{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction to Image Processing\n", "\n", "The simplest signal is a sinusoidal wave. Sinusoidal waves have three independant parameters. They are: \n", "* Amplitude, $A$\n", "* Frequency, $f$\n", "* Phase, $\\phi$\n", "\n", "The relationship between these parameters is given by the mathematical formula: \n", "\\begin{equation}\n", " f(t) =A \\cdot cos(2 \\pi f \\cdot t - \\phi)\n", "\\end{equation}\n", "\n", "Where the variable $t$ represents time. \n", "\n", "In the following Illustrative, you can play around these values to get an intuitive feel of these variables\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "068c9312a466412d8e1b6dc582b9e587", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(IntSlider(value=2, description='Amplitude', max=4, min=-4), IntSlider(value=4, descripti…" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from misc import *\n", "play_with_wave()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "Signals in real life applications, such as those recieved by your phone during a call, or a radio telescope observing the universe, or the signals from the gravitational wave detectors (LIGO/VIRGO) are quite obviously not simple sinusoids. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Processing any piece of data would require a mathematical way to describe these signals. Given that real life data are not simple sinusoids, it would require near infinite amounts of parameters to describe such data mathematically. Fortunately, as we shall see in this course, $all$ data can be expressed as a sum of simple sinusoids. Thus, you learn a powerful way to process real life data with arbitrary precision through this course! " ] } ], "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": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 4 }