737 lines
169 KiB
Plaintext
737 lines
169 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "4cc6c96f",
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"metadata": {},
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"source": [
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"# Ćwiczenia 4"
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]
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},
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{
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"cell_type": "markdown",
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"id": "1276423e",
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"metadata": {},
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"source": [
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"***TEMAT:*** szeregi Fouriera"
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]
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},
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{
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"cell_type": "markdown",
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"id": "377a729f",
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"metadata": {},
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"source": [
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"## Ortogonalność układu trygonometrycznego"
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]
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},
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{
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"cell_type": "markdown",
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"id": "20c2c5c3",
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"metadata": {},
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"source": [
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"#### Zadanie 1\n",
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"Pokaż, że:\n",
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"\n",
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"1.\n",
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"\n",
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" $$\\int_{-\\pi}^\\pi \\sin(nx)\\sin(mx)dx=\\begin{cases}\\pi, & n=m;\\\\\n",
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"0,& n\\not= m;\n",
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"\\end{cases}\n",
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"$$\n",
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"dla każdego $n,m\\geq 1$.\n",
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"\n",
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"2.\n",
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"\n",
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"$$\\int_{-\\pi}^\\pi \\cos(nx)\\cos(mx)dx=\\begin{cases}\\pi, & n=m\\not=0;\\\\\n",
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"2\\pi, & n=m=0;\\\\\n",
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"0,& n\\not= m;\n",
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"\\end{cases}\n",
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"$$\n",
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"dla każdego $n,m\\geq 0$.\n",
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"\n",
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"3. \n",
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"\n",
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"$$\\int_{-\\pi}^\\pi \\sin(nx)\\cos(mx)dx=0\n",
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"$$\n",
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"dla każdego $n,m\\geq 0$.\n",
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"\n",
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"\n",
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"***Uwaga:*** na wykładzie 6 okaże się, że powyższe rachunki oznaczają ortogonalność rodziny funkcji $\\{\\sin(nx),\\cos(mx): n\\geq 1, m\\geq 0\\}$."
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]
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},
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{
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"cell_type": "markdown",
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"id": "a9fe3612",
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"metadata": {},
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"source": [
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"##### Rozwiązanie:\n",
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"1. \n",
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"Jeśli $n=m$, to z \"jedynki trygonometrycznej\" i wzoru na cosinus podwojonego kąta wynika, że \n",
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"\n",
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"$$\n",
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"\\int_{-\\pi}^\\pi \\sin(nx)\\sin(nx)dx=\\frac{1}{2}\\int_{-\\pi}^\\pi 1- \\cos(2nx)dx=\\frac{1}{2}x-\\frac{\\sin(2nx)}{4n}\\biggr|_{-\\pi}^\\pi=\\pi.\n",
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"$$\n",
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"\n",
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"Jeśli $n\\not=m$, to wiadomo że \n",
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"\n",
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"$$\n",
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"\\sin(nx)\\sin(mx)=\\frac{1}{2}\\left( \\cos((n-m)x)-\\cos((n+m)x)\\right).\n",
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"$$\n",
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"\n",
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"Zatem\n",
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"$$\n",
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"\\int_{-\\pi}^\\pi \\sin(nx)\\sin(mx)dx=\\frac{1}{2}\\left(\\frac{\\sin((n-m)x)}{n-m}-\\frac{\\sin((n+m)x)}{n+m}\\right)\\biggr|_{-\\pi}^\\pi=0\n",
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"$$\n",
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"\n",
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"2. Dowodzi się tego w identyczny sposób jak wzoru w 1. \n",
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"\n",
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"3. Wystarczy zauważyć, że jak $n=0$, to $\\sin(nx)\\cos(mx)$=0, a dla $n\\geq 1$ funkcja $\\sin(nx)\\cos(mx)$ jest nieparzysta.\n",
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"\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "a92c3fcc",
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"metadata": {},
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"source": [
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"## Szereg Fouriera dla funkcji 2$\\pi$ okresowej: postać rzeczywista"
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]
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},
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{
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"cell_type": "markdown",
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"id": "be2929df",
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"metadata": {},
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"source": [
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"### Rozwijanie funkcji w szereg Fouriera"
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]
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},
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{
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"cell_type": "markdown",
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"id": "cb209cea",
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"metadata": {},
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"source": [
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"***Twierdzenie*** \n",
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"\n",
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"Jeżeli szereg trygonometryczny \n",
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"\n",
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"$$\n",
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"\\frac {\\displaystyle {a_0}}{\\displaystyle 2}+ \\sum_{n=1}^{\\infty}\n",
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"(a_n\\cos nx+b_n\\sin nx)\n",
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"$$\n",
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"\n",
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"jest zbieżny jednostajnie do funkcji $f$ na przedziale $[-\\pi,\\pi]$, to\n",
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"\n",
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"$$\n",
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"a_0=\\frac{1}{\\pi}\\int_{-\\pi}^{\\pi}f(x)\\; dx,\\quad\n",
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"a_n=\\frac {\\displaystyle 1}{\\displaystyle {\\pi}} \\int_{-\\pi}^{\\pi}f(x)\\cos nx\\; dx,\\quad\n",
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"b_n=\\frac {\\displaystyle 1}{\\displaystyle {\\pi}} \\int_{-\\pi}^{\\pi}f(x)\\sin nx \\; dx,\n",
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"$$ \n",
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"\n",
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"dla $n=1,2,\\ldots$. "
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]
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},
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{
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"cell_type": "markdown",
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"id": "cd1dc617",
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"metadata": {},
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"source": [
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"***Definicja***\n",
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"\n",
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"Szereg \n",
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"\n",
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"$$\\frac {\\displaystyle {a_0}}{\\displaystyle 2}+ \\sum_{n=1}^{\\infty}(a_n\\cos nx+b_n\\sin nx),\n",
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"$$\n",
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"\n",
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"w którym liczby $a_0,a_1,a_2,\\ldots$, $b_1,b_2,\\ldots$ są takie jak w twierdzeniu powyżej nazywamy szeregiem Fouriera odpowiadającym funkcji $f$."
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]
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},
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{
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"cell_type": "markdown",
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"id": "08b840ff",
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"metadata": {},
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"source": [
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"***Bardzo ważne uwagi:***\n",
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">* na razie nic nie powiedzieliśmy o zbieżności szeregu Fouriera odpowiadającego funkcji $f$.\n",
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">* jeśli $f$ jest funkcją parzystą, to w jej szeregu Fouriera wszystkie $b_n=0$.\n",
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">* jeśli $f$ jest funkcją nieparzystą, to w jej szeregu Fouriera wszystkie $a_n=0$."
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]
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},
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{
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"cell_type": "markdown",
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"id": "dca41719",
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"metadata": {},
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"source": [
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"### Zbieżność szeregu Fouriera\n",
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"\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "fc09b556",
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"metadata": {},
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"source": [
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"***Definicja (funkcja kawałkami gładka)***\n",
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"\n",
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">* Mówimy, że funkcja $f$ ma nieciągłość skokową w punkcie $x_0$, gdy istnieją granice jednostronne\n",
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"\n",
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"$$\n",
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"f(x_0-):=\\lim_{x\\to x_0^-}f(x),\\quad f(x_0+):=\\lim_{x\\to x_0^+}f(x). \n",
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"$$\n",
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"\n",
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">* Mówimy, że funkcja $f$ jest kawałkami gładka, gdy w dowolnym przedziale $(a,b)$ jest ciągła poza skończoną liczbą punktów przedziału $(a,b)$, jej punkty nieciągłości są nieciągłościami skokowymi, a pochodna funkcji $f$ jest ciągła poza skończoną liczbą punktów przedziału $(a,b)$."
