{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## ThinkDSP\n",
"\n",
"This notebook contains an example related to Chapter 5: Autocorrelation\n",
"\n",
"Copyright 2015 Allen Downey\n",
"\n",
"License: [Creative Commons Attribution 4.0 International](http://creativecommons.org/licenses/by/4.0/)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"# Get thinkdsp.py\n",
"\n",
"import os\n",
"\n",
"if not os.path.exists('thinkdsp.py'):\n",
" !wget https://github.com/AllenDowney/ThinkDSP/raw/master/code/thinkdsp.py"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"from thinkdsp import decorate"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The case of the missing fundamental\n",
"\n",
"This notebook investigates autocorrelation, pitch perception and a phenomenon called the \"missing fundamental\".\n",
"\n",
"I'll start with a recording of a saxophone."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"if not os.path.exists('100475__iluppai__saxophone-weep.wav'):\n",
" !wget https://github.com/AllenDowney/ThinkDSP/raw/master/code/100475__iluppai__saxophone-weep.wav"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from thinkdsp import read_wave\n",
"\n",
"wave = read_wave('100475__iluppai__saxophone-weep.wav')\n",
"wave.normalize()\n",
"wave.make_audio()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The spectrogram shows the harmonic structure over time."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
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\n",
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