdEVfBEXEV\nHK5cacl4lHVcgZaMT2DRsiyI+laR2J8E1rzPh+eBiKvgiLgKDreg4O0Vf4q5A7c9qihYuEjsTwIr\nSi/kjoir4HDjamOlH2IuQEvG3TwAI3OgNxzpeSJttHjMVYH1lEvbxko/xBzB0y5tkcByh5vW8HzF\nn2LuQC2S2jsrTzE3oMak3TsrTzHHMVcF1h+wD45faMl4VHvHBVoy3g/cYmlKAY/N0uNUNbRkXAes\nnqZjRBOLHy4BspbjKE7NG58ArBnZI65KwJwUWObEchbwOfPv4tl9oqrHu4HLga8Crzf5i+ACLRm/\nDkgC1wPtWjIebYx7QEvG7wXOxuDqdC0Zj1IxeUBLxp8GTgWuBd4O/HB2n2huQkg5+2bUwcHB/EO0\ntraK2XyWuYC+vj65du3aiKcAiLgKjoir4Ii4Co4w5/c5qWFFiBAhQoT5h0hgRYgQIUKEOYFIYEWI\nECFChDmBSGBFiBAhQoQ5gUhgRYgQIUKEOYGSBZYQ4i1CiKeEELoQ4lU+120UQjwhhNCEEH8r9X4R\nIkSIEGF+o5zyIuuATuC7Ba6TwGlSyqiybYQIESJEKBklCywp5XoAIQK51UfxChEiRIgQoSxUYg9L\nAr8VQvQJIS6twP0iRIgQIcJ+CN9MF0KIB4AVLqc+JaX8hXnNH4CPSikf9fiMlVLKbUKIA4EHgMuk\nlH+2XmONhI4QIUKECPsnys104WsSlFKeUc6Hm5+xzfy/SwjRDZwA/Nn/XREiRIgQIYIdYZkEXaWm\nEKJJCLHQfN0MnInhrBEhQoQIESIUhZKT3wohOoEbgGXAIKBJKc8WQrQBN0kpzxFCrAbuMt9SC/xI\nSnl1CM8dIUKECBHmGaoiW3uECBEiRIhQCLOe6UIIcZYQYr0QIiWE+PhsP89sQwhxqBDiD2ZQ9pNC\niA+a7UuFEA8IITYIIe4XQiy2vOeTJn/rhRBnzt7Tzw6EEDEzMD3nCBRx5QIhxGIhxM+FEM8IIZ4W\nQpwYceUN8/s/JYRYJ4T4sRCiIeLLgBDi+0KIHUKIdZa2orkRQhxv8psSQnyj4I2llLP2B8SA54BV\nQB1GJdyjZ/OZZvsPwyvzOPN1C/AscDRG4bcrzfaPA181X7/M5K3O5PE5oGa2v0eFOfsI8CPgHvM4\n4sqdp1uBd5qva4HWiCtPrlYBzwMN5vHtwL9HfOX5ORVIAOssbcVwk7Pu/Q04wXz9K+Asv/vOtoZ1\nAvCclHKjlDIN/BQ4b5afaVYhpdwupXzMfD0CPAMcDJyLMeFg/u8wX58H/ERKmZZSbsToDCdU9KFn\nEUKIQ4A3At9j2vkn4kqBEKIVOFVK+X0AKWVGSjlIxJUXhoA00CSEqAWagH4ivgCQRmjSPqW5GG5O\nFEKsBBZKKXMp+26zvMcVsy2wDgY2W463mG0RACHEKoxVzMPAcinlDvPUDmC5+boNg7cc5huH/w18\nDMha2iKunHgJsEsIcYsQ4lEhxE2m527ElQukkUruOmAThqAakFI+QMSXH4rlRm3fSgHOZltgRR4f\nHhBCtAB3Ah+SUg5bz0lDf/bjbl7wKoR4E7BTSqnhEVoRcZVHLfAq4H+llK8CRoFPWC+IuJqGEGIN\ncDmGCasNaBFCvN16TcSXNwJwUxJmW2BtBQ61HB+KXeLOSwgh6jCEVZeUssds3iGEWGGeXwnsNNtV\nDg8x2+YDTgLOFUK8APwEeJ0QoouIKzdsAbZIKR8xj3+OIcC2R1y5Yi3wkJRyj5QygxGe007Elx+K\nGXdbzPZDlHZfzmZbYPUBcSHEKiFEPfBW4J5ZfqZZhTCyCd8MPC2l/B/LqXswNn0x//dY2i8UQtQL\nIV4CxDE2Mvd7SCk/JaU8VEr5EuBC4PdSyiQRVw5IKbcDm4UQR5pNpwNPAb8g4soN64FXCyEazTF5\nOvA0EV9+KGrcmX1yyPRWFUDS8h53VIG3ydkYnnDPAZ+c7eeZ7T/gFIz9mMcAzfw7C1gK/BbYANwP\nLLa851Mmf+uBN8z2d5gl3l7LtJdgxJU7R68EHgEex9AYWiOufPm6EkOor8NwIqiL+Mp/159g7O1N\nYfghXFIKN8DxJr/PATcUum8UOBwhQoQIEeYEZtskGCFChAgRIgRCJLAiRIgQIcKcQCSwIkSIECHC\nnEAksCJEiBAhwpxAJLAiRIgQIcKcQCSwIkSIECHCnEAksCJEiBAhwpxAJLAiRIgQIcKcwP8HzAZw\nyBKFBv4AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10b4fa410>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sin_5 = create_sine_k_N(5,N)\n",
"plt.plot(x, label=\"x\")\n",
"plt.plot(sin_5, label=\"sine (0.5Hz)\")\n",
"plt.plot(sin_5*x, label=\"sine (0.5 Hz)*x\")\n",
"plt.title(\"Correlation={}\".format(np.sum(sin_5*x)))\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Great! The correlation with a 0.5 Hz sinusoidal has a high amplitude. We're on to something now!\n",
"Yes, we want to detect the presence of a particular frequency and not really worry about phase for the moment. \n",
"\n",
"So, for each frequency that we find our correlation with the original signal, we can have two components- the correlation with the cosine (called the real component) and the correlation with the sine of that frequency (called the imaginary component). This is exactly what those weird looking DFT equations mean! A high absolute value of either of these components suggests the presence of that particular frequency in our signal. \n",
"\n",
"So, for every frequency in 0 to N-1 Hz, we repeat this procedure and obtain the DFT coefficients. Finally, the mathematics looks something like the following:\n",
"\n",
"$ \\mathrm{DFT(K)} = \\sum{x_n\\times \\cos{\\frac{2\\pi K}{N}}} - \\iota \\sum{x_n\\times \\sin{\\frac{2\\pi K}{N}}} $\n",
"\n",
"Now, if you are guessing that there is some relation with Euler's formula, you are right!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us repeat the procedure once again to find the presence of the 2 Hz component. For that we'll have to set K to 20. (2 Hz wave will complete 20 periods in 10 seconds)."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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0NLq+gw3vfGSPm4+bPrbtw12vM/a+Z3nPP17hsRVrC6dHAu/XPnIN7rV1F2G1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\nkmsgUMR2W1qcWff9mvo1qQibDedcyp5jxArA/uJ760aw2aQLr2vqYmZtS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/fZPNmz31Zg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\nWYm3NoefAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10b642350>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(12,4))\n",
"sin_20 = create_sine_k_N(20,N)\n",
"plt.plot(x, label=\"x\")\n",
"plt.plot(sin_20, label=\"sine (2 Hz)\")\n",
"plt.plot(sin_20*x, label=\"sine (2 Hz)*x\")\n",
"plt.title(\"Correlation={}\".format(np.sum(sin_20*x)))\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"How about the DC component?"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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RxUI7IqaLUxciaZCInJXAn3KWBy0fl76i7U6U1BqRjpNCR2RTroWLN/rZ3azd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EybQ+UcksYmrYJ00NLHAOAW/q7fvRutfVekBnRIJbFPoqd8Vw+fWVgE48nkElhIaMLvNtZt2vrs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\nREXDBQkRERERERXN/wN3uAMYDFN+nwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10b70c910>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(12,4))\n",
"cos_0 = create_cosine_k_N(0,N)\n",
"plt.plot(x, label=\"x\")\n",
"plt.plot(cos_0, label=\"cosine 0 Hz)\")\n",
"plt.plot(cos_0*x, label=\"cosine (0 Hz)*x\")\n",