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]
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},
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{
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"cell_type": "markdown",
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"id": "d7523627",
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"metadata": {},
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"source": [
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"***Twierdzenie***\n",
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"\n",
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"Jeśli $2\\pi$ okresowa funkcja $f$ jest kawałkami gładka na $\\mathbb{R}$, to jej szereg Fouriera jest zbieżny dla dowolnego \n",
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"$x$ do wartości $\\frac{f(x-)+f(x+)}{2}$.\n",
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"\n",
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"***Uwaga:*** jeśli $f$ jest ciągła w punkcie $x$, to $\\frac{f(x-)+f(x+)}{2}=f(x)$."
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]
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},
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{
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"cell_type": "markdown",
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"id": "fd37d0aa",
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"metadata": {},
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"source": [
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"#### Zadanie 2: sygnał prostokątny \n",
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"Rozwiniemy w szereg Fouriera funkcję $2\\pi $ okresową $f$ taką, że \n",
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"$$\n",
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"f(x)=\\begin{cases}\n",
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"1, & x\\in[ 0,\\pi];\\\\\n",
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"0, & x\\in (-\\pi,0).\n",
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"\\end{cases}\n",
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"$$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "a5896f29",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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UpLi4OEdGOJdmG6KqTuGLjIy0DlERERGKjIxkMrgJNfcM6u5+1NwzWrVq5fjX5v0A9ce+7hnU3f2ouWc0pO51/ZoPF5YAAAAAAAuEKAAAAACwQIgCAAAAAAuEKAAAAACwQIgCAAAAAAuEKAAAAACwQIgCAAAAAAuEKAAAAACwQIgCAAAAAAuEKAAAAACwQIgCAAAAAAuEKAAAAACwQIgCAAAAAAvBnu4ApPJy6bPPpIMHpdhYafBgKSjI071CQzCm/ocx9U/l5VJOTuX/c3KkhATG1dcxV/0T4+p/fH1MveJI1KeffqoxY8aoU6dOCggI0IoVK865ztq1azVgwACFhYXpJz/5iZYtW9bk/WwKb78txcdLQ4dKN9xQ+W98fOVy+CbG1P8wpv6palxnzqz8PHHmzGDG1ccxV/0T4+p//GFMveJI1IkTJ9SvXz/dfPPNuuaaa87ZfufOnRo9erRuu+02vfzyy8rKytItt9yi2NhYpaSkuKHHjePtt6XrrpOMcV6+f3/l8jfflOpQDniRt9+WrrvWyMjozM8o9u+r0HXXBujNi2brmvM+8VwHLQQZo8GFhQrKyJACAjzdHY95++gQXbctw/WYXhfIPPVRznP1P3xxrvqipnh9qXGu8p7q03z9fZX30ur8Zq4aLyPJvPPOO7W2+f3vf2969+7ttGz8+PEmJSWlzts5duyYkWSOHTtm1b/S0lKzYsUKU1paarXe2U6fNqZLF2MqI1T1W0CAMXFxle2au8aqeVP7z5iWux5TlZs47TanFVjzwHPzqttpBZou2lPzmDbyPPWVfd3XVZ+rOUbS//3LXPXFm7vnqq/ytdcY3lf97+auuVqffd02G3jFkShb2dnZSk5OdlqWkpKiu+66q8Z1SkpKVFJS4rhfVFQkSSorK1NZWVmdt13V1mYdVz75JED79tVcfmOkvXuljz8+rSFDTIO25esaq+ZN7T9j6vosWaNA7dX5+kyDdaW891Mz/MdnGqx9iqvx8caep76yr/s65qr/cfdc9VW+9hrDXPU/7pqr9dnXbeeFT4ao/Px8RUdHOy2Ljo5WUVGRTp48qRYtWlRbJyMjQ3Pnzq22fM2aNYqIiLDuQ2ZmpvU6Z/r0086SLjtnuw8+yNWJE/sbtC1/0dCaN7W6julBxTZ9Z9Ao6jpWjT1PvX1f93XMVf/jqbnqq3zlNYa56n/cPVdt9vXi4mKr5/bJEFUfs2fPVlpamuN+UVGR4uLiNHz4cEVGRtb5ecrKypSZmalhw4YpJCSk3v1p2TJACxacu93Ikf01ZEi/em/HHzRWzZtaXcc0VgebvjNoFHUdq8aap76yr/s65qr/cfdc9VW+9hrDXPU/7pqr9dnXq85SqyufDFExMTEqKChwWlZQUKDIyEiXR6EkKSwsTGFhYdWWh4SE1OuFpL7rVRk6VOrSpfJLdMbF0cqAgMrHhw4N9qnLPTalhta8qTnGdF+FjItTDwJUoS6hhzT40jIp4Gce6KGdCmNUWFiotm3bKrCZfhl2sClTl68KtL80yvWYNtE89fZ93df521z1RY39+uKpueqrfOU1xh/mKu+lztw9V232dds54ZMhKikpSStXrnRalpmZqaSkJA/1yF5QkPTnP1dehSQgwDlIVc2xhQt963r5zd1/xjRQAXI1poFa+GqMgq75h4d6aKe8rEyfrVypUaNGKdAH3mybQpCkP//fVTRdjynz1Bf521z1RY39+sJc9U/+MFd5L3XmT3PVK/5O1I8//qjc3Fzl5uZKqryEeW5urvbs2SOp8lS8SZMmOdrfdttt+te//qXf//73ysvL01/+8he