{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## ThinkDSP\n", "\n", "This notebook contains code examples from Chapter 1: Sounds and Signals\n", "\n", "Copyright 2015 Allen Downey\n", "\n", "License: [Creative Commons Attribution 4.0 International](http://creativecommons.org/licenses/by/4.0/)\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "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 matplotlib.pyplot as plt\n", "\n", "from thinkdsp import decorate" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Read a wave\n", "\n", "`read_wave` reads WAV files. The WAV examples in the book are from freesound.org. In the contributors section of the book, I list and thank the people who uploaded the sounds I use." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "if not os.path.exists('92002__jcveliz__violin-origional.wav'):\n", " !wget https://github.com/AllenDowney/ThinkDSP/raw/master/code/92002__jcveliz__violin-origional.wav" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "from thinkdsp import read_wave\n", "\n", "wave = read_wave('92002__jcveliz__violin-origional.wav')" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "wave.make_audio()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I pulled out a segment of this recording where the pitch is constant. When we plot the segment, we can't see the waveform clearly, but we can see the \"envelope\", which tracks the change in amplitude during the segment." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "start = 1.2\n", "duration = 0.6\n", "segment = wave.segment(start, duration)\n", "segment.plot()\n", "plt.xlabel('Time (s)');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Spectrums\n", "\n", "Wave provides `make_spectrum`, which computes the spectrum of the wave." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "spectrum = segment.make_spectrum()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Spectrum provides `plot`" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "spectrum.plot()\n", "plt.xlabel('Frequency (Hz)');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The frequency components above 10 kHz are small. We can see the lower frequencies more clearly by providing an upper bound:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "spectrum.plot(high=10000)\n", "plt.xlabel('Frequency (Hz)');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Spectrum provides `low_pass`, which applies a low pass filter; that is, it attenuates all frequency components above a cutoff frequency." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "spectrum.low_pass(3000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is a spectrum with fewer components." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "spectrum.plot(high=10000)\n", "plt.xlabel('Frequency (Hz)');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can convert the filtered spectrum back to a wave:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "filtered = spectrum.make_wave()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can listen to the original segment and the filtered version." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "segment.make_audio()" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "filtered.make_audio()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The original sounds more complex, with some high-frequency components that sound buzzy.\n", "\n", "The filtered version sounds more like a pure tone, with a more muffled quality.\n", "\n", "The cutoff frequency I chose, 3000 Hz, is similar to the quality of a telephone line, so this example simulates the sound of a violin recording played over a telephone." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Interaction\n", "\n", "The following shows the same example using interactive IPython widgets." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "def filter_wave(wave, start, duration, cutoff):\n", " \"\"\"Selects a segment from the wave and filters it.\n", " \n", " Plots the spectrum and displays an Audio widget.\n", " \n", " wave: Wave object\n", " start: time in s\n", " duration: time in s\n", " cutoff: frequency in Hz\n", " \"\"\"\n", " segment = wave.segment(start, duration)\n", " spectrum = segment.make_spectrum()\n", "\n", " spectrum.plot(color='0.7')\n", " spectrum.low_pass(cutoff)\n", " spectrum.plot()\n", " plt.xlabel('Frequency (Hz)');\n", " plt.show()\n", " \n", " audio = spectrum.make_wave().make_audio()\n", " display(audio)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Adjust the sliders to control the start and duration of the segment and the cutoff frequency applied to the spectrum." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from ipywidgets import interact, fixed\n", "from IPython.display import display\n", "\n", "wave = read_wave('92002__jcveliz__violin-origional.wav')\n", "interact(filter_wave, wave=fixed(wave), \n", " start=(0, 5, 0.1), duration=(0, 5, 0.1), cutoff=(0, 10000, 100));" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.10" } }, "nbformat": 4, "nbformat_minor": 4 }