"plt.title(\"Correlation={}\".format(np.sum(cos_0*x)))\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Using numpy's DFT implementation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, instead of rolling out our own implementation of DFT, we'll use the efficient inbuilt numpy DFT implementation. Now, the DFT implementation is called fft. But, let us not worry about it for the moment."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"fft_x = np.fft.fft(x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So, the `fft` routine returns an array of length 1000, which is equal to the number of samples. This refers to the 1000 DFT coefficients, from K=0 to 999."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"1000"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"len(fft_x)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(-499.99999999999977+0j)"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"fft_x[0]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The above was the DFT coefficient for K=0. It has two components (real and imaginary) arising from the cosine and the sine waves respectively. However, we are concerned with the amplitude of the signal. This can be done by considering the absolute value of these coefficients.\n",
"\n",
"We will now plot these DFT coefficients."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x10b7471d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(abs(fft_x))\n",
"plt.xlim((-100, 1100))\n",
"plt.ylim((-5, 520))\n",
"plt.xlabel(\"K\")\n",
"plt.ylabel(\"|DFT(K)|\");"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"Now, barring the zeroth point, the remaining signal seems to be reflected about the middle value of K. This is what we'd expect as per the Nyquist sampling criteria, sampling at fs, we can't see a signal of frequency more than fs/2. So, all that information is redundant. We'll thus plot only till fs/2 now."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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JWsXGFmwDbKyq2W57FtjYbZ/O4SH2MHDGEp5n3o5ty66ZDcAX6dXhLcBBYPsSnkeStMJS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\nwSZJaorBJklqisEmSWqKwSZJasr/ByfcRDIIjWGhAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10b3cbdd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(abs(fft_x)[:500])\n",
"plt.xlim((-5, 500))\n",
"plt.ylim((-5, 520))\n",
"plt.xlabel(\"K\")\n",
"plt.ylabel(\"|DFT(K)|\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The above plot isn't focused enough to allow us to clearly see what's going on. So, let's restict the x axis to 120."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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4r7YKuAc4bWJtyupgm27Hh4YrAmonocwb3TjY8C9jaLiyG/i5Oi+9e3Tj4H3T+fxuGBkZ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\nYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10aa3afd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(abs(fft_x)[:500])\n",
"plt.xlim((-5, 120))\n",
"plt.ylim((-5, 520))\n",
"plt.xlabel(\"K\")\n",
"plt.ylabel(\"|DFT(K)|\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Ok, at K=0, 5, 20, 100, we can see spike. Now, remember that K refers to the number of periods completed in N in 10 seconds. Thus, the frequencies correpsonding to these K are: 0 Hz, 0.5 Hz, 2 Hz and 10 Hz respectively. The above plot with frequency on the x-axis would look like the following."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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GRkb2LA8PD+fq9SstzLJ5HtcDP4+I9zVsvyTb9vEswJZExOQAkKupnydbAdwK/NbkXJCN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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10a40d890>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(np.arange(0, 500)/10.,abs(fft_x)[:500])\n",
"plt.xlim((-1, 12))\n",
"plt.ylim((-5, 520))\n",
"plt.xlabel(\"Freq(Hz)\")\n",
"plt.ylabel(\"|DFT(K)|\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Energy preservation under the transform"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The energy of the signal in the time domain is given by: $E_t = \\sum(x^2)$, and in the frequency domain is given by $E_f = \\sum(X^2)\\times1/N$"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"455.0\n",
"455.0\n"
]
}
],
"source": [
"Et = np.sum(x*x)\n",
"print Et\n",
"\n",
"Ef = np.sum(abs(fft_x)*abs(fft_x))/N\n",
"print Ef"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So, we can see that the energy is preserved under the transform. A very quick check now. How about the energy of the individual time components and their frequency transform equivalents?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Energy of DC component"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(250.0, 250.0)\n"
]
}
],
"source": [
"Et_DC = np.sum(-0.5*components[0]*-0.5*components[0])\n",
"ft_DC = np.fft.fft(-0.5*components[0])\n",
"Ef_DC = np.sum(abs(ft_DC)*abs(ft_DC))/N\n",
"\n",
"print(Et_DC, Ef_DC)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Energy of 10 Hz component"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(5.0000000000000018, 5.0)\n"
]
}
],
"source": [
"Et_10hz = np.sum(0.1*components[1]*0.1*components[1])\n",
"ft_10hz = np.fft.fft(0.1*components[1])\n",
"Ef_10hz = np.sum(abs(ft_10hz)*abs(ft_10hz))/N\n",
"\n",
"print(Et_10hz, Ef_10hz)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So, there you go. We can see that under the transform the energy remains the same. This also tells us how to interpret the DFT coefficients. These coefficients are an indicator of energy contribution in the aggregate signal. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### FT of a square wave!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Can we construct a square wave from a combinations of sinusoids? Let us think the other way around. Can we decompose a square wave to get sine waves of different frequencies? Let us use our new friend's help"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"sqr_wave = np.hstack([np.ones(250), np.zeros(250), np.ones(250), np.zeros(250)])"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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YDg1lYHWTSyRluCRYhv29JQwsSVIjGFjd5IizDGdYZdjfW8LA6iYvlPVgO0yGdW4JA0vg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\nkiQ1goElSWoEA0uS1Aj/H6OSbYxcFdTCAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10af7ce90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(sqr_wave)\n",