98cYbuvvuuz3R/Xq75prKyzh27uy8vEsXH7q8I5wwpv6HMfVPjKv/YUz9E+Pqf/xlTL3iSNSXX36poUOHOu5XfXdp8uTJWrZsmQ4ePOgIVJLUrVs3vf/++7r77rv15z//WV26dNHzzz/vU38jqso110i//rVv/8VmOGNM/Q9j6p+qxvXZZ09r5kzpL385rRkzGFdfxlz1T4yr//GHMfWKEHXllVfKuPpi0P9ZtmyZy3W++uqrJuyV+wQFSVde6eleoDExpv6HMfVPQUFSQkLl/xMSfOsNHK4xV/0T4+p/fH1MveJ0PgAAAADwFYQoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC14TohYtWqT4+HiFh4crMTFRX3zxRa3tFy5cqB49eqhFixaKi4vT3XffrVOnTrmptwAAAACaK68IUa+//rrS0tKUnp6uTZs2qV+/fkpJSdGhQ4dctn/llVd03333KT09XVu2bNELL7yg119/Xffff7+bew4AAACgufGKELVgwQJNnz5dU6dO1cUXX6zFixcrIiJCS5Yscdl+/fr1+vnPf64bbrhB8fHxGj58uCZOnHjOo1cAAAAA0FDBnu5AaWmpcnJyNHv2bMeywMBAJScnKzs72+U6gwYN0ksvvaQvvvhCAwcO1L/+9S+tXLlSN910U43bKSkpUUlJieN+UVGRJKmsrExlZWV17m9VW5t10DDU3DOou/tRc884s+7U3j3Y1z2DursfNfeM+tTddow8HqKOHDmi8vJyRUdHOy2Pjo5WXl6ey3VuuOEGHTlyRJdffrmMMTp9+rRuu+22Wk/ny8jI0Ny5c6stX7NmjSIiIqz7nZmZab0OGoaaewZ1dz9q7l47duyQJG3YsEFHjhzxcG+aF/Z1z6Du7kfNPcOm7sXFxVbP7fEQVR9r167Vo48+qr/85S9KTEzU9u3bdeedd+rhhx/WAw884HKd2bNnKy0tzXG/qKhIcXFxGj58uCIjI+u87bKyMmVmZmrYsGEKCQlp8M+Cc6PmnkHd3Y+ae0bVqeCJiYkaOHCgh3vTPLCvewZ1dz9q7hn1qXvVWWp15fEQ1aFDBwUFBamgoMBpeUFBgWJiYlyu88ADD+imm27SLbfcIkm65JJLdOLECc2YMUP//d//rcDA6l/1CgsLU1hYWLXlISEh9dqp67se6o+aewZ1dz9q7l5Vtabu7kfNPYO6ux819wybutuOj8cvLBEaGqqEhARlZWU5llVUVCgrK0tJSUku1ykuLq4WlIKCgiRJxpim6ywAAACAZs/jR6IkKS0tTZMnT9Zll12mgQMHauHChTpx4oSmTp0qSZo0aZI6d+6sjIwMSdKYMWO0YMECXXrppY7T+R544AGNGTPGEaYAAAAAoCl4RYgaP368Dh8+rDlz5ig/P1/9+/fXqlWrHBeb2LNnj9ORpz/84Q8KCAjQH/7wB+3fv19RUVEaM2aMHnnkEU/9CAAAAACaCa8IUZKUmpqq1NRUl4+tXbvW6X5wcLDS09OVnp7uhp4BAAAAwH94/DtRAAAAAOBLCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWvCZELVq0SPHx8QoPD1diYqK++OKLWtsXFhZq1qxZio2NVVhYmC666CKtXLnSTb0FAAAA0FwFe7oDkvT6668rLS1NixcvVmJiohYuXKiUlBRt3bpVHTt2rNa+tLRUw4YNU8eOHfXmm2+qc+fO2r17t9q2bev+zgMAAABoVrwiRC1YsEDTp0/X1KlTJUmLFy/W+++/ryVLlui+++6r1n7JkiU6evSo1q9fr5CQEElSfHy8O7sMAAAAoJnyeIgqLS1VTk6OZs+e7VgWGBio5ORkZWdnu1znvffeU1JSkmbNmqV3331XUVFRuuGGG3TvvfcqKCjI5TolJSUqKSlx3C8qKpIklZWVqaysrM79rWprsw4ahpp7BnV3P2ruGWfWndq7B/u6Z1B396PmnlGfutuOkcdD1JEjR1ReXq7o6Gin5dHR0crLy3O5zr/+9S999NFHuvHGG7Vy5Upt375dM2fOVFlZmdLT012uk5GRoblz51ZbvmbNGkVERFj3OzMz03odNAw19wzq7n7U3L127NghSdqwYYOOHDni4d40L+zrnkHd3Y+ae4ZN3YuLi62e2+Mhqj4qKirUsWNHPfvsswoKClJCQoL279+v+fPn1xiiZs+erbS0NMf9oqIixcXFafjw4YqMjKzztsvKypSZmalhw4Y5TiVE06LmnkHd3Y+ae0bVhYwSExM1cOBAD/emeWBf9wzq7n7U3DPqU/eqs9TqyuMhqkOHDgoKClJBQYHT8oKCAsXExLhcJzY2ViEhIU6n7vXq1Uv5+fkqLS1VaGhotXXCwsIUFhZWbXlISEi9dur6rof6o+aeQd3dj5q7V1Wtqbv7UXPPoO7uR809w6butuPj8Uuch4aGKiEhQVlZWY5lFRUVysrKUlJSkst1fv7zn2v79u2qqKhwLNu2bZtiY2NdBigAAAAAaCweD1GSlJaWpueee04vvviitmzZottvv10nTpxwXK1v0qRJTheeuP3223X06FHdeeed2rZtm95//309+uijmjVrlqd+BAAAAADNhMdP55Ok8ePH6/Dhw5ozZ47y8/PVv39/rVq1ynGxiT179igw8D95Ly4uTqtXr9bdd9+tvn37qnPnzrrzzjt17733eupHAAAAANBMeEWIkqTU1FSlpqa6fGzt2rXVliUlJenzzz9v4l4BAAAAgDOvOJ0PAAAAAHwFIQoAAAAALBCiAAAAAMACIQoAAAAALBCiAAAAAMACIQoAAAAALBCiAAAAAMACIQoAAAAALBCiAAAAAMACIQoAAAAALBCiAAAAAMACIQoAAAAALBCiAAAAAMACIQoAAAAALBCiAAAAAMACIQoAAAAALBCiAAAAAMACIQoAAAAALBCiAAAAAMACIQoAAAAALBCiAAAAAMACIQoAAAAALBCiAAAAAMACIQoAAAAALBCiAAAAAMBCcENWLisrU35+voqLixUVFaXzzjuvsfoFAAAAAF7J+kjU8ePH9fTTT2vIkCGKjIxUfHy8evXqpaioKHXt2lXTp0/Xxo0bm6KvAAAAAOBxViFqwYIFio+P19KlS5WcnKwVK1YoNzdX27ZtU3Z2ttLT03X69GkNHz5cI0aM0Pfff99U/QYAAAAAj7A6nW/jxo369NNP1bt3b5ePDxw4UDfffLMWL16spUuX6rPPPtOFF17YKB0FAAAAAG9gFaJeffVVx/+PHz+u1q1bu2wXFham2267rWE9AwAAAAAvVO+r8w0ePFj5+fmN2RcAAAAA8Hr1DlGXXnqpEhMTlZeX57Q8NzdXo0aNanDHAAAAAMAb1TtELV26VFOmTNHll1+udevWadu2bbr++uuVkJCgoKCgxuwjAAAAAHiNBv2dqLlz5yosLEzDhg1TeXm5rrrqKmVnZ2vgwIGN1T8AAAAA8Cr1PhJVUFCgO++8U3/84x918cUXKyQkRFOmTCFAAQAAAPBr9Q5R3bp106effqrly5crJydHb731lmbMmKH58+c3Zv8AAAAAwKvU+3S+JUuWaMKECY77I0aM0Mcff6xf/vKX2rVrlxYtWtQoHQQAAAAAb1LvI1FnBqgqAwYM0Pr16/XRRx81qFMAAAAA4K3qHaJqEh8fr/Xr1zf20wIAAACAV7AKUXv27KlTu3bt2kmS9u/fb98jAAAAAPBiViHqpz/9qW699VZt3LixxjbHjh3Tc889pz59+uitt95qcAcBAAAAwJtYXVhi9OjRatWqlYYNG6bw8HAlJCSoU6dOCg8P1w8//KDvvvtOmzdv1oABA/T4449r1KhRTdVvAAAAAPAIqxD10ksvae/evXr44YcVFRWl2NhYHTlyRCdPnlSHDh104403KiUlRX369Gmq/gIAAACAR1mFqE6dOik3N1cpKSk6efKkHn30UXXs2LGp+gYAAAAAXsfqO1H33HOPxowZo8GDBysgIEAvv/yyNm7cqJMnTzZV/wAAAADAq1iFqN/+9rf68ssvNWLECBljtGjRIiUlJSkyMlK9evXShAkTNG/ePH3wwQdN1V8AAAAA8Cir0/kkqW/fvurbt6+WLVum7OxstWzZUl9//bVyc3OVm5urd999V4888oiOHz/eFP0FAAAAAI+yDlFVvv/+e8f/ExMTlZiY6LhvjGlYrwAAAADAS1mdzldXAQEBTfG0AAAAAOBxTRKiAAAAAMBfEaIAAAAAwAIhCgAAAAAsEKIAAAAAwAIhCgAAAAAsEKIAAAAAwAIhCgAAAAAsEKIAAAAAwAIhCgAAAAAsEKIAAAAAwAIhCgAAAAAsEKIAAAAAwAIhCgAAAAAsEKIAAAAAwAIhCgAAAAAsEKIAAAAAwAIhCgAAAAAsEKIAAAAAwAIhCgAAAAAsEKIAAAAAwAIhCgAAAAAsEKIAAAAAwAIhCgAAAAAsEKIAAAAAwIJXhahFixYpPj5e4eHhSkxM1BdffFGn9V577TUFBARo7NixTdtBAAAAAM2e14So119/XWlpaUpPT9emTZvUr18/paSk6NChQ7Wut2vXLv3Xf/2XBg8e7KaeAgAAAGjOvCZELViwQNOnT9fUqVN18cUXa/HixYqIiNCSJUtqXKe8vFw33nij5s6dq+7du7uxtwAAAACaq2BPd0CSSktLlZOTo9mzZzuWBQYGKjk5WdnZ2TWu99BDD6ljx46aNm2aPvvss1q3UVJSopKSEsf9oqIiSVJZWZnKysrq3NeqtjbroGGouWdQd/ej5p5xZt2pvXuwr3sGdXc/au4Z9am77Rh5RYg6cuSIysvLFR0d7bQ8OjpaeXl5LtdZt26dXnjhBeXm5tZpGxkZGZo7d2615WvWrFFERIR1nzMzM63XQcNQc8+g7u5Hzd1rx44dkqQNGzboyJEjHu5N88K+7hnU3f2ouWfY1L24uNjqub0iRNk6fvy4brrpJj333HPq0KFDndaZPXu20tLSHPeLiooUFxen4cOHKzIyss7bLisrU2ZmpoYNG6aQkBDrvsMeNfcM6u5+1Nwzqi5ilJiYqIEDB3q4N80D+7pnUHf3o+aeUZ+6V52lVldeEaI6dOigoKAgFRQUOC0vKChQTExMtfY7duzQrl27NGbMGMeyiooKSVJwcLC2bt2qCy64wGmdsLAwhYWFVXuukJCQeu3U9V0P9UfNPYO6ux81d6+qWlN396PmnkHd3Y+ae4ZN3W3HxysuLBEaGqqEhARlZWU5llVUVCgrK0tJSUnV2vfs2VPffPONcnNzHbdf/epXGjp0qHJzcxUXF+fO7gMAAABoRrziSJQkpaWlafLkybrssss0cOBALVy4UCdOnNDUqVMlSZMmTVLnzp2VkZGh8PBw9enTx2n9tm3bSlK15QAAAADQmLwmRI0fP16HDx/WnDlzlJ+fr/79+2vVqlWOi03s2bNHgYFeceAMAAAAQDPmNSFKklJTU5WamurysbVr19a67rJlyxq/QwAAAABwFg7tAAAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFrwpRixYtUnx8vMLDw5WYmKgvvviixrbPPfecBg8erHbt2qldu3ZKTk6utT0AAAAANAavCVGvv/660tLSlJ6erk2bNqlfv35KSUnRoUOHXLZfu3atJk6cqI8//ljZ2dmKi4vT8OHDtX//fjf3HAAAAEBz4jUhasGCBZo+fbqmTp2qiy++WIsXL1ZERISWLFnisv3LL7+smTNnqn///urZs6eef/55VVRUKCsry809BwAAANCcBHu6A5JUWlqqnJwczZ4927EsMDBQycnJys7OrtNzFBcXq6ysTOedd57Lx0tKSlRSUuK4X1RUJEkqKytTWVlZnfta1dZmHTQMNfcM6u5+1Nwzzqw7tXcP9nXPoO7uR809oz51tx0jrwhRR44cUXl5uaKjo52WR0dHKy8vr07Pce+996pTp05KTk52+XhGRobmzp1bbfmaNWsUERFh3efMzEzrddAw1NwzqLv7UXP32rFjhyRpw4YNOnLkiId707ywr3sGdXc/au4ZNnUvLi62em6vCFENNW/ePL322mtau3atwsPDXbaZPXu20tLSHPeLiooc36OKjIys87bKysqUmZmpYcOGKSQkpMF9x7lRc8+g7u5HzT2j6qJEiYmJGjhwoId70zywr3sGdXc/au4Z9al71VlqdeUVIapDhw4KCgpSQUGB0/KCggLFxMTUuu4TTzyhefPm6cMPP1Tfvn1rbBcWFqawsLBqy0NCQuq1U9d3PdQfNfcM6u5+1Ny9qmpN3d2PmnsGdXc/au4ZNnW3HR+vuLBEaGioEhISnC4KUXWRiKSkpBrXe/zxx/Xwww9r1apVuuyyy9zRVQAAAADNnFcciZKktLQ0TZ48WZdddpkGDhyohQsX6sSJE5o6daokadKkSercubMyMjIkSY899pjmzJmjV155RfHx8crPz5cktWrVSq1atfLYzwEAAADAv3lNiBo/frwOHz6sOXPmKD8/X/3799eqVascF5vYs2ePAgP/c+Ds6aefVmlpqa677jqn50lPT9eDDz7ozq4DAAAAaEa8JkRJUmpqqlJTU10+tnbtWqf7u3btavoOAQAAAMBZvOI7UQAAAADgKwhRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFghRAAAAAGCBEAUAAAAAFoI93QFIxkj//rf0449Sq1ZS+/ZSQICne4WGYEz9D2Pqn4yRfvih8v8//FB5n3H1bcxV/8S4+h9fH1OORHlQYaH05z9LvXpJUVFSt26V//bqVbm8sNDTPYQtxtT/MKb+6cxxHTGi8vPEESOCGVcfxlz1T4yr//GXMSVEecjq1VLXrtJ//ZfUv7/0xhtSZmblv/37Vy7v2rWyHXwDY+p/GFP/dPa4zptXuXzePMbVVzFX/RPj6n/8akxNM3Xs2DEjyRw7dsxqvdLSUrNixQpTWlpa722vWmVMcLAxo0cbc/Cg6zYHD1Y+Hhxc2b45a4yaNzV/HFNfqHtT8sSYNveau4Orcc3JyTGSTE5OjjHG9+aqL2rMfd0fX3+bii+9xvjLuPpSzZuaO8e0PnW3zQZedSRq0aJFio+PV3h4uBITE/XFF1/U2n758uXq2bOnwsPDdckll2jlypVu6mn9FRZK118vpaRIK1ZIMTGu28XEVD6eklLZ3lcObTZHjKn/YUz9E+PqfxhT/8S4+h9/HFOvubDE66+/rrS0NC1evFiJiYlauHChUlJStHXrVnXs2LFa+/Xr12vixInKyMjQL3/5S73yyisaO3asNm3apD59+njgJ6ibF1+Uioul55+Xgs9R/eBg6bnnpPPjKvTX/gt1R+xy93TSywQZo8GFhQrKyPDKbxy+ePB6FZ+4U88/H1j3MT1f+utfpTvucE8fYcdT89Tb93Vfx1z1P7yn2vGV1xjmqv+p11z19jGt72GyxjZw4EAza9Ysx/3y8nLTqVMnk5GR4bL99ddfb0aPHu20LDEx0dx666112p4nTuerqDCmRw9jxo+3W+/668pNj+DvTUXlhUy4edGtQjI9gr83468vtxvT6yv3hYoKu33BnZrrKQjMU/+81TZXzz6dz2lcfWCu+qLGeH1hrvrnzd/eV5vre+mZ6j1XGzCm7jidzyuORJWWlionJ0ezZ892LAsMDFRycrKys7NdrpOdna20tDSnZSkpKVqxYoXL9iUlJSopKXHcLyoqkiT17NlTgYF1P6vRGKOSkhKFhYUpwPJTnIoK6eBB6fBhqUuXuq938qR09LTUWQEKlLHaJppWhQJ18PSVOvxhPcb0qNS5s2Sx+7lVQ/Z1X8Y89U+1zdXS0lJJ0ogRIxQaGur0mC/MVV/UGK8vzFX/5G/vq831vfRMDZqr9RzT+tS9oqLCahteEaKOHDmi8vJyRUdHOy2Pjo5WXl6ey3Xy8/Ndts/Pz3fZPiMjQ3Pnzq22/ODBg/Xsdf0dPVq/9dzfU5xbhaT99R9TBtVrMU/9zbnn6uHDh2t8jLnqvZir/ob3VX/lb2PqFSHKHWbPnu105KqoqEhxcXGKjY11+5Go886TWrSo+3pVSTxWB/jUzMtUKFAHFVv/MY31rk/MztRcPz1jnvqn2uZqaWmpDh8+rKioqBqPRHnzXPVFjXkkirnqX/ztfbW5vpeeqcFztR5jWt8jUTYHV7wiRHXo0EFBQUEqKChwWl5QUKCYGi7fERMTY9U+LCxMYWFh1Zbn5eUpMjKyzn0tKyvTypUrNWrUKIWEhNR5PanyZN9evSqvg//aa3Vfb/z1FfrnygPa0mecN38PtMlUGKPCwkK1bdtWgV5WAGOkXt8uV//kTnrt9brP8PHjpX/+U9qyxXu/29uQfd2XeXKeevO+7utqm6ubNm1SQkKCVq1apQEDBjg95gtz1Rc1xusL76n2fOE1xt/eV5vre+mZ6j1XGzCm9al7UVGR2rRpU+dteEWICg0NVUJCgrKysjR27FhJlWkwKytLqampLtdJSkpSVlaW7rrrLseyzMxMJSUluaHH9RMQIN1+e+UfEsvPr/nyjmc6eFB6+51A/elPXRRwh+vvh/m78rIyffZ/EyHQy16AAiTd/ud6jOnb0p/+5F0v9KjkyXnqzfu6r2Ou+h/eU+35wmsMc9X/1HuuevmYes0Bz7S0ND333HN68cUXtWXLFt1+++06ceKEpk6dKkmaNGmS04Un7rzzTq1atUp/+tOflJeXpwcffFBffvlljaHLW0yeLEVESLfcIp0+XXvb06el6dMr20+a5J7+wR5j6n8YU//EuPofxtQ/Ma7+xx/H1GtC1Pjx4/XEE09ozpw56t+/v3Jzc7Vq1SrHxSP27NnjdJ7ioEGD9Morr+jZZ59Vv3799Oabb2rFihVe/TeiJKltW+mNN6TVq6WxY2v+stzBg5WPr14tLV9euR68E2PqfxhT/8S4+h/G1D8xrv7HH8fUK07nq5KamlrjkaS1a9dWWzZu3DiNGzeuiXvV+FJSpP/938q/xHz++dI110jXXiu1ayf98IP01luVhzAjIqT335eGD/d0j3EujKn/YUz9k6txvfTSysfWrJEee4xx9TXMVf/EuPoffxtTrwpRzUlKirR7d+VfYv7LXyrTeZUePSrPAZ08WbL4fhs8jDH1P4ypf6ppXGfPZlx9FXPVPzGu/sefxpQQ5UFt20p33CH99reVl3A8flxq3bryEpDe+iU61I4x9T+MqX86c1wzM08rJUVavfq0hg1jXH0Vc9U/Ma7+x1/GlBDlBQICpPbtK2/wD4yp/2FM/VNAwH/OuW/b1rfewOEac9U/Ma7+x9fH1GsuLAEAAAAAvoAQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWCFEAAAAAYIEQBQAAAAAWgj3dAU8xxkiSioqKrNYrKytTcXGxioqKFBIS0hRdw1mouWdQd/ej5p7x448/Ov61fU9A/bCvewZ1dz9q7hn1qXvV639VRjiXAFPXln5m3759iouL83Q3AAAAAHiJvXv3qkuXLuds12xDVEVFhQ4cOKDWrVsrICCgzusVFRUpLi5Oe/fuVWRkZBP2EFWouWdQd/ej5p5B3d2PmnsGdXc/au4Z9am7MUbHjx9Xp06dFBh47m88NdvT+QIDA+uUMmsSGRnJZHAzau4Z1N39qLlnUHf3o+aeQd3dj5p7hm3d27RpU+e2XFgCAAAAACwQogAAAADAAiHKUlhYmNLT0xUWFubprjQb1NwzqLv7UXPPoO7uR809g7q7HzX3DHfUvdleWAIAAAAA6oMjUQAAAABggRAFAAAAABYIUQAAAABggRAFAAAAABYIUWd55JFHNGjQIEVERKht27Yu2+zZs0ejR49WRESEOnbsqN/97nc6ffp0rc979OhR3XjjjYqMjFTbtm01bdo0/fjjj03wE/i+tWvXKiAgwOVt48aNNa535ZVXVmt/2223ubHnvi8+Pr5aDefNm1frOqdOndKsWbPUvn17tWrVStdee60KCgrc1GPftmvXLk2bNk3dunVTixYtdMEFFyg9PV2lpaW1rse+bm/RokWKj49XeHi4EhMT9cUXX9Tafvny5erZs6fCw8N1ySWXaOXKlW7qqe/LyMjQT3/6U7Vu3VodO3bU2LFjtXXr1lrXWbZsWbV9Ojw83E099g8PPvhgtRr27Nmz1nXYzxvG1XtmQECAZs2a5bI9+3n9fPrppxozZow6deqkgIAArVixwulxY4zmzJmj2NhYtWjRQsnJyfr+++/P+by27wtnI0SdpbS0VOPGjdPtt9/u8vHy8nKNHj1apaWlWr9+vV588UUtW7ZMc+bMqfV5b7zxRm3evFmZmZn63//9X3366aeaMWNGU/wIPm/QoEE6ePCg0+2WW25Rt27ddNlll9W67vTp053We/zxx93Ua//x0EMPOdXwt7/9ba3t7777bv3973/X8uXL9cknn+jAgQO65ppr3NRb35aXl6eKigo988wz2rx5s5588kktXrxY999//znXZV+vu9dff11paWlKT0/Xpk2b1K9fP6WkpOjQoUMu269fv14TJ07UtGnT9NVXX2ns2LEaO3asvv32Wzf33Dd98sknmjVrlj7//HNlZmaqrKxMw4cP14kTJ2pdLzIy0mmf3r17t5t67D969+7tVMN169bV2Jb9vOE2btzoVO/MzExJ0rhx42pch/3c3okTJ9SvXz8tWrTI5eOPP/64/ud//keLFy/Whg0b1LJlS6WkpOjUqVM1Pqft+4JLBi4tXbrUtGnTptrylStXmsDAQJOfn+9Y9vTTT5vIyEhTUlLi8rm+++47I8ls3LjRseyDDz4wAQEBZv/+/Y3ed39TWlpqoqKizEMPPVRruyFDhpg777zTPZ3yU127djVPPvlkndsXFhaakJAQs3z5cseyLVu2GEkmOzu7CXro/x5//HHTrVu3Wtuwr9sZOHCgmTVrluN+eXm56dSpk8nIyHDZ/vrrrzejR492WpaYmGhuvfXWJu2nvzp06JCRZD755JMa29T0nou6S09PN/369atze/bzxnfnnXeaCy64wFRUVLh8nP284SSZd955x3G/oqLCxMTEmPnz5zuWFRYWmrCwMPPqq6/W+Dy27wuucCTKUnZ2ti655BJFR0c7lqWkpKioqEibN2+ucZ22bds6HUVJTk5WYGCgNmzY0OR99nXvvfee/v3vf2vq1KnnbPvyyy+rQ4cO6tOnj2bPnq3i4mI39NC/zJs3T+3bt9ell16q+fPn13qqak5OjsrKypScnOxY1rNnT51//vnKzs52R3f9zrFjx3Teeeedsx37et2UlpYqJyfHaR8NDAxUcnJyjftodna2U3up8nWefbp+jh07Jknn3K9//PFHde3aVXFxcfr1r39d43sqavb999+rU6dO6t69u2688Ubt2bOnxrbs542rtLRUL730km6++WYFBATU2I79vHHt3LlT+fn5TvtymzZtlJiYWOO+XJ/3BVeC69/t5ik/P98pQEly3M/Pz69xnY4dOzotCw4O1nnnnVfjOviPF154QSkpKerSpUut7W644QZ17dpVnTp10tdff617771XW7du1dtvv+2mnvq+O+64QwMGDNB5552n9evXa/bs2Tp48KAWLFjgsn1+fr5CQ0OrfX8wOjqafbsetm/frqeeekpPPPFEre3Y1+vuyJEjKi8vd/m6nZeX53Kdml7n2aftVVRU6K677tLPf/5z9enTp8Z2PXr00JIlS9S3b18dO3ZMTzzxhAYNGqTNmzef87UflRITE7Vs2TL16NFDBw8e1Ny5czV48GB9++23at26dbX27OeNa8WKFSosLNSUKVNqbMN+3viq9lebfbk+7wuuNIsQdd999+mxxx6rtc2WLVvO+QVMNEx9xmHfvn1avXq13njjjXM+/5nfMbvkkksUGxurq666Sjt27NAFF1xQ/477OJu6p6WlOZb17dtXoaGhuvXWW5WRkaGwsLCm7qrfqM++vn//fo0YMULjxo3T9OnTa12XfR2+YtasWfr2229r/W6OJCUlJSkpKclxf9CgQerVq5eeeeYZPfzww03dTb8wcuRIx//79u2rxMREde3aVW+88YamTZvmwZ41Dy+88IJGjhypTp061diG/dy/NIsQdc8999T6yYAkde/evU7PFRMTU+3qHVVXIouJialxnbO/qHb69GkdPXq0xnX8UX3GYenSpWrfvr1+9atfWW8vMTFRUuWn+835F8uG7P+JiYk6ffq0du3apR49elR7PCYmRqWlpSosLHQ6GlVQUNCs9u2z2db8wIEDGjp0qAYNGqRnn33Wenvs6zXr0KGDgoKCql0xsrZ9NCYmxqo9XEtNTXVcSMn2U/aQkBBdeuml2r59exP1zv+1bdtWF110