{"nbformat_minor": 0, "worksheets": [{"cells": [{"source": ["Introduction to Signal Processing\n", "=================================\n", "\n*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_matlab/) for details about how to install the toolboxes.\n", "$\\newcommand{\\dotp}[2]{\\langle #1, #2 \\rangle}$\n", "$\\newcommand{\\enscond}[2]{\\lbrace #1, #2 \\rbrace}$\n", "$\\newcommand{\\pd}[2]{ \\frac{ \\partial #1}{\\partial #2} }$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\umax}[1]{\\underset{#1}{\\max}\\;}$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\uargmin}[1]{\\underset{#1}{argmin}\\;}$\n", "$\\newcommand{\\norm}[1]{\\|#1\\|}$\n", "$\\newcommand{\\abs}[1]{\\left|#1\\right|}$\n", "$\\newcommand{\\choice}[1]{ \\left\\{  \\begin{array}{l} #1 \\end{array} \\right. }$\n", "$\\newcommand{\\pa}[1]{\\left(#1\\right)}$\n", "$\\newcommand{\\diag}[1]{{diag}\\left( #1 \\right)}$\n", "$\\newcommand{\\qandq}{\\quad\\text{and}\\quad}$\n", "$\\newcommand{\\qwhereq}{\\quad\\text{where}\\quad}$\n", "$\\newcommand{\\qifq}{ \\quad \\text{if} \\quad }$\n", "$\\newcommand{\\qarrq}{ \\quad \\Longrightarrow \\quad }$\n", "$\\newcommand{\\ZZ}{\\mathbb{Z}}$\n", "$\\newcommand{\\CC}{\\mathbb{C}}$\n", "$\\newcommand{\\RR}{\\mathbb{R}}$\n", "$\\newcommand{\\EE}{\\mathbb{E}}$\n", "$\\newcommand{\\Zz}{\\mathcal{Z}}$\n", "$\\newcommand{\\Ww}{\\mathcal{W}}$\n", "$\\newcommand{\\Vv}{\\mathcal{V}}$\n", "$\\newcommand{\\Nn}{\\mathcal{N}}$\n", "$\\newcommand{\\NN}{\\mathcal{N}}$\n", "$\\newcommand{\\Hh}{\\mathcal{H}}$\n", "$\\newcommand{\\Bb}{\\mathcal{B}}$\n", "$\\newcommand{\\Ee}{\\mathcal{E}}$\n", "$\\newcommand{\\Cc}{\\mathcal{C}}$\n", "$\\newcommand{\\Gg}{\\mathcal{G}}$\n", "$\\newcommand{\\Ss}{\\mathcal{S}}$\n", "$\\newcommand{\\Pp}{\\mathcal{P}}$\n", "$\\newcommand{\\Ff}{\\mathcal{F}}$\n", "$\\newcommand{\\Xx}{\\mathcal{X}}$\n", "$\\newcommand{\\Mm}{\\mathcal{M}}$\n", "$\\newcommand{\\Ii}{\\mathcal{I}}$\n", "$\\newcommand{\\Dd}{\\mathcal{D}}$\n", "$\\newcommand{\\Ll}{\\mathcal{L}}$\n", "$\\newcommand{\\Tt}{\\mathcal{T}}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\al}{\\alpha}$\n", "$\\newcommand{\\la}{\\lambda}$\n", "$\\newcommand{\\ga}{\\gamma}$\n", "$\\newcommand{\\Ga}{\\Gamma}$\n", "$\\newcommand{\\La}{\\Lambda}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\Si}{\\Sigma}$\n", "$\\newcommand{\\be}{\\beta}$\n", "$\\newcommand{\\de}{\\delta}$\n", "$\\newcommand{\\De}{\\Delta}$\n", "$\\newcommand{\\phi}{\\varphi}$\n", "$\\newcommand{\\th}{\\theta}$\n", "$\\newcommand{\\om}{\\omega}$\n", "$\\newcommand{\\Om}{\\Omega}$\n"], "metadata": {}, "cell_type": "markdown"}, {"source": ["This numerical tour explores some basic signal processing tasks."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 2, "cell_type": "code", "language": "python", "metadata": {}, "input": ["addpath('toolbox_signal')\n", "addpath('toolbox_general')\n", "addpath('solutions/introduction_2_signal')"]}, {"source": ["Loading and Displaying Signals\n", "------------------------------\n", "Signals are 1D vectors, usually stored as |(n,1)| arrays, where |n| is the number of samples."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 3, "cell_type": "code", "language": "python", "metadata": {}, "input": ["n = 512;"]}, {"source": ["Load a signal. (function load_signal.m should be in the toolbox of each course)"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 4, "cell_type": "code", "language": "python", "metadata": {}, "input": ["f = load_signal('Piece-Regular', n); % signal of size n"]}, {"source": ["One can force to be a column vector (just to be sure)."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 5, "cell_type": "code", "language": "python", "metadata": {}, "input": ["f = f(:);"]}, {"source": ["One can rescale to [0,1] the entries of the signal."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 6, "cell_type": "code", "language": "python", "metadata": {}, "input": ["f = rescale(f);"]}, {"source": ["Display the signal."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 7, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "plot(1:n, f);\n", "axis('tight');\n", "title('My title'); % title\n", "set_label('variable x', 'variable y'); % axis"]}, {"source": ["You can display several figures using |subplot|\n", "\n", "divide the screen in 2x2 and select 1st quadrant"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": "iVBORw0KGgoAAAANSUhEUgAAAkAAAAGwCAIAAADOgk3lAAAACXBIWXMAAAsSAAALEgHS3X78AAAA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\nrkJggg==\n", "output_type": "display_data"}], "prompt_number": 8, "cell_type": "code", "language": "python", "metadata": {}, "input": ["subplot(2, 2, 1);\n", "plot(f); axis('tight');"]}, {"source": ["select the last quadrant"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 9, "cell_type": "code", "language": "python", "metadata": {}, "input": ["subplot(2, 2, 4);\n", "plot(f.^2); axis('tight');"]}, {"source": ["You can display several signals on the same figure"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 10, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "plot(1:n, [f f.^2]');\n", "legend('signal', 'signal^2');"]}], "metadata": {}}], "nbformat": 3, "metadata": {"kernelspec": {"name": "matlab_kernel", "language": "matlab", "display_name": "Matlab"}, "language_info": {"mimetype": "text/x-matlab", "name": "matlab", "file_extension": ".m", "help_links": [{"url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md", "text": "MetaKernel Magics"}]}}}