"plt.ylim((-0.2,1.2));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The above is our square wave obtained under the same experimental setup as above- 100 Hz sampling for 10 seconds. Let us do a DFT on it and plot it."
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"dft_sqr = np.fft.fft(sqr_wave)"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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yTyUBbLq7904AuZZ4nGwOsAx4Ue9akOlgVvZgByoIo0OBXzep9mz3ws6OVrRnKHV1dfmC\nBQta8roOJx3nyDEajhFGx3HuzOd7K88T+zPi5a9+a2bdSdli4FLgBjM7m2RqPoC7LzezG4DlxGNV\n59dgUeMyY2bqZhQRabGWBTN3/zn5E06OyXnMEmDJkDWqujJjZpoAIiLSYqNtOaqBKpOZjQ3CSK+r\niEgL6UO3mjKZGSg7ExFpKQWzaspkZqBxMxGRllIwq0aZmYhIDSmYVaPMTESkhhTMqlFmJiJSQwpm\n1SgzExGpIQWzapSZiYjUkIJZNcrMRERqSMGsGmVmIiI1pGBWjTIzEZEaUjCrRpmZiEgNKZhV0L2w\n063c9UGVmYmItJCCWUUlXzBlZiIiLaRgVtGYcpfEU2YmItJCCmYVlQxmysxERFpIwawidTOKiNSP\ngllFY00TQERE6kbBrKJyvYzKzEREWknBrKKxmgAiIlI7CmYVacxMRKR+FMwq0tR8EZH6UTCraEy5\nFUCUmYmItJCCWUXKzERE6kfBrCKdNC0iUj8KZhWVfMGUmYmItJCCWUXKzERE6kfBrKKxugSMiEjt\nKJhVpMxMRKR+FMwq0piZiEj9KJhVpMxMRKR+FMwqGqNV80VEakfBrCKtzSgiUj/jhrsB7Wag3YxB\nGB0M/Alwe/fCzicHqVkiIqNayzIzM/umma0xs3tTZTPMbKmZPWhmt5nZ9NR9i80sMrMHzOzYVrWz\nmYFMAAnC6AjgHuBa4L+DMNpt0BomIjKKtbKb8UrguEzZImCpux8I3J5sY2bzgVOA+cljLjezWnSJ\nlryeWV5mdjo7At1M4IRBaJKIyKjXsgDh7ncCT2eKTwSuTm5fDbwhuX0ScJ27b3b3FcBDwGGtaGcz\nNrCTpvfMbM8aWGtERASGfwLILHdfk9xew44P972Alal6K4E5rWxYngFmZtluRXUziogMgtpMAHF3\nNyuc9557X1dXV6l0aTCMYVLTOnMmbn15ozbts8tUHtswdvv2UdM3Lu7q6lo8uC0cPK18XYeTjnPk\nGA3HCCP/ODs7Oys/ZriD2Roz29PdV5vZbKB3dt8qYG6q3t5JWUMLFiwoly8Ngisfv6/Rm2gzqWxs\n1caxDyxYsODgbKXH7o/+B9i/d/uOZyZed9kJL/nrIWnoAHV1dXkrX9fhouMcOUbDMcLoOM6enp7K\nwXq4uxlvBs5Mbp8J3JQqP9XMJpjZPKAT+OUwtK+fnBfs+cx23piZuhlFRIZAyzIzM7sOeDWwu5n9\nHrgYuBS4wczOBlYAJwO4+3IzuwFYDmwBznf3WqTVOSuAPA9MT233GzMLwmgM0JEpnp6tJyIi1bUs\nmLn7aTl3HZNTfwmwZOhatHNyTppen9lulJlNo39ip8xMRGQQDHc3Y9sZ27g4283YaDZjoyxMmZmI\nyCBQMKvIGmdmZcbMFMxERIaIgllFA8jMGnUpTgzCqPlcfxERKaRgVlHBBJC0splZUbmIiJSkYFZR\nzgu2AdiW2rYgjLJJXN5kD00CEREZIAWzinJmM25OftKy2ZkyMxGRIaJgVlHOC7Yp+UnLjpspmImI\nDBEFs4oGkJmpm1FEZIgM99qMbSdnAsiQZGZBGBlwNLCpe2HnnWXbKCIy2igzqyjnBWuUmWWD2c5k\nZl8FlgE/C8Lo4yWaJyIyKimYVZTTzdgoMxvQBJAgjKYAZ6WK3plkaiIikqFgVlHOSdNlMrOq3Yx7\n07cbuKOgrojIqKZgVlHOclabGPwJII2urF2Lq22LiNSNgllFYxtf8Hozgz8BZO+SZSIio56CWUUF\nY2a5mVkQRuOBKTm7zAtmysxEREpSMKuo4DyzosysaKxL3YwiIgOk88wqKlgBpGjMrCiYDVo3YxBG\nxwPHA8u6F3beWFRXRGQkUWZW0U5mZkXnkk0PwqjR36FSZhaE0WHAD4C/Ab4XhNFrCp5TRGREUTCr\naEzjCSADycwMmNagvGo34xsy228sqCsiMqIomFU0dvDHzPrdn0wY2bNBvaJuxoMy2wc2eU4RkRFD\nwayinCU4mmVmzRYTzt6/Z85T/VEQRrvk7CMbvJoGsyCMXhGE0Wu0soiItDsFs4pakZlR3J24V7Yg\nGXPrzBTvF4TRxLydBGH098AvgR8DVzdpn4hIrSmYVbSTsxmrZmZF3YmN7psLZAOXAQc02kGSib0v\nVbQwCKNG3ZoiIm1BU/MryrkETCszs0b3ZcfL0uXLG5TPBWZmyg4Fbs170iCMXg6cBvwKuKF7YWfD\nF0JEZDgomFW0MyuA0D9Y/YG+wWSgwSxvfCyvPMgpaxjMgjDai7g7ctdU8bfzGigi0moKZhXt5PXM\nst2Ij9A3mA20m7FqMDu0ZFmvk+kbyM6hIJgFYTQZWATMA/6pe2Hn3QX7FhEZMI2ZVbST1zPLZl4r\nMtt1yczyHJnZPiI5fSDPx4APAacDtwRhNKOgLkEYjQ/C6OggjOYV1RMRyaNgVlHBqvlVMzMK7h/M\nMbNGGgWueUEY9RvbSyaLZIPZFOBPGu44jMYCZ6aKZgKvy2lHb/0fAbcDDwdhdFJe3dRjpgdhdHgQ\nRupZEBFAwayyguuZVZkAkg1m2+9PgkfpbsbkvLN9c+rODMJot0z9mQX7bxSgDgBmNSjPBrhehwJ/\nlCn7i5y6AMcAR6e2P1lQlyCMXgasAu4C7io47663/pQgjE4Jwuh1SeAUkRFIwayiCleangDbg1Pp\nYAbMoO80+42ZurMzazkeQO653ED/88+KuhMbjZu9KqduXjBrFLiOzVl/EuBNme2DgzB6cU5dgE8B\nk5PbL6dvFthH8trfAFwP/JC4+zNXEEYWhNGFQRj9KAij84rqph6zRzJBRkSGkYJZRRXGzHozs8n0\nzdI2AKszddPZU7Yb8VHg6dT2OGCP1HZeV2Le/UXBrNF9eUHryJyVQxoFsz2AP+73ZHGmlF1TEnLW\nlUzOhTs2U3x6Tvsgbnu6i/O9SWaa5wzgc8TH8JUgjLKBNtue84j/lquCMPpgUd2k/ilBGH0/CKOL\nyqy6EoTRy4Iwem3Rye8iElMwq6hg1fy8qfnZrOyZ5CctXSfbBbgy+SGnTrNlq7L3D1Yw2wN4UZ8H\nh1EH8Mqc+o2C3J/SNzD3ygsip9L/PXtkwcSRd2S2JwBvbVQxyRwXZ4oX5wWdIIxmA5exIyv+aBBG\n2Sw4Xf/PiTPEE4FL6XvSeqP67wB+A9xGPIkmt4s0ySjfG4TRE0EY/SwIo2aXChqT1P96EEavKKqb\n1J8QhNHJQRgd3axuUn9yEEbzmkwSEhlUCmYVFayan5eZZSd3NApmRZnZquSHnDrZYHVPZrtKMDs4\nmVYfVwyjPRo8Pi0b6I4mtye2YTDLW9l/QRBG+zQoX5hTv192FoTR7sBfNah7bk6X5+von8UuID+Y\nvw9Ij9eNAT7QqGLyfJ/OFH8wb5ZnEEZziDPEXq8FzsppB8TB/7PEa3q+CvhOQbcuwBeS+mcDPw/C\nKPc9kYxJ3kF8KsbtQRh9omC/BGF0EPBb4GHgzuTvUFT/+CCMVgRh9HAQRkVjq71B+91BGP0kCKNL\nmgXLZLz0Q0EY/WMQRnOL6ib19wrC6IKyl08Kwmh+MhbbNHNO2v7iIIwajT83qj8uO94txWodzMzs\nODN7wMwiM7touNsDg5KZPQ2sA7alyiYHYdRbf6DB7AeZ7e33B2E0LVPfgSdS22OAl6a2/4xi2fG0\n4wrqHpk8f29bjPwMDDKBLgij+eSfC3d6gwzqTPqeHtHrRfSdcNLrvTn77leedFU2GlNbGITR/g3K\n30z/tncAee/pS9kxLtjrE0nmm23LNOLglHYE8PZGO04+qN+ZKpoAXJl6/2V9gr7Z9geCMMp29fbu\nezLwPXYso3Y4cFVeYE2ywhuJJzDNA24KwqjhLNnEh4DPA0cBHwa+mFcxCKNJwFLgo8B7gK6iUz+S\n572P+LX8cRBGDb+YpOr/HXAv8VhsV1GQStpyE3A/sCIIo7c12ffLgP8G1gZh9MOgwSzjTP2zgzBa\nk3wpOLFJ3SlBGH0l+fLwlSCMpjSp/5Kka3xpEEb/r6huUv+0IIxuDsLo4qD55KxpyZeHzwVh9NKi\numXUNpiZ2Vjgn4g/IOcDp5nZwcPbqsKTpvMys37djMlSUNnsrPeDqmo3YzabuCWzfWDqwyQ7bvU7\n4BeZsvS39GxW8tvM9vb7k2CS/Wa9NXV7HJD+xhuQPwsT+ge6vKwM4gC9vbssOd5sF2Nan0AUhNGh\nxB+QjZzYoPvwPfQPNhBnpYsy+x4PfDxn3xckWVi6/hE0HgecCTQal/sIjU/XuDTJrNP7ngJ8vUHd\nP862O6n/58THmnVVEEbZGasQB4JDMmXHAxc22PdM4sCXDqK7ADc2ykiCMPr/xMeadl4QRuc3qDsG\n+BZ9g/AewK05+96f+PSQ9P/qJ4IwOidbN6l/LnEXc+//1UuA23L2PQn4PnH3cu8xfiMvoCXvxZ+w\n4//6dcCyRll8ku19iPhvugfx/9O/BmH01px97058Csx5xF8eziPOthtmz0mm/J9J249J6ubte1wQ\nRl8GrgVOIP5b3Z59D6bqH5Ds+wvE74+uZkG+GXOv5xJ7ZvZK4BJ3Py7ZXgTg7pcC9PT0bG94R0dH\nyy5h8uO7fu3vjdKLYbC1e2HnuCCM3gx8J1V+N/AZ4uzl3anya7sXdr4lCKOH6LsQ8DuJJxMsJp6l\n1+uNxB9kX0s3A7ic+B/jX1LlG4nPAftf+v5jng30EL8h0x/k1xF/G01/2N4KfPO8Oc9/96urpiwn\n/iLR60zgm/TtSjwDWE88CzPdxo3ANfTtHvs+EKaO6y2p+/6LvtmLEwewDcn25+kbxJ/JHOP3kuMB\n2J/+3XppW5Jj2Zgc560UnAsHfJd4vAviY/8GMDWn7mbiY34h2T4ceH/BvtPthjioLCjY99uB55Pt\n3YAryP9SehPJ+yM5zpD8LwWbib8APJtsjyH+wM475/EHwFWp7YOIs7hGtgDnA2tTZX9L3y83abfR\n9700Dfgyjb9AbCX+/1qdHOObibtl877M/BT4Ump7DLCEzPhvYhtxd/JjqbIDiDPnRp85vf/zaefS\nf9ISxO/vDwBRqmxX4te8XwZOPH76ccBTx3k08evayEfp++VzbFLWaMLY74CL6fvlszN5vkbDBp8l\nPjUmLe84VxB/CUvPyp5BPCu5UTfqV4Db7zhxj+/2FpT9fK9zMHsz8Bfufk6yfTpwuLu/C4YvmP3k\nrl/7e/oGsxe6F3ZOTtL775fYxeXdCzv/NgijLvoGrTyHEQezH5aoe1/3ws6XBGF0d/K4Zv6euDsj\nd4HhjNnAzaSyoAJLibuBsplinjOIs4CibqZe64G/ofyla64nzj7KZvbXAn9dsu6TwHPEAbSMR4i/\nFZeVDdpFNtN35qxIW7rjxB0JXdnP99p2M0LjmRbDbXz/VfM3ZH4383TmdzOr6N/NmOfBzO9mupOf\nMh7qXti5Gvh5yfr/TjxxIDuW2MgW4m/6N5bc903EExKyXbV5vkqcwZTxO+LMKjtOmeezxN/sy9hA\nnI1EzSombiLOYMo6mXgcp4xHyJnZmeNzwK9L1t0I/EOFfd9J/2/6Ra6k/OfD6or7vpO+49lFttC/\n673Iw8ljynqseZXtnqX/UEeRngp1veK+qxxj7/4HrM6Z2RHAh1PdjIuBbe7+KeibmUVR2c+GwbHk\nkSk8siFeSWnBtE28Y+8XeH6rcVE0jY1e/CXiffs8x0FTtvKjpybwvScnFdadM3Erl8x7jm3A4oem\n8fSW4u8eZ8xez6umb+ZXz47na6sa9cjsMHXsNi590Tomjul7PHneOHMDr9t9I49tGMMnHpnKtoLz\ntCeNcT6y/zp2G+9c9fgk/qMnb25B7JUdmzhrrxd4arPx4YensWFb/r7H4Fy03/PsP2krNz05kR8+\nVTjGzAGTtnDRvs+zfhtc8vA0epq8hm/faz2Hd2zmjqcncM3q4r/PjHHb+MgB6xhn8NGHp/LEpuIF\nRl6/+wZOmrmRe9aN48srC8fdmWjOxfs/x8zx2/jsY1N4cH3x3+fl0zZx3t4v8ND6sXz20SlsLfj7\nGM6F+zzPwVO28rVVk/jVs8V/n3122cri/Z7jD5viv32z9/hb9nyBo3bbxPWrd+H2p4sn+k0ft41/\nmPcc2xzWPWL2AAAHVElEQVQ+9shU1m0t/vscvdtGTttzA//2vxO58Q/Ff/sJ5rx/3+fZffw2Pvno\nFJ5s8vc5ZMpm3jl3Pf/ZM55vPVH8/2M458x5gZdM2cznHpvCiib/P7MnbOV9+z7PQ+vHcsWqyYX/\nPwAn7L6Bv/ijjVy+cjLLny9OtqeN3caF+zzPuq3G5b+f0vTv84pdN3HGni/wrdXN//YTzHn7nPVM\nG+t8eeVknmvy99l/0hbeMWc9t/7vRH76TPHf3nDeOHMD86ds4fKVU1ib+t/cmcyszsFsHPG35D8H\nHie+KvJp7n4/9A1mIiIyMpUNZrVdqNXdt5jZO4m7q8YC3+gNZCIiImm1zcyaUWYmIjLytX03o4iI\nSFl1ns0oIiJSioJZBXVcXmuwmdlcM/uJmd1nZv9tZhcMd5uGipmNNbNuMyt7LlzbMbPpZvZdM7vf\nzJYns4RHHDNbnLxn7zWza81sRFxpwMy+aWZrzOzeVNkMM1tqZg+a2W1mVvY8xNrKOc7PJO/b35jZ\njWbW6GTy7RTMSqrr8lpDYDNwobsfQrzG39+O0OOEeOWI5dT0nMZB8gXgVnc/GHgZ8fqAI4qZ7Qec\nAxzq7i8lnjB26nC2aRBdSf81TxcBS939QOLlqfotRdaGGh3nbcAh7v7HxOfOZq9q0YeCWXmHAQ+5\n+wp330y8qsRJw9ymQefuq939nuT2c8QffiPu4pNmtjfxElZfp/jipm0r+Sb7Knf/JsQzhN29ysmy\n7eJZ4i9hk5NTeiZT/qT3WnP3O+m/wMKJ7Fj95moaXxOwrTQ6Tndf6u69J7DfTf91a/tQMCtvDvD7\n1PZK8tetGxGSb7wB8RtppLmMeM3Esqs9tKN5wB/M7Eoz+y8z+2czKz4buA25+1rgH4lXzHgceMbd\nlw1vq4bULHdfk9xeA5S6rEybO4smy+4pmJU3krui+jGzqcQL7L47ydBGDDN7PfCku3czQrOyxDji\nxZsvd/dDiRcoHgldUn2Y2QHA3wH7EfciTDWztxQ+aITweDr6iP5sMrMPApvc/dqiegpm5a0C0hf4\nm0v5NRPbipmNJ17N/V/c/abhbs8Q+FPgRDN7hHjF+qPN7FvD3KahsBJY6e6/Sra/S/414drZAuAX\n7v6Uu28hXuPzT4e5TUNpjZntCWBms4kXux6RzOytxMMBTb+cKJiV1wV0mtl+ZjYBOIV4BfkRxcyM\n+BIny93988PdnqHg7h9w97nuPo94osCP3f2M4W7XYHP31cDvzaz3gqzHEF/yZ6R5ADjCzCYl799j\niCf2jFQ3E1/CiOT3SPzCiZkdRzwUcJK7N13IXcGspOQbX+/yWsuBb4/Q5bX+jPjikK9Jpq13J2+q\nkWwkd9O8C7jGzH5DPJux7Ar/bcPdf0N8Mc4udqxi/7X8R7QPM7uO+AK6B5nZ783sbcTXU3utmT1I\nfE2zS4ezjYOhwXGeRXzduanA0uRz6PLCfWgFEBERaXfKzEREpO0pmImISNtTMBMRkbanYCYiIm1P\nwUxERNqegpmIiLQ9BTORNmJmE5NLnQx4PT4zO8HMrh+MdokMNwUzkUFiZivMbL2ZrUt+nu1ddmgQ\nnQv8tHehWTO7ysw+lmnHfma2zcwK/7/d/RbgEDN76SC3UaTlFMxEBo8Dr3f3acnPrsmSUgAklycZ\nqHcAYeY5B7LywXXEAVKkrSmYiQyhJEM638wi4HdJ2evN7B4ze9rM/iOdGZlZkFyu5Vkzuz75+Vhy\n3z7A/lS4JI+Z7ZXKFNclmWP6sjd3AMcPxrGKDCcFM5HB1eiSMicBrwDmm1lAvJDzOcAM4ArgZjMb\nnyxgfRPxBRd3A74DvIkdmddLgYdTFywsek4A3P3xVKY4jXhF+etSVR4A9ksu+SPStgaj20NEYgbc\nZGZbku07kt+fdPdnAMzsXOCK1GVZvmVmHwBemWyPc/cvJLe/Z2a99QCmA+saPOf7zOydqbIxNOh6\nNLOLgIOAI1PFvfubDoyo69bJ6KJgJjJ4nPhyFT/uLUi69NJXKN8XOMPM3pUqGw/MJg5MqzL7fDR1\n+2lgWoPn/Iy7X5x6zn2BR9KVzOwvgQuAw9x9Y+qu3v09U3xoIvWmbkaRoZfOkh4DPuHuu6V+prr7\nt4EngDmZx+6buv1bYF6DWYrZbsY+22Z2EHAV8Ffung2WBwMrRtrVxGX0UTATaa1/Bs4zs8MsNsXM\njk/GrH4BbDGzC5IxtDcRj7UB4O4rgYeAw1P7yx0vAzCzXYHvAx909180qPJq4NYBHpPIsFMwExla\nfcau3P3XxJM//glYC0TAGcl9m4knfLwVeAo4mXjCRjpgXQEszOy/0dT83rJDgQOBy9Lnv6XqnZrs\nU6St6eKcIjVmZlcCK939Q8n2BKAbOLr3xOkB7PsE4C3ufurAWyoyvDQBRKTe+nQjuvsm4JDB2HGy\nAsgtg7EvkeGmbkaRehvoCh8io4K6GUVEpO0pMxMRkbanYCYiIm1PwUxERNqegpmIiLQ9BTMREWl7\nCmYiItL2/g8F4IBLAkD9dwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10b2f5250>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(np.arange(0, 500)/10.,abs(dft_sqr)[:500])\n",
"plt.xlim((-1, 12))\n",
"plt.ylim((-5, 520))\n",
"plt.xlabel(\"Freq(Hz)\")\n",
"plt.ylabel(\"|DFT(K)|\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Taking a step further- DFT and STFT on Star wars sound"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"--2016-01-19 14:46:33-- http://www.thesoundarchive.com/starwars/swvader01.wav\n",
"Resolving www.thesoundarchive.com (www.thesoundarchive.com)... 64.85.5.170\n",
"Connecting to www.thesoundarchive.com (www.thesoundarchive.com)|64.85.5.170|:80... connected.\n",
"HTTP request sent, awaiting response... 200 OK\n",
"Length: 46146 (45K) [audio/wav]\n",
"Saving to: ‘swvader01.wav.2’\n",
"\n",
"swvader01.wav.2 100%[=====================>] 45.06K 37.2KB/s in 1.2s \n",
"\n",
"2016-01-19 14:46:36 (37.2 KB/s) - ‘swvader01.wav.2’ saved [46146/46146]\n",
"\n"
]
}
],
"source": [
"!wget http://www.thesoundarchive.com/starwars/swvader01.wav"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from IPython.display import Audio"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"\n",
" <audio controls=\"controls\" >\n",
" <source 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\" type=\"audio/x-wav\" />\n",
" Your browser does not support the audio element.\n",
" </audio>\n",
" "
],
"text/plain": [