UY01ZD9vPLt379aHH35ofTYA+3nDVe2vBQUFio2NdSwvKChQ//79Xa5Tn/cFV5pFiIqKilJUVFSjPFdSUpIeeeQRHTp0yHGKXmZmpiIjI3XxxRfXuE5hYaFycnKUkJAgSfroo49UUVHh+OWnObAdB2OMli5dqkmTJikkJMR6e7m5uZLkNKmao4bs/7m5uQoMDKx2OmqVhIQEhYSEKCsrS9dee60kaevWrdqzZ4/Tp23NjU3N9+/fr6FDhyohIUFLly5VYKD9V1XZ12sWGhqqhIQEZWVlaezYsZIqTzHLyspSamqqy3WSkpKUlZWlu+66y7EsMzOzWe/TNowx+u1vf6t33nlHa9euVbdu3ayfo7y8XN98841GjRrVBD1sHn788Uft2LFDN910k8vH2c8bz9KlS9WxY0eNHj3aaj3284br1q2bYmJilJWV5QhNRUVF2rBhQ41X2q7P+4JLNlfEaA52795tvvrqKzN37lzTqlUr89VXX5mvvvrKHD9+3BhjzOnTp02fPn3M8OHDTW5urlm1apWJiooys2fPdjzHhg0bTI8ePcy+ffscy0aMGGEuvfRSs2HDBrNu3Tpz4YUXmokTJ7r95/MlH374oZFktmzZUu2xffv2mR49epgNGzYYY4zZvn27eeihh8yXX35pdu7cad59913TvXt3c8UVV7i72z5r/fr15sknnzS5ublmx44d5qWXXjJRUVFm0qRJjjZn190YY2677TZz/vnnm48++sh8+eWXJikpySQlJXniR/A5+/btMz/5yU/MVVddZfbt22cOHjzouJ3Zhn29YV577TUTFhZmli1bZr777jszY8YM07ZtW8dVVm+66SZz3333Odr/4x//MMHBweaJJ54wW7ZsMenp6SYkJMR88803nvoRfMrtt99u2rRpY9auXeu0TxcXFzvanF3zuXPnmtWrV5sdO3aYnJwcM2HCBBMeHm42b97siR/BJ91zzz1m7dq1ZufOneYf//iHSU5ONh06dDCHDh0yxrCfN5Xy8nJz/vnnm3vvvbfaY+znjeP48eOO38clmQULFpivvvrK7N692xhjzLx580zbtm3Nu+++a77++mvz61//2nTr1s2cPHnS8Ry/+MUvzFNPPeW4f673hbogRJ1l8uTJRlK128cff+xos2vXLjNy5EjTokUL06FDB3PPPfeYsrIyx+Mff/yxkWR27tzpWPbvf//bTJw40bRq1cpERkaaqVOnOoIZXJs4caIZNGiQy8d27tzpNC579uwxV1xxhTnvvPNMWFiY+clPfmJ+97vfmWPHjrmxx74tJyfHJCYmmjZt2pjw8HDTq1cv8+ijj5pTp0452pxdd2OMOXnypJk5c6Zp166diYiIMFdffbVTCEDNli5d6vL15szPt9jXG8dTTz1lzj//fBMaGmoGDhxoPv/8c8djQ4YMMZMnT3Zq/8Ybb5iLLrrIhIaGmt69e5v333/fzT32XTXt00uXLnW0Obvmd911l2N8oqOjzahRo8ymTZvc33kfNn78eBMbG2tCQ0NN586dzfjx48327dsdj7OfN43Vq1cbSWbr1q3VHmM/bxxVv1effauqbUVFhXnggQdMdHS0CQsLM1dddVW18ejatatJT093Wlbb+0JdBBhjTN2PWwEAAABA88bfiQIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAAAAALBAiAIAAAAAC4QoAECz8+qrr6pFixY6ePCgY9nUqVPVt29fHTt2zIM9AwD4ggBjjPF0JwAAcCdjjPr3768rrrhCTz31lNLT07VkyRJ9/vnn6ty5s6e7BwDwcsGe7gAAAO4WEBCgRx55RNddd51iYmL01FNP6bPPPiNAAQDqhCNRAIBma8CAAdq8ebPWrFmjIUOGeLo7AAAfwXeiAADN0qpVq5SXl6fy8nJFR0d7ujsAAB/CkSgAQLOzadMmXXnllXrmmWe0bNkyRUZGavny5Z7uFgDAR/CdKABAs7Jr1y6NHj1a999/vyZOnKju3bsrKSlJmzZt0oABAzzdPQCAD+BIFACg2Th69KgGDRqkK6+8UosXL3YsHz16tMrLy7Vq1SoP9g4A4CsIUQAAAABggQtLAAAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAIAFQhQAAAAAWCBEAQAAAICF/w/pi75ZCXBHegAAAABJRU5ErkJggg==\n",
|
|
"text/plain": [
|
|
"<Figure size 1000x600 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"import numpy as np\n",
|
|
"import matplotlib.pyplot as plt\n",
|
|
"\n",
|
|
"# Define the piecewise function that is 0 on (-pi, 0) and 1 on [0, pi)\n",
|
|
"def periodic_piecewise(x):\n",
|
|
" # Bring x into the interval [-pi, pi] using modulo\n",
|
|
" x_mod = np.mod(x + np.pi, 2 * np.pi) - np.pi\n",
|
|
" # Define the piecewise function\n",
|
|
" return np.where(x_mod >= 0, 1, 0)\n",
|
|
"\n",
|
|
"# Generate x values from -3pi to 3pi\n",
|
|
"x = np.linspace(-3 * np.pi, 3 * np.pi, 1000)\n",
|
|
"y = periodic_piecewise(x)\n",
|
|
"\n",
|
|
"# Plot the periodic function without vertical lines at discontinuities\n",
|
|
"plt.figure(figsize=(10, 6))\n",
|
|
"\n",
|
|
"# Split the data into segments between -pi and pi to avoid vertical lines\n",
|
|
"for n in range(-3, 3):\n",
|
|
" x_segment = x[(x >= n * np.pi) & (x < (n + 1) * np.pi)]\n",
|
|
" y_segment = y[(x >= n * np.pi) & (x < (n + 1) * np.pi)]\n",
|
|
" plt.plot(x_segment, y_segment, color='r',linewidth=4)\n",
|
|
"\n",
|
|
"# Mark closed and open dots at the ends of intervals\n",
|
|
"for n in range(-3,4):\n",
|
|
" plt.plot(n * np.pi, 1, 'bo',) # Closed dot for x = n*pi and f(x) = 1\n",
|
|
"\n",
|
|
"for n in range(-3,4):\n",
|
|
" plt.plot(n * np.pi, 0, 'wo', markersize=10, markeredgecolor='b') # Open dot for x = n*pi and f(x) = 1\n",
|
|
"\n",
|
|
"# Add axis lines\n",
|
|
"plt.axhline(0, color='black', linewidth=2)\n",
|
|
"plt.axvline(0, color='black', linewidth=1)\n",
|
|
"\n",
|
|
"# Set labels and title\n",
|
|
"plt.title(r'2$\\pi$-Periodic Function on $[-3\\pi, 3\\pi]$')\n",
|
|
"plt.xlabel(r'$x$')\n",
|
|
"plt.ylabel(r'$f(x)$')\n",
|
|
"\n",
|
|
"# Add grid \n",
|
|
"plt.grid(True)\n",
|
|
"\n",
|
|
"# Show the plot\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "32158b3c",
|
|
"metadata": {},
|
|
"source": [
