{ "cells": [ { "cell_type": "markdown", "id": "48a03804", "metadata": {}, "source": [ "# Plants and Signals" ] }, { "cell_type": "markdown", "id": "9148e5af", "metadata": {}, "source": [ "This notebook illustrates the construction of a lowpass filter as the solution of an ordinary differential equation, using SymPy." ] }, { "cell_type": "code", "execution_count": 1, "id": "8e309495", "metadata": {}, "outputs": [], "source": [ "using Plots" ] }, { "cell_type": "code", "execution_count": 2, "id": "c8afb277", "metadata": {}, "outputs": [], "source": [ "using SymPy" ] }, { "cell_type": "markdown", "id": "3f9c8737", "metadata": {}, "source": [ "### 1. low and high frequency signals" ] }, { "cell_type": "markdown", "id": "72fa31bc", "metadata": {}, "source": [ "Consider a low frequency signal which takes 1000 seconds to complete one cycle, and a high frequency signal which completes 1000 cycles in one second." ] }, { "cell_type": "code", "execution_count": 3, "id": "fb5f38fc", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "lowfreq (generic function with 1 method)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lowfreq(t) = sin(2*pi*t/1000)" ] }, { "cell_type": "code", "execution_count": 4, "id": "6f778185", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(0:0.1:2000, lowfreq, xlabel=\"t\", label=\"low frequency\")" ] }, { "cell_type": "code", "execution_count": 5, "id": "8d6b9607", "metadata": {}, "outputs": [], "source": [ "# savefig(\"figlowfreqsignal.png\")" ] }, { "cell_type": "code", "execution_count": 6, "id": "ffe9ace8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "highfreq (generic function with 1 method)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "highfreq(t) = sin(2*pi*t*1000)" ] }, { "cell_type": "code", "execution_count": 7, "id": "7f60d32b", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(0:0.01/1000:2/1000, highfreq, xlabel=\"t\", label=\"high frequency\")" ] }, { "cell_type": "code", "execution_count": 8, "id": "0e7f7dee", "metadata": {}, "outputs": [], "source": [ "# savefig(\"fighighfreqsignal.png\")" ] }, { "cell_type": "markdown", "id": "76272130", "metadata": {}, "source": [ "### 2. a first order ordinary differential equation" ] }, { "cell_type": "markdown", "id": "00d587b8", "metadata": {}, "source": [ "Consider the following as the left hand side of an ordinary differential equation." ] }, { "cell_type": "code", "execution_count": 9, "id": "dc50e767", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$t$" ], "text/plain": [ "t" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t = Sym(\"t\")" ] }, { "cell_type": "code", "execution_count": 10, "id": "63aeea8d", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$y$" ], "text/plain": [ "y" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "y = SymFunction(\"y\")" ] }, { "cell_type": "code", "execution_count": 11, "id": "049f813c", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$y{\\left(t \\right)} + \\frac{d}{d t} y{\\left(t \\right)}$" ], "text/plain": [ " d \n", "y(t) + --(y(t))\n", " dt " ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "leftode = diff(y(t), t) + y(t)" ] }, { "cell_type": "markdown", "id": "2e8a1c76", "metadata": {}, "source": [ "The initial condition is zero." ] }, { "cell_type": "code", "execution_count": 12, "id": "6b11b0a1", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "\\begin{equation*}\\begin{cases}y{\\left(0 \\right)} & \\text{=>} &0\\\\\\end{cases}\\end{equation*}" ], "text/plain": [ "Dict{Sym{PyCall.PyObject}, Int64} with 1 entry:\n", " y(0) => 0" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "initcond = Dict(y(0) => 0)" ] }, { "cell_type": "markdown", "id": "77fb04a9", "metadata": {}, "source": [ "The lowpass filter will take as right hand side the signal on input." ] }, { "cell_type": "code", "execution_count": 13, "id": "d635af5f", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$y{\\left(t \\right)} + \\frac{d}{d t} y{\\left(t \\right)} = \\sin{\\left(0.00628318530717959 t \\right)}$" ], "text/plain": [ " d \n", "y(t) + --(y(t)) = sin(0.00628318530717959*t)\n", " dt " ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "filtlow = Eq(leftode, lowfreq(t))" ] }, { "cell_type": "code", "execution_count": 14, "id": "ac073ad3", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$y{\\left(t \\right)} = 0.99996052314088 \\sin{\\left(0.00628318530717959 t \\right)} - 0.00628293726675839 \\cos{\\left(0.00628318530717959 t \\right)} + 0.00628293726675839 e^{- t}$" ], "text/plain": [ " \n", "y(t) = 0.99996052314088*sin(0.00628318530717959*t) - 0.00628293726675839*cos(0\n", "\n", " -t\n", ".00628318530717959*t) + 0.00628293726675839*e " ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "outlow = dsolve(filtlow, ics=initcond)" ] }, { "cell_type": "markdown", "id": "580cadf9", "metadata": {}, "source": [ "Observe that the first term in the solution is almost identical to the ``lowfreq(t)``. The second term has a small coefficient and the third term is decaying." ] }, { "cell_type": "code", "execution_count": 15, "id": "5ede1ae7", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(0:0.1:2000, outlow.rhs(), xlabel=\"t\", title=\"output of low frequency signal\", label=\"\")" ] }, { "cell_type": "code", "execution_count": 16, "id": "e0c567e0", "metadata": {}, "outputs": [], "source": [ "# savefig(\"figlowfreqsignaloutput.png\")" ] }, { "cell_type": "markdown", "id": "b1847ab9", "metadata": {}, "source": [ "Let us now do the same for the high frequency signal." ] }, { "cell_type": "code", "execution_count": 17, "id": "18eaa744", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$y{\\left(t \\right)} + \\frac{d}{d t} y{\\left(t \\right)} = \\sin{\\left(6283.18530717959 t \\right)}$" ], "text/plain": [ " d \n", "y(t) + --(y(t)) = sin(6283.18530717959*t)\n", " dt " ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "filthigh = Eq(leftode, highfreq(t))" ] }, { "cell_type": "code", "execution_count": 18, "id": "f3cb63a7", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$y{\\left(t \\right)} = 2.53302952689605 \\cdot 10^{-8} \\sin{\\left(6283.18530717959 t \\right)} - 0.000159154939060454 \\cos{\\left(6283.18530717959 t \\right)} + 0.000159154939060454 e^{- t}$" ], "text/plain": [ " \n", "y(t) = 2.53302952689605e-8*sin(6283.18530717959*t) - 0.000159154939060454*cos(\n", "\n", " -t\n", "6283.18530717959*t) + 0.000159154939060454*e " ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "outhigh = dsolve(filthigh, ics=initcond)" ] }, { "cell_type": "markdown", "id": "ccba2e9f", "metadata": {}, "source": [ "Observe that the coefficient of the first term is really tiny and also the other coefficients, of the cosine, and of the decaying exponential, are small." ] }, { "cell_type": "code", "execution_count": 19, "id": "73492b8c", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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