"<IPython.lib.display.Audio object>"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Audio(\"swvader01.wav\")"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from scipy.io.wavfile import read,write"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"fs,data = read('swvader01.wav')"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"22050"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"fs"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x10cf90a90>]"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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EXOWc2yt/PMM5tzhf/jfgVc65d+UdLL5P1rS0HXAdsKurOcnSpUtXLw8NDU34izSM04F8\ngyRRsLpcRkZG3PDwcN1yaqV8ao9Zs/9ZZN3cu+m/kyg4od4TYZxOAZ4Zu7421ryZ831kXfEvTqJg\n3G/yicqqm7rwPv1gEgXnF3xMwM9nqt57r0pq31d5s/pbgR2BOImCv3gNrmRa+X5vVcOalZnNBg4G\ntjazB4EzgEPMbB+yJr57gQ8AOOfmmtllwFxgBXCiayYbii+9+Nt8AKibrJjgZ34Yp8cAn2TtUcJf\nBXywuNBK67wwTpeSdZq5H/jmRElaeupDwFfy5S+HcTpJNz33RsNk5Zw7ts7qce/fcc7NAmZ1EtSg\nC+M0TKIgKfiYi4E9kyio17OzVMI4fTswu85TJ1CyZBXG6Su6dOjv1yxvAXy2S+fpujBOZ5NdDjgj\niYJ1atIV85Uxj48FLvERyKDRCBbldHsYpy8A77pgj8KOOR14IozTe4BbgX8r7MjtG69m96OeRtGZ\nL/fgHJ+hwsmKNTd+TyarmfSTL6Bk1RO6Ybe8NgQuW7ai8Ob+lwP/THbv3MyiD15PGKeb9+I8nkzU\n21LWdkrjTSpH98f1iGpW5Tbp109uwCG+o+jcYmCTIg6UdxBIgX9IouCPRRyzCsI4XU/XRnovjNN9\ntpq8GY/PG79jShin6ydRsKKXcQ2i0taswjjV9NvAiv7onjIljNO9CzxeQHmaxXrV0+26ME436NG5\nZI0vPb684dfk78M49Tnty0AoZbIK4/Rs4G7fcZTBqv5IVgBzwjgdO3rCth0c752dBFOgl/ToPIcC\nx4RxamGcvi6M09dPNDqJFOZ1TWyzP3mPaOme0iWrME43oYVRHPrd7U/31ewTd4xJWF/v5GBhnB7Q\nYTxVczGwErie7B7G5WGcHtLszmGcbt2luJoWxulQGKfvC+P0mA4Hbu66ME7HHcasjk91LRABynnN\naj/fAZTJIy9OGr1OsxA4MomCeb5j6sAMspuQR+c3ek2Hx7spjNMpFZ2wsV21talJwA1hnL6brIb3\nSuBF4DbgwtprXGGcTgYe62Wg43iyZvkAytErdR35UGYLWthlSrdikUwZf9m8x3cAJbUrMDeM06qP\nQfWRME6LHLT12bw2PsguIbv/571kzVHfAv48ppnw5z4Ca+DDvgOYwCdp8XpkGKcujNPveZ4frm+V\nMVkd7zuAknsyjNNrKz4U1UjBx1sWxukzP1yy0ejwTD0RxmlZOnnUsyP5yPf5xf/D/IZTOX/f5n7v\nBv4QxuklYZxuWmRAg66psQGLNNHYUfmEfQ/2NCDpdzOSKHik1Z3y+aW+x9oX2OeQjVQ/j/pzvJXR\nJOBnwJsabehDWccNLPDH4HeBk4BlwOlkPyBuBU5MouCpgs5RGt0cG9B7ssovsu5Mdnd7la/HSPld\nTtZMtjyJgqX1Nsh/Da8k6436sh7GNsgWAYfny39JoqAn19ZG/9Zjr3mON8Byl5xB1tFoK2AjYHOy\nCVEnAf8OfIPsHsWlSRSUvjWlb5PVIVc+GpDd4Cniw5+BG4CtyTp7aGLC8kjIaiB/AX5IdqvCPcBy\nss4MPyK7pnQUWceS28k6IU0nq/W+layz1g/IvuxfD3wH+CnZ+JJfHXO+Z8kSxxe6+Jo69ROyH1Hr\nA9eSdap5gOxH1aNkN9+vAJYlUbBovIN0Uz8nq56eW0RkwEzu5ega3UxWZexgISIixVjeLzePK1mJ\niPS3k30HUAQlKxGR/vY13wEUQclKRKS/9WLOta5TshIR6W+n+w6gCEpWIiL9a+skCl7wHUQRfA9k\nGwOR5xhksN0H7OQ5BlnXo8BsYDfgKeB8svvgdiQbROBlwHnANGB3YAvgKuB54GqyG22/CewLHAHM\nJbspfEuyoac+P+Z8t5Ldq/UY8C7Kc0P4I8BU4A9kc7g9Sfa9vTPZDe47ko3AP4vsvrJ9gYuSKPiz\nl2i7qAwjWBxP9sZ6luyNJNItnyObZmM6MD+Jgsdh9YjkuwJPJ1GwKIzTqcDj/sIcSBcB/w3c28MR\nLDYHptQbjqtHY28eRzYowpP5/zsD55Il04eAl4830kpZ9e1NwXXGBtwNGJipyqXr/juJghPa2TGM\n02+xZlDlZ4GXJFHwTBinBwEXAH9TUIzdFpCNAlHWsQw3Bl4o21BCYZxeQTY6Rid2TKLggTBO3w78\nF2tqa9cBxyVR8HCHxy+dbiYr382Aa0miYEEYpw/T2QyyUn7zkijYswe/Xs/oYN//AIaA7YFZSRQ8\nA5BEwe+APQDCOD0Q+F2nQXbRsUkULAQI43KOapZEwfO+YxjHXbSfrN6SRMFPRx8kUfBj4MeFRDXA\nSpWscjPJRiqWic2iur18bury8VcCuyRRsKTdA+T7Ht1gm9+XNQnkHqpZ/gbZ6N/SnK+QzWnVqvWT\nKFhZdDBSzt6AgzTrayf+y3cAHfh0/v+vCzjWU2QjVp+5zeSVkA1W+rdJFNxfwLGrYsN8qo3aL9d5\nrF3rO623ITUl9h3AeJIoeAI4tMXdpitRdU8Zk1XiO4ASujr/MjoC+Diwc9UuvNb4xyQKHsiXbyjg\neC9NouCJJApOn7XrMpIoeF8SBf9bwHGrYtskCl7Ml2eR9WT7CHDQmOtAZWpuu4isJ9v7fQcykSQK\nbmxh8z06qclLY6VrBkyi4E8lb1rpqbdt8zyXP7bRkQBJFPwS+KXnkDqSt9+Puoo1tax2j1fVpF2E\nXyRRsHj0QZ6cZtfbMImCFWGcnkk5algfSaLgSd9BNOknZNONTOSHSRTM70Uwg6yMNSvIJh4T4LCp\nL5BEwXLfcRRk5pjHqzo83gONN+kLtwPvIetyP1obXQx8rJWDJFFQhmucn61QoiKJgredtP0zkHUt\nH2+qjU/0LqLBVcpklUTBKmAv33GUwAcml/Iv1LLfAy9LouDsJrdv9lpGKadqL9gOSRTsl0TBJXkz\n0xvI7gnbPYmCezzH1rIkCjrpoenF3putIImC3YAN6jy9KIkCNQX1QGm/CpMouNt3DL4lUfCtBpvs\n05NAOvPGJAoOSqLg3hb2OZnsBtGJrJ9EwdwO4qqC742d8TWJgpVJFPwpiYKnfQXVgbpNlFUxzr1g\nB/Y8kAFV2mQlNGwqSaLgjl4E0qFrJ3iubs/PJAqWJlFwQt6ppO7NrH3c6+oosk5GP6f/mpfKcL2s\nU/vWLP+wprOQdFnpOljIas3ei7QFTSQ2XxqMTNDMBz0CflZQOKWXRMGVwJW+4+iCD/bD7QRJFCRA\nX8y8WzWqWZXTCuCjzWyY94Yb23Ghn/ycdQc7/qaPQKRt/0TjZl2RCSlZlc/NwIEtXjxv9gbh3YE7\nyWpiO7YaWBs6Hvk5iQKXRMH3yGqQpwH/Cny40+OWVF9MkjdWEgVx2cb+k+pRM2D5fCaJglta2SGJ\nAtfEvWk/SKJgAbD36Ioe3M/23qIOlNcgzyrqeCX0NE3WpkUGkWpW5TPS5n7jDQ3zGPB6spENeunA\nJAp+08Z+8wqPpBouV+1DZHwNk5WZXWRmS8zsrpp1U83sWjNbYGbXmNkWNc+dZmapmc03s8O7FXif\nuq7duXzyoWHqNQe+PYmCX+X3rvXKph0MefRooZFUhxKVyASaqVl9h2xMulozgWudc7sB1+ePMbM9\nyUaq3jPf51wzU+2tef/Ryc5JFJxKNs/S/WRzMJ1HdkNuT41Op9GmpwoLRET6RsNrVs6535rZTmNW\nHwkcnC9fDNxIlrCOAmY755YD95nZQmB/uj8lRD9YDLR0raqeJAr+SHWmaa9X25vV8yg68wTZtOOd\nWme2WhFZo91azzTn3OgIw0uAafnytkDtHfeLgO3aPMegeWuPm+q8S6LghTqrqzZ0zdhu9c26rmZ5\nJX3aE1CkKB030TnnHBO3t6stvglJFNzsOwZPaqcJmZdEwePeImnPL9rc7+vAqcD3gEPbvVYpMigs\nyzUNNsqaAa9yzu2VP54PHOKce8TMZgA3OOf+xsxmAjjnzsq3uxo4wzm3+ot46dKlq0+YphP/iD5+\n3lCrr6eyLtij9zNdfHfxxvz2yXpjc3amldfy4iq4/okNWOGM1099gSkVHG9/5sLNeHx5a7/7Ttnh\nGfbadLxBvLun15+pw6a+wNHTyjSVlnRTEASrl4eGhgod6aPd+6yuBI4Dzs7/v6Jm/ffN7MtkzX8B\nE1yHGR4envjFzEsHpVb28PDwcN3m0pGREdewnNp0fJxOIuvSvh1wZlHHbTXe1xR03m6W1UQen5fe\nD7y0lX3OeXCTv0uioN1aWft6/Jm67okN/+4Lf/+K3r/OAvl6X1VRbWWkaA2TlZnNJutMsbWZPQh8\niuzmzMvM7P3AfcA7AZxzc83sMmAu2ZBBJ7pmqm7yER8nzQeDjQHyifmkd273dN5vko0C0gs3AFf3\n6FzS55rpDXjsOE8dNs72s6hejy7flNAHyxyPU6CfRW+S1auARDc6S1F0D1Q59NMH2leNoTKSKAg9\nnnsRcFsPzjPSx9O4iAdKVlK0hb4DkIZe9B2ASKuUrMqh3v1GVfVJ3wFIQ+osIJWjZFWcdsfCgxJP\nntiiTydRULWbekWkApSsijEbeGMH+/fFNaskCj7jOwYR6U9KVsU4I4mCZb6DEG+q9mOjavGKKFkV\n5OEO99eXh4jIBJSsCtDhlBhSfZf5DkCk3ylZiXRuUGc3FukZJatyUDNgf7rWdwAi/ULJSqR7ltdZ\nN7fnUaxLP46kcpSsykFfHoPjp74DEKmisierZ30H0COa0rzaWhkRogw/TJ72HYBIq8qerDajWu3+\n72hnpyQK/lR0ICITeMp3ACKtKnWySqJgVRIFh7ex63NjHt9aRDyNJFHwo16cRypl7PBT13iJQqTi\nSp2sOnAMMDqX9oXA6T089+IenqtMzvYdQEm9jzU1mf8BfuMxFpHK6stklUTBlcAuwB7A8cCvgB/k\nT/8ZOAL4WZdO/74uHbfsvuI7gDJKouB3wK7AK4AjNRmhSHsazhRcVUkUPMyaYZBcGKfHAicAzyZR\n8GIYp2/u0nmvDuOBG3j8Ex5nvi2DCRNQEgWPAY/1KBaRvtS3yWqs/Bdtv0zFUTYrfAcgIv2tL5sB\nK+Yk3wEUQE1bItJVSlb+ne87