|
|
"##### Rozwiązanie:\n",
|
|
"Mamy:\n",
|
|
"\n",
|
|
"1.\n",
|
|
"$$\n",
|
|
"a_0=\\frac{1}{\\pi}\\int_{-\\pi}^\\pi f(x)dx=\\frac{1}{\\pi}\\int_0^\\pi 1dx=1.\n",
|
|
"$$\n",
|
|
"\n",
|
|
"2. Dla $n\\geq 1$\n",
|
|
"$$\n",
|
|
"a_n = \\frac{1}{\\pi} \\int_{-\\pi}^{\\pi} f(x) \\cos(nx) \\, dx = \\frac{1}{\\pi} \\int_0^\\pi \\cos(nx) \\, dx = \\frac{\\sin(nx)}{\\pi n} \\bigg|_0^\\pi = 0.\n",
|
|
"$$\n",
|
|
"\n",
|
|
"3. Dla $n\\geq 1$\n",
|
|
"$$\n",
|
|
"b_n = \\frac{1}{\\pi} \\int_{-\\pi}^{\\pi} f(x) \\sin(nx) \\, dx = \\frac{1}{\\pi} \\int_{0}^{\\pi} \\sin(nx) \\, dx = -\\frac{\\cos(nx)}{\\pi n} \\bigg|_{0}^{\\pi} = -\\frac{(-1)^n - 1}{\\pi n}=\\frac{1-(-1)^n}{\\pi n}.\n",
|
|
"$$\n",
|
|
"\n",
|
|
"Ostatecznie szereg Foueriera naszej funkcji, to szereg\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\frac{1}{2}+\\sum_{n=1}^\\infty\\frac{1-(-1)^n}{\\pi n}\\sin(nx).\n",
|
|
"$$\n",
|
|
"\n",
|
|
"Zgodnie z twierdzeniem powyżej, dla $x$ będących całkowitymi wielokrotnościami $\\pi$ jest on zbieżny do $1/2$, dla pozostałych \n",
|
|
"$x$ jest on zbieżny do $f(x)$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 2,
|
|
"id": "adb272c0",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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\n",
|
|
"text/plain": [
|
|
"<Figure size 1000x600 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"import numpy as np\n",
|
|
"import matplotlib.pyplot as plt\n",
|
|
"\n",
|
|
"# Function to compute the Fourier series approximation\n",
|
|
"def fourier_series_step_function(x, n_terms):\n",
|
|
" result = 0.5 # a_0 / 2 term\n",
|
|
" for n in range(1, n_terms + 1, 2): # Only odd terms contribute\n",
|
|
" result += (2 / (n * np.pi)) * np.sin(n * x)\n",
|
|
" return result\n",
|
|
"\n",
|
|
"# Generate x values from -3pi to 3pi\n",
|
|
"x = np.linspace(-3 * np.pi, 3 * np.pi, 1000)\n",
|
|
"\n",
|
|
"# Compute Fourier series approximation with a certain number of terms\n",
|
|
"n_terms = 10 # You can increase this for a better approximation\n",
|
|
"y = fourier_series_step_function(x, n_terms)\n",
|
|
"\n",
|
|
"# Plot the Fourier series\n",
|
|
"plt.figure(figsize=(10, 6))\n",
|
|
"plt.plot(x, y, color='b')\n",
|
|
"\n",
|
|
"\n",
|
|
"\n",
|
|
"# Add axis lines\n",
|
|
"plt.axhline(0, color='black', linewidth=2)\n",
|
|
"plt.axhline(0.5, color='red', linewidth=0.5)\n",
|
|
"plt.axvline(0, color='black', linewidth=2)\n",
|
|
"\n",
|
|
"# Set labels and title\n",
|
|
"plt.title(r'Fourier Series Approximation of Step Function on $[-3\\pi, 3\\pi]$')\n",
|
|
"plt.xlabel(r'$x$')\n",
|
|
"plt.ylabel(r'$f(x)$')\n",
|
|
"\n",
|
|
"# Add grid, legend, and show the plot\n",
|
|
"plt.grid(True)\n",
|
|
"\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "c5696a45-314e-475f-8aae-ffdf77d1834d",
|
|
"metadata": {},
|
|
"source": [
|
|
"***Zadanie domowe:***\n",
|
|
"Zapoznaj się z materiałem znajdującym się tutaj: https://en.wikipedia.org/wiki/Gibbs_phenomenon."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "9bc09abd",
|
|
"metadata": {},
|
|
"source": [
|
|
"#### Zadanie 3: sygnał trójkątny\n",
|
|
"\n",
|
|
"Rozwiniemy w szereg Fouriera funkcję $2\\pi $ okresową $f$ taką, że \n",
|
|
"$f(x)=|x|$ dla $x\\in[-\\pi,\\pi]$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "11e821aa",
|
|
"metadata": {},
|
|
"source": [
|
|
"##### Rozwiązanie\n",
|
|
"\n",
|
|
"\n",
|
|
"1. Obliczamy $a_0$:\n",
|
|
"\n",
|
|
"$$\n",
|
|
"a_0 = \\frac{1}{\\pi} \\int_{-\\pi}^{\\pi} f(x) \\, dx = \\frac{2}{\\pi} \\int_{0}^{\\pi} x \\, dx = \\pi.\n",
|
|
"$$\n",
|
|
"\n",
|
|
"\n",
|
|
"\n",
|
|
"2. Obliczamy $a_n$:\n",
|
|
"\n",
|
|
"$$\n",
|
|
"a_n = \\frac{1}{\\pi} \\int_{-\\pi}^{\\pi} f(x) \\cos(nx) \\, dx = \\frac{2}{\\pi} \\int_{0}^{\\pi} x \\cos(nx) \\, dx=\n",
|
|
"\\frac{2}{\\pi}\\left( \\frac{x \\sin(nx)}{n} + \\frac{\\cos(nx)}{n^2} \\right) \\bigg|_{0}^{\\pi}=\n",
|
|
"2\\frac{(-1)^n-1}{\\pi n^2}\n",
|
|
"$$\n",
|
|
"\n",
|
|
"\n",
|
|
"\n",
|
|
"3. Wszystkie współczynniki $b_n$ są równe 0, bo funkcja jest parzysta.\n",
|
|
"\n",
|
|
"Ostatecznie, szereg Fouriera funkcji $f(x) = |x|$ to\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\frac{\\pi}{2} + \\sum_{n=1}^{\\infty} 2\\frac{(-1)^n-1}{\\pi n^2} \\cos(nx).\n",