ABk4+nEhlaNk1bkPdrJzEgUriwpERKRfKVl1KIkC1YykalSzksrp\nx2T11ya3K+IDq2GSMr/wHYC0pJXhoURKod+S1TLg3T08n36hAkkU3O07BmmJkpVUTj91XX8J8EIS\nBb0c9+z9PTyXiMjA6ptkld942YplBZz2ugKOIdWnmopIl/VbM2ArOk40SRTUm1xPREQKNsjJSl3G\nRUQqYpCTlZpupCjqaCPSZYOcrESkO+7yHYD0HyUrESnaDxpvItIaJSsRKZpG4ZfCKVmJDB51LpLK\nUbJqTe3wShpiSKrqat8BiLRKyao1xwK3kN2j9SHPsUj53e87gHHompJUTkcjWJjZfcBTZM0Ky51z\n+5vZVLIPw47AfcA7nXN9MUNvEgU3Agc0sem7gO93N5rSuMB3ACW1EvhP30HUk0TB85f+JuHs+zf1\nHYpI0zqtWTngEOdc6JzbP183E7jWObcbcH3+eNBcCvyL7yB64BpUwxzPwUkUPOw7iPHsOmUlqDlQ\nKqSIZsCxN9ceCVycL18MvKWAc1RKEgUuiYILge+MeeovPuJp0qUtbn8LcEQSBc91I5iqS6Lg975j\nEOknRdSsrjOzETM7Pl83zTm3JF9eAkzr8Bzdcl8PzvFpsjIAeAz4VA/O2a5P0FoyPTSJAo3cUG2z\nfQcg0ixzrv3vGzOb4ZxbbGbbANcCJwNXOue2rNnmCefc1NHHS5cuXX3CNE2bOs/x84YabnPBHktb\niByeXQkfWtD4uJ2cA+CpFcYDz0/ipRut5P7nJ3HOg5t0fMxuWbrCePD5SUw2xxcfGP96xrQNVvKf\nuxQxaH1/eHy5MXPh5qsfb7vhSj7zsvKXzwoHH5zf2megGW/b5jnetPWLhR9Xyi8IgtXLQ0NDhQ5p\n11EHC+fc4vz/x8zsJ8D+wBIzm+6ce8TMZgCPjrf/8PBwcy9mXtowozZ9rFwYp+vR4v0mrZ6jzjnf\nyJjrBI2OOTIy4jo9b6vCON0TuGe855e8OGnB8PDw7j0MqSk+ymrUzIXpmWTXZ//y8AuT3jo8PPw7\nH3E0a2TDF0poAAAHxklEQVRkxL36VcPG/MafrVZd/tjGM//jiFeeXfRxffH5vqqa2spI0dpuBjSz\nKWa2Wb68CXA42ZhgVwLH5ZsdB1zRaZDdkETBKg+nvZGs9+Son3iIoRlq3mtREgWnAUPADkkUlDpR\niVRRJ9espgG/NbM5wM3Az5xz1wBnAW8wswXA6/LHAiRR8AIQkdVafg2c6jciKVISBU8lUfC87zg6\n9HASBapFSOm03QzonLsX2KfO+ieAwzoJqg1v6PH52pZEwZVktU+RMrif7J7IUXN8BSIykX4YweLd\nSRRoenmR9vxzzfJK4KPjbHdZ90MRGV/Vk9V9SRQMykgRIoXLR2V5E1lz/d8mUTCviMMWcAyRtXTU\nG1BEqi+JgqtpPJrFH5s83K1kt7GIFKrqNSvpDvUGlLEWTfDcr4B9gaPIamd6/0jhVLOSdnzCdwBS\nCjcBJwFzkihYiZr/pIuUrKRVlwFX+Q5Ceq5ebenhJApu63kkMpCUrKQlSRQc7TsGKY1xR6cRKVpV\nrll90XcAIsLJYx5/3ksUMpCqUrM6g6wZ4mMeY/hnj+cWKYPzyYaU2gf4dhIFE3W6EClUJZJVEgXP\nAh8P4/Q1wIE1T/28B6f/Gll33EG6n0u9uWQdSRSsQLUp8aQSyarGScD/AhsDj9ODacOTKPhwt88h\nIiITq8o1KwCSKJhD1gTxLmDvJAoWew5JRER6oGo1K5IoWAAs8B2HiIj0TqVqViIiMpiUrKSe5b4D\nEBGppWQl9dyLmlpFpESUrGQd+UCkb/Edh5TKQ74DkMGmZCV15fMabQk8XbP6WE/hSO/VDlZ8L42n\nEBHpqsr1BpTeSaLgyTBO9yVLUnckUXCl75ikZ84kmxZke7LRKlZ5jkcGnJKVTCiJgoXA53zHIb2V\nNwV/13ccIqPUDCgiIqWnZCUiIqWnZCUiIqWnZCUiIqWnZCUiIqWnZCUiIqWnZCUiIqWnZCUiIqU3\n6Mnq5jGPF3mJQkREJjToyeokYEm+fDFwm8dYRERkHAOdrJIoGAF2AWYA7/UcjoiIjGPgxwZMouAZ\n4BmAME49RyMiIvUMdM1KRESqQclqbY/4DkBERNalZLW2u3wHICIi6+pKsjKzI8xsvpmlZnZqN84h\nIiKDo/BkZWaTgG8ARwB7Asea2R5Fn6dLbhjz+H4vUYiIyFq6UbPaH1jonLvPObccuBQ4qgvnKVwS\nBXOBi/KHT6Hu7CIipdCNZLUd8GDN40X5uqr4F2AnYKckCsbWtERExANzzhV7QLO3A0c4547PH78H\nOMA5dzLA0qVLiz2hiIiUztDQkBV5vG7UrB4Cdqh5vAMac09ERDrQjWQ1AgRmtpOZbQAcDVzZhfOI\niMiAKHy4JefcCjM7CfglMAm40Dk3b/T5oquGIiLS/wq/ZiUiIlK0no5gMag3C5vZRWa2xMzuqlk3\n1cyuNbMFZnaNmW1R89xpeRnNN7PDa9bvZ2Z35c99rWb9hmb2g3z9TWa2Y+9eXbHMbAczu8HM7jGz\nu83slHy9ymsMM9vIzG42szlmNtfMzszXq6zGYWaTzCwxs6vyxyqrcZjZfWZ2Z15et+Tr/JWXc64n\n/8iaBBeSdQufDMwB9ujV+X3+A14LhMBdNev+C/h4vnwqcFa+vGdeNpPzslrImhrwLcD++fLPyXpd\nApwInJsvHw1c6vs1d1BW04F98uVNgT8Ce6i8xi2vKfn/6wM3AQeprCYsr38HLgGuzB+rrMYvq3uB\nqWPWeSuvXr7w/wNcXfN4JjDT9x+kh69/J9ZOVvOBafnydGB+vnwacGrNdlcDryabc2tezfpjgPNr\ntjkgX14feMz36y2w3K4ADlN5NSynKcCtwMtVVuOW0fbAdcChwFX5OpXV+OV1L7DVmHXeyquXzYBV\nv1m4aNOcc6OzFC8BpuXL27J2V//Rchq7/iHWlN/qsnXOrQCWmtnULsXdM2a2E1mN9GZUXnWZ2Xpm\nNoesTG5wzt2Dymo8XwE+BqyqWaeyGp8DrjOzETM7Pl/nrbx6OfmienKMwznnzEzlU8PMNgV+DHzI\nOfe02ZpOpCqvNZxzq4B9zGwI+KWZHTrmeZUVYGZvBh51ziVmdki9bVRW6zjQObfYzLYBrjWz+bVP\n9rq8elmz0s3Ca1tiZtMBzGwG8Gi+fmw5bU9WTg/ly2PXj+7z0vxY6wNDzrknuhd6d5nZZLJEFTvn\nrshXq7wm4JxbCvwPsB8qq3peAxxpZvcCs4HXmVmMympczrnF+f+PAT8hG/fVW3n1MlnpZuG1XQkc\nly8fR3ZtZnT9MWa2gZntDATALc65R4CnzOwAy6oZEfDTOsf6R+D6XryAbshf24XAXOfcV2ueUnmN\nYWZbj/bGMrONgTcACSqrdTjnTnfO7eCc25nsusmvnHMRKqu6zGyKmW2WL28CHE4235+/8urxBbs3\nkfXuWgic5vsCYg9f92zgYeBFsjba9wJTyS72LgCuAbao2f70vIzmA2+sWb9f/oZZCJxTs35D4DIg\nJesRtpPv19xBWR1Edk1hDtkXb0I23YzKa92y2gu4PS+rO4GP5etVVhOX28Gs6Q2osqpfRjvn76s5\nwN2j39c+y0s3BYuISOlpWnsRESk9JSsRESk9JSsRESk9JSsRESk9JSsRESk9JSsRESk9JSsRESk9\nJSsRESm9/w/gJdGLboJF+gAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10cf05bd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(data)"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"2"
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"k = np.arange(len(data))\n",
"\n",
"T = len(data)/fs\n",
"T"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us now plot the DFT of our sound signal."
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x10cf9e290>"
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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Dl7f2ZcD9VfVWVW0CXgQWJDkZOL6qVrf17u306Y71MHBBa18MrKyq0aoaBVYBl7SAPR94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\nAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10cf52210>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"k = np.arange(len(data))\n",
"frq = k/T\n",
"plt.plot(frq[:len(data)/2], abs(np.fft.fft(data))[:len(data)/2])\n",
"plt.xlabel(\"Freq(Hz)\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Wait! We do not see anything! This is due to the fact that zero frequency or DC component dominates other components. We can work around this by subtracting the mean from the signal. "
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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wv6QZwLyIeLBRX/r6+p6oqtVa/VXALQB3PjKT2i5OGeyv3Mbd9f1+QT63e84fv2f58y+l\nRw0MDEQ+b4CROY7HU/bR5RrmXRJlzb2seUN5cx8aGmpLQR/P1ZICrgS2RMQncos2Auem9rnA9bn4\nSkmzJB0DVIBNEbELeFjSsrTPfuCGBvs6g+wClfG4csTrz4yy3ivGuT8zMyuA8YzcXgb8HvAdSYMp\ntgb4CHCtpFXAduBMgIjYIulaYAuwD1gdEcOVeTXZI2jmADdFxM0pfiVQk1QH9gArx9n/xU1eDztw\nnPszM7MCaFrcIuJfGH2Ed8oo26wF1jaI3wEsbRB/lFQcp6paq/9FK/ZjZma9q4h3KLmw0x0wM7PO\nKmJxa6R0J2nNzMqsLMXNzMxKpNeLW+k+E2JmZs31enErhT17RbVWf2+1Vn9tp/tiZtYLXNy6XLVW\nP/hD9x4M2c2k/6Faq5/d4S6ZmXW9Xi9u452W7OULSs778WP7/TN9rlMdMTPrFb1e3MpgSac7YGbW\na3q9uJXhgpLHRwaqtXpLPvBuZlZUvV7cyuqayWxUrdV7eXrWzGzcxv3Im25SrdXPA/6m0/1oh2qt\nfhzwNGBgsL9ShpGpmVnL9Vxxq9bqT2fiha0nRizVWv184LL0ch3w1hYfQkBUa/XnAW8B6sBfDfZX\nHmvxcczMOqrnihuTu3dkr4yALsu1V1dr9f9Fi/terdXnAv8KHJxCs4CPtvIYZmad1ovn3BZMYpue\nGLk1sIjW9/0PeLKwAfxli/dvZtZxvVjcemUU1o0EHNbpTpiZtVsvFrcy6dURp5lZR/VicZvMyK1X\ni4Ro7Uj11S3cl5lZ1+rF4lYmrS7KV7R4f2ZmXcnFrXyO73QHzMzarWlxk/RpSbslbc7FPiBph6TB\n9PWa3LI1kuqStkpanoufIGlzWnZpLj5b0jUpfruko5p0qUwXlLR6WnIRsLzpWmZmPW48I7fPACtG\nxAL4eERU09eXACQtAc4iu9nvCmCdpOGptcuBVRFRASqShve5CtiT4peQPdrFMr16rtDMrKOaFreI\n+Gfghw0WNXrjPQ24OiL2RsR2YBuwTNIi4JCI2JTW2wCcntqnAutT+zrg5GZdatbncfa1FxxC7/bd\nzKxjpnKHkvMlnQMMAO+OiIfIPkN1e26dHcDhwN7UHrYzxUnf7wOIiH2ShiQtiIgHp9C3kbp6KrNa\nqz8T+FiDRYdMd1/MzIpgssXtcuCDqf0hsjfmVS3pURMnzX/0j7760OwJbbN07t7XDQwMdG2BO3H+\nQXytQU5vX/zjm779oxkNl7XSp75yZzxv7j5mduHlRd3879ZuZc29rHlDOXOvVCpt2e+kiltEPDDc\nlnQFcGN6uRNYnFv1CLIR287UHhkf3uZI4H5JM4B5Y43avvrQ7HXA6on0d/OPZ97U19f3uolsM53O\nq9Ub/kJfdt/c15JN276lncdft2MuwDeBl3fTkwgGBgair6+vlNOyZc29rHlDeXMfGhpqy3vOpP5W\nT+fQhr0BGL6SciOwUtIsSccAFWBTROwCHpa0LF1g0g/ckNvm3NQ+A7ityeG75s13GkznL/pLgV+b\nxuOZmbVN05GbpKuBE4FnSboP+DPgJEnHkxWae4E3A0TEFknXAluAfcDqiBguRquBq4A5wE0RcXOK\nXwnUJNWBPcDKFuVWBLOm+XhLga9P8zHNzFquaXGLiLMbhD89xvprgbUN4neQvXmOjD8KnNmsH/lN\nJrDusF4d6p9NVvCnS6/+nMzM9tOFlxBYzuFMb8FxcTOzQnBx627TXWxc3MysEHqxuJXpghKY3nxd\n3MysEHqxuFn7uLiZWSH0YnEr28htOrm4mVkh9GJxm4xefdMWcOA0H8/MrOeVpbitqNbqT/kYQg8I\nnvpEBjMza6IXi9tkpyW/Wa3V57a0J+0nsluTTZep3EjbzKxr9OKb2dMnud3BZDd3vmyslaq1+izg\nHOBxYMNgf2XfJI/Xi9p7h2Yzs2nSi8Xt96ew7aLmq/BZ4LdT+xXAG6dwvF7jc25mVgi9OC3ZNmnU\n9tu50LmjrdvCYz6t3ccwMysbF7f9zezAMafznFozHrmZWSG4uJmZWeGUrbg1u9JyOj9TNqybPpTu\nkZuZFUIvXlAyFc+u1uq3AH3AeuDdg/2Vx3PLT+hAn8YqbtNd+FzczKwQyjZy+wPgVcAzgD8Glo1Y\n3olRVDeN3MzMCqFsI7eRvlit1beQ/Rz+BKh2uD8jTfdIyoXWzAqh7MXtsPQFsAFY0oE+zB9j2XQX\nt7L/PphZQZRtWnIsnShsAM/t0HEbeXWnO2Bm1gpNi5ukT0vaLWlzLrZA0q2S7pF0i6T5uWVrJNUl\nbZW0PBc/QdLmtOzSXHy2pGtS/HZJR7Uywamq1uqdvMhiuqcJJ3trMzOzrjKekdtneOqd6S8Abo2I\n5wC3pddIWgKcRTYKWgGskzRcHC4HVkVEBahIGt7nKmBPil8CXDSFfGxqntnpDpiZtULT4hYR/wz8\ncET4VLJL6UnfT0/t04CrI2JvRGwHtgHLJC0CDomITWm9Dblt8vu6Djh5Enm0U7tHbt10EcdBne6A\nmVkrTPac28KI2J3au4GFqX0YsCO33g7g8AbxnSlO+n4fQETsA4YkLZhkv4rmJZ3ugJlZL5ry1XER\nEZK6afTRUp/8laHHBgYG2rb/PzhsJlfc3x33Tp59QMwdGBjoqn/LbuvPdCpr7mXNG8qZe6VSact+\nJ1vcdks6NCJ2pSnHB1J8J7A4t94RZCO2nak9Mj68zZHA/ZJmAPMi4sFJ9qvl3rx13sx2PtPtvFr9\nd4C/bdf+J+LRx/Xjvr6+g6u1+iFkn/ubCVw82F/pyL/HwMBA9PX1lfKuKWXNvax5Q3lzHxoaaktB\nn+y05EaefBzMucD1ufhKSbMkHQNUgE0RsQt4WNKydIFJP3BDg32dQXaBinXWBuB/A2uAv+twX8zM\nJqzpyE3S1cCJwLMk3Uf2pvcR4FpJq4DtwJkAEbFF0rXAFmAfsDoihqvyauAqYA5wU0TcnOJXAjVJ\ndWAPsLI1qbVM2/6SqtbqL6FLRm3J3GqtPggcn4udWK3VVwH/Odhf+WpnumVmNjFNi1tEnD3KolNG\nWX8tsLZB/A5gaYP4o6TiOE4/ozhX9X220x1o4PgGsSsAqrX6Wwf7K+umuT9mZhPWi3coeWyaj9fO\nOfBfbOO+2+GvO90BM7Px6MXiNt0nXEt3gtfMrNf1YnErhGqtPqvTfTAzKyoXt+baNXJ7dpv2a2ZW\nei5unePpTjOzNvHzu5p7ShGq1uqzyZ7kvRe4ZLC/MpkPIbq4mZm1iYtbcy8Evj4i9rNc+2O4UJmZ\ndZVenJac7kLy+fyLaq3+/JErVGv1X57EfnuyIFZr9bmd7oOZWTO9WNym+8aii0a8bvTZtKcUvALr\n73QHzMya6cXi1mmtKq49OXIje3yRmVlX68Xi1umi8KsdPn6nPavTHTAza6YXi9u0q9bq9Wqt/pr0\n8s8brDKZgtvpIj1ZvdpvMysRF7fx+WXgb6q1+mg/r2OmszNmZjY2F7fxOwI4dJRlH53E/jwCMjNr\nk178nFsni8KoF5NUa/V3kxXAvxrsr/zn9HVp2rkom1nX88itdS4mu2vJN6q1+nj+aHh/m/vTLi5u\nZtb1erG4Tffn3CZqIfDBcay3qt0dMTMrq14sbp105DjXW1Ot1X+lrT3pnF6cyjazkplScZO0XdJ3\nJA1K2pRiCyTdKukeSbdImp9bf42kuqStkpbn4idI2pyWXdrssFPp8xRdNoF1L25bLzrrTdVafbxF\n3sysI6Y6cgvgpIioRsSLUuwC4NaIeA5wW3qNpCXAWcASYAWwTtJwobocWBURFaAiacUU+9UuL2q+\nyhNe2LZedN6d1Vr9GZ3uhJnZaFoxLTlyJHUqsD611wOnp/ZpwNURsTcitgPbgGWSFgGHRMSmtN6G\n3Da97Bc63YE2egbwrk53wsxsNK0Yuf2TpAFJ56XYwojYndq7yS6wgOyehDty2+4ADm8Q35niozlo\nin2eNtVa/Z3VWr2oVxcWeWRqZj1uqhcHvCwivi/p2cCtkrbmF0ZESOr2qxvb6ePAd4FbO90RM7My\nmVJxi4jvp+8/kPT3ZOekdks6NCJ2pSnHB9LqO4HFuc2PIBux7UztfHznVPrVZW75100DHCA4cL8x\n3LxO9acljpu799UDAwNt/8NlOo7Rrcqae1nzhnLmXqlU2rLfSRc3SU8DDoyIH0maCywnu6nwRuBc\n4KL0/fq0yUbgc5I+TjbtWAE2pdHdw5KWAZvInhc2kasSu97q/5gH8D3g9YP9lbsBuLve07/Ed/14\n5i19fX2vbucxBgYGoq+vr6jTumMqa+5lzRvKm/vQ0FBb3gunMnJbCPx9uuBxBvC3EXGLpAHgWkmr\ngO3AmQARsUXStcAWYB+wOiKGk1oNXAXMAW6KiJun0K9u9YvAJ4C2FgQzM5tCcYuIe4HjG8QfBE4Z\nZZu1wNoG8TuApZPtSw9Z3nwVMzObKt+hZJqN8dicXlO66RMz6x1FeaPtJasK/PEAM7Ou4PsETr+/\nAX7e6U60gB/QamZdyyO3zriq0x1ogV/udAfMzEbj4mZmZoXj4mZmZoXj4mZmZoXj4mZmZoXj4mZm\nZoXj4mZmZoXj4maTVq3Vn9npPpiZNeLiZlPxP77bipl1Ixc3m6pbq7X6zE53wswsz8XNpupk4NRO\nd8LMLM/3lrRWeB9wXac7MVK1Vp8BfIzseYE3AOcM9ld+0tlemdl0cHGzVnhhpzswilcBb0/t3wJ+\nXq3V30X2oN3vDPZXevpp6GY2Ohc3a4lqrT4XeDHw74P9lR92uj/JTSNen52+AKjW6nMG+ys/m8oB\nqrX6ycAFwH8D7xnsrzw4lf2ZWWu4uFmrPDLcqNbq3wLeNNhf2dLqg6SrM48HHh7sr/xnij2P7CkF\n3wIeA4aA541jdz+t1urzgD8C9gHrBvsrPx3juK8A9g32V75RrdWPAhYBN/Pk/6OfAm+bbG5m1jou\nbsW0jc4+kmYZcFe1Vgc4EXgZ8B/AV1swsvk56fc27X+qhnLti6u1+sLB/soDDdb7HnB0k+O+tVqr\nvxW4FLgQWE42/fm9VnS0LNLT6jXYX3msWqsfCMwFHhnsrzw+yf0tInv+4B2D/ZVHJ7jtwcAc4EDg\noMH+yvZR1lsMvC4d49/Gue8DU3M2sO9Txz5l+UzggOE+p/UPBfYM9ld+ll7/KrCL7P/FG4GvD/ZX\nNk0gxfzxBLwZOA34MvDxwf7KY5PZVzdQRHecdpC0AvgE2S/RFRFx0fCyoaGhJzp50sZG7zs2wtfJ\nRhnd7JtkF3lcATwL+H/Ad4BfIhuZ0X/oT6jtetrJZOfNvgEcSWdGRmuAD7doX/9OlutbgGcA/wf4\nAXA+MB/4KFB/3ty9N373xzOXk015HgqcCzwA/BhYCtxLNhU6G/gF4Ptko893ARfnjjcLeBx4fLC/\nEtVa/WhgA/BrwLVpv69P+9uRjrEEuD61VwIzgTcBzwVuSeu+C3gN8CWyC4reAXw35Te83fnAnwO7\nyS7qGf6drKU8v9PkZ3UHcMIYyz8K/Aj4YJP9jMd70v6Gj/sTsp+Rjc9jwKGD/ZX/meiG+ff3efPm\ntexzs11R3CQdSPaX/SnATuDfgLMj4m5wcZugL5BdMNHtxc3MiufYwf7K1ols0K7i1i2fc3sRsC0i\ntkfEXuDzZENja+4TwF2pvQ14/yjrbZue7phZid3d6Q4M65bidjhwX+71jhSz0X0LeMlgf+WdZNNU\n84Alg/2VOtDoasWXTmfnzMw6qVumJX8LWBER56XXvwcsi4jzYf9hq5mZFVMRpyV3AotzrxeTjd7M\nzMwmrFuK2wBQkXS0pFnAWcDGDvfJzMx6VFd8zi0i9kl6G/CPZB8FuHL4Sklo7VDVzMyKryvOuZmZ\nmbVSt0xLjkrSCklbJdUlva/T/WkFSYslfUXSXZK+K+ntKb5A0q2S7pF0i6T5uW3WpJ/BVknLc/ET\nJG1Oyy7tRD4TJelASYOSbkyvy5L3fElflHS3pC2SlpUh95THXanPn5M0u6h5S/q0pN2SNudiLcs1\n/eyuSfHbJR01fdmNbZTcP5p+378t6e8kzcsta2/uEdG1X2RTlNvIbns0E7gTOLbT/WpBXocCx6f2\nwWQfYD9pxnd2AAAGS0lEQVQW+EvgvSn+PuAjqb0k5T4z/Sy28eSoexPwotS+ieyq047n2CT/dwF/\nC2xMr8uS93rgTak9g+zjG4XOPfX9e8Ds9PoasruiFDJvsruaVIHNuVjLciW708u61D4L+Hync26S\n+6uAA1L7I9OZe8d/IE1+WC8Bbs69vgC4oNP9akOe15PdnWUrsDDFDgW2pvYa4H259W8muwP/IuDu\nXHwl8H87nU+TXI8A/gl4JXBjipUh73nA9xrEC507sIDsj7dnkBX0G9MbXmHzTm/W+Tf4luWa1lmW\n2jOAH3Q637FyH7HsDcBnpyv3bp+WLPyHuyUdTfbXzrfI/gPsTot2k91GC+Aw9v9oxPDPYWR8J93/\n87mE7D5++ZvgliHvY4AfSPqMpH+X9ClJcyl47hHxINkDY/8buB94KCJupeB5j9DKXJ94T4yIfcCQ\npAVt6nervYknH0PV9ty7vbgV+moXSQeTPcH6HRHxo/yyyP48KVT+kl4PPBARg0DDK2CLmHcyA3gB\n2bTKC8hugHxBfoUi5i7pl4A/JvuL/jDgYGU3aXhCEfMeTZlyzZP0fuDnEfG56Tpmtxe3wn64W9JM\nssJWi4jrU3i3pEPT8kVkd1eHp/4cjiD7OexM7Xx8Zzv7PUUvBU6VdC9wNfDrkmoUP2/I+r0jIoYf\nh/JFsmK3q+C59wHfjIg96a/tvyM73VD0vPNa8fu9I7fNkWlfM4B5aXTctSS9EXgt8Lu5cNtz7/bi\nVsgPd0sScCWwJSI+kVu0kexkO+n79bn4SkmzJB0DVIBNEbELeDhddSegP7dN14mICyNicUQcQzaX\n/uWI6KfgeQOkPt8n6TkpdArZDa9vpNi5bwVeLGlO6u8pwBaKn3deK36/b2iwrzOA26YjgclS9iiz\n9wCnRUT+qfftz73TJyDHcYLyNWQnpLcBazrdnxbl9HKyc053AoPpawXZyfd/Au4he27W/Nw2F6af\nwVbg1bn4CcDmtOyyTuc2gZ/BiTx5tWQp8iZ7sOS/Ad8mG8HMK0PuwHvJCvlmsitGZxY1b7IZifvJ\nHh56H/D7rcyV7Pl91wJ14Hbg6E7nPEbub0r9/K/c+9y66crdH+I2M7PC6fZpSTMzswlzcTMzs8Jx\ncTMzs8JxcTMzs8JxcTMzs8JxcTMzs8JxcTPrUukRH3dJWth87ab7+g1Jn29Fv8x6gYub2SRI2i7p\nJ5J+lL4eHr7FUgv9IfC1SDfdlXSVpA+N6MfRkh6XNOb/5Yi4EThO0tIW99GsK7m4mU1OAK+PiEPS\n19Mju3UQ8MS976bqzUBtxDGncteFq8kKplnhubiZtUgaQa2WVCe7ZRySXi/pTkk/lPSN/MhJUjU9\n/uZhSZ9PXx9Ky44EfpHsUUjjPf5huZHkj9LIMv9ooa8Cr2tFrmbdzsXNbPIaPbbnNOCFwBJJVbIb\nZJ9Hdn/BTwIbJc1MNwK/nuxei88AvgD8Jk+OzJaSPdz08RH7b/ioIICIuD83kjyE7P6VV+dW2Qoc\nnR61ZFZorZg6MSsjAddL2pdefzV9/3BEPAQg6Q+BT8aTj7nZIOlCske+AMyIiEtT+zpJw+sBzAf2\ne8ZfOuafSHpbLnYADaYqJb0PeC7ZTbqHDe9vPvBI8xTNepeLm9nkBNljPL48HEhTgPknxx8FnCPp\n/FxsJrCIrFCNfB7Zf+XaPwQOaXDMj0bE/84d8yjg3vxKkl4DvB14UUQ8mls0vL+Hxk7NrPd5WtKs\ntfKjqP8G/iIinpH7OjgirgG+Dxw+Ytujcu3vAMc0uApy5LTkfq8lPRe4CvjtiBhZPI8FtkeER21W\neC5uZu3zKeAtkl6kzFxJr0vnvL4J7JP09nQO7jfJztUBEBE7yJ5ntSy3v1HPtwFIejrZgx3fHxHf\nbLDKicBNU8zJrCe4uJm1zn7nviLiDrKLSf4KeJDsIYvnpGV7yS4geSOwBziT7AKQfAH7JNmTiPP7\nb/RRgOHYC4DnAJfkP3+XW29l2qdZ4flhpWZdQtJngB0R8afp9Syypxf/+vAHuaew798AfjciVk69\np2bdzxeUmHWP/aYdI+LnwHGt2HG6Q8mNrdiXWS/wtKRZ95jqHUjMLPG0pJmZFY5HbmZmVjgubmZm\nVjgubmZmVjgubmZmVjgubmZmVjgubmZmVjj/H0wRiUUKenzgAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10d7c4090>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"k = np.arange(len(data))\n",
"frq = k/T\n",
"plt.plot(frq[:len(data)/2], abs(np.fft.fft(data-np.mean(data)))[:len(data)/2])\n",
"plt.xlabel(\"Freq(Hz)\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Great! Now, we are able to see the frequency transform of the signal. But, do we have any idea of what frequency exists at what point in time? This is where short time fourier transform (STFT) would come into picture. Now, our goal is to not only see the frequency components, but see at what time what components exists. Turns out that to do that we have already done the basic foundation by computing the DFT. Now, we need to compute the DFT over windows of time.\n",
"\n",
"Let us plot a spectogram of the data. While matplotlib provides a spectogram plot, I found the one produced in the [following](http://www.frank-zalkow.de/en/code-snippets/create-audio-spectrograms-with-python.html) tutorial more interpretable."
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from stft_implementation import *"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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gRUhBqBpBSbhBJWtwjT/Cvoi0MBD7KZHIEQusJJ1W4gNSSkzdJYZ4EwHWC3l/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BGni54Z9XIdWeQdZUlav5c/y8gZjzxTYs2lCtaSlUz6NKXGj6MZUO7Pqb3KudL2B9jrrbcM9l9w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FY65pOg/noIbyL+f8+qf9IbGBGMlsToaa4pfb/H1MK2L4HQUIXkj+nbVnDCFDxxqQ/xGCKGSC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\nw9odAb0QJemBzivtOAlI7CrkdUXv2NLlNXZcksqrvKjNKUCpL8hjBsL2Tu8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cAoGkhEHa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UmS4ySNStP0ijRNX06S5E5JL6uJantJ+l5pt9W/b802tz6J8CJIAKW4FoLJSBGVkD/g0KzL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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10cf32d50>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<matplotlib.figure.Figure at 0x10b2ba590>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plotstft(\"swvader01.wav\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There you go! Now, does FT sound all that difficult?\n",
"\n",
"I have used a number of wonderful references for developing my understanding. I'll try and list a few here:\n",
"\n",
"1. [Jake's blog post on understanding the FFT algorithm](https://jakevdp.github.io/blog/2013/08/28/understanding-the-fft/)\n",
"2. [Franks's code for spectograms](http://www.frank-zalkow.de/en/code-snippets/create-audio-spectrograms-with-python.html)\n",
"3. [Glowing Python tutorial on plotting frequency spectrum](http://glowingpython.blogspot.in/2011/08/how-to-plot-frequency-spectrum-with.html)\n",
"4. [Barry's youtube tutorial on STFT](https://www.youtube.com/watch?v=NA0TwPsECUQ)\n",
"5. [R tutorial on FFT](http://www.di.fc.ul.pt/~jpn/r/fourier/fourier.html)\n",
"6. [Interactive guide to FT](http://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/)\n",
"7. [Intuitive DFT tutorial](http://practicalcryptography.com/miscellaneous/machine-learning/intuitive-guide-discrete-fourier-transform/)\n",
"8. [David's youtube video on FFT](https://www.youtube.com/watch?v=B2iUDBZzBpY)"
]
}
],
"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": "2.7.11"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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