|
|
"$$\n",
|
|
"\n",
|
|
"Dla każdego $x$ jest on zbieżny do $f(x)$.\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 3,
|
|
"id": "38bcc701",
|
|
"metadata": {
|
|
"scrolled": true
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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\n",
|
|
"text/plain": [
|
|
"<Figure size 1000x600 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"import numpy as np\n",
|
|
"import matplotlib.pyplot as plt\n",
|
|
"\n",
|
|
"# Function to compute the Fourier series of |x|\n",
|
|
"def fourier_series_abs_x(x, n_terms):\n",
|
|
" # Start with the a_0 term which is pi/2\n",
|
|
" result = np.pi / 2\n",
|
|
" for n in range(1, n_terms + 1):\n",
|
|
" # Add the cosine terms with alternating signs\n",
|
|
" result += (2 / np.pi) * (((-1)**n -1)/ n**2) * np.cos(n * x)\n",
|
|
" return result\n",
|
|
"\n",
|
|
"# Generate x values from -3pi to 3pi\n",
|
|
"x = np.linspace(-3 * np.pi, 3 * np.pi, 1000)\n",
|
|
"\n",
|
|
"# Compute Fourier series approximation for |x|\n",
|
|
"n_terms = 10 # Number of terms in the series\n",
|
|
"y = fourier_series_abs_x(x, n_terms)\n",
|
|
"\n",
|
|
"# Plot the Fourier series\n",
|
|
"plt.figure(figsize=(10, 6))\n",
|
|
"plt.plot(x, y, label=f'Fourier series approximation with {n_terms} terms')\n",
|
|
"plt.axhline(0, color='black',linewidth=0.5)\n",
|
|
"plt.axvline(0, color='black',linewidth=0.5)\n",
|
|
"plt.title(r'Fourier Series Approximation of $|x|$ on $[-3\\pi, 3\\pi]$')\n",
|
|
"plt.xlabel(r'$x$')\n",
|
|
"plt.ylabel(r'$f(x)$')\n",
|
|
"plt.grid(True)\n",
|
|
"plt.legend()\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "bd160a96-1974-4b77-a4cc-28426c86492d",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Szereg Fouriera dla funkcji 2$\\pi$ okresowej: postać zespolona"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "f3c90b20",
|
|
"metadata": {},
|
|
"source": [
|
|
"#### Zadanie 4\n",
|
|
"\n",
|
|
"Wyprowadzimy zespoloną postać szeregu Fouriera."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "f884eb58",
|
|
"metadata": {},
|
|
"source": [
|
|
"##### Rozwiązanie:\n",
|
|
"Wiemy, że\n",
|
|
"\n",
|
|
"$$\n",
|
|
"e^{ix}=\\cos x +i\\sin x\\quad\\text{oraz}\\quad e^{-ix}=\\cos x -i\\sin x. \n",
|
|
"$$\n",
|
|
"\n",
|
|
"Stąd\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\cos x=\\frac{e^{ix}+e^{-ix}}{2}\\quad\\text{i}\\quad\\sin x=-i\\frac{e^{ix}-e^{-ix}}{2}.\n",
|
|
"$$\n",
|
|
"\n",
|
|
"Zatem\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\begin{align}\n",
|
|
"\\frac{a_0}{2}+\\sum_{n=1}^\\infty\\left( a_n\\cos(nx)+b_n\\sin(nx)\\right)=&\\frac{a_0}{2}+\n",
|
|
"\\sum_{n=1}^\\infty \\left(a_n\\frac{e^{inx}+e^{-inx}}{2}-ib_n\\frac{e^{inx}-e^{-inx}}{2}\\right)\\\\\n",
|
|
"=&\\frac{a_0}{2}+\\sum_{n=1}^\\infty\\left(\\frac{a_n-ib_n}{2}e^{inx}+\\frac{a_n+ib_n}{2}e^{-inx}\\right)\\\\\n",
|
|
"=& \\sum_{n=-\\infty}^\\infty c_ne^{inx},\n",
|
|
"\\end{align}\n",
|
|
"$$\n",
|
|
"gdzie \n",
|
|
"\n",
|
|
"$$\n",
|
|
"c_0=\\frac{a_0}{2},\\quad c_n=\\begin{cases}\n",
|
|
"\\frac{a_n-ib_n}{2}, & n>0;\\\\\n",
|
|
"\\frac{a_{-n}+ib_{-n}}{2},& n<0.\n",
|
|
"\\end{cases}\n",
|
|
"$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "7161cd41-8b0a-4ebf-86db-2b65f458a7f8",
|
|
"metadata": {},
|
|
"source": [
|
|
"***Uwaga:***\n",
|
|
"\n",
|
|
"Można sprawdzić, że dla każdego $n\\in\\mathbb{Z}$ mamy:\n",
|
|
"\n",
|
|
"$$\n",
|
|
"c_n=\\frac{1}{2\\pi}\\int_{-\\pi}^\\pi f(x)e^{-inx}dx.\n",
|
|
"$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "ca4bdcd9",
|
|
"metadata": {},
|
|
"source": [
|
|
"#### Zadanie 5: sygnał prostokątny po raz drugi\n",
|
|
"Rozwiniemy w zespolony szereg Fouriera funkcję $2\\pi$ okresową $f$ taką, że \n",
|
|
"$$\n",
|
|
"f(x)=\\begin{cases}\n",
|
|
"1, & x\\in[ 0,\\pi];\\\\\n",
|
|
"0, & x\\in (-\\pi,0).\n",
|
|
"\\end{cases}\n",
|
|
"$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "c375f201-b97b-4c4b-a8a3-92789821a471",
|
|
"metadata": {},
|
|
"source": [
|
|
"##### Rozwiązanie I\n",
|
|
"Wiemy już, że:\n",
|
|
"\n",
|
|
"$$\n",
|
|
"a_0=1 \\text{ oraz } a_n = 0, b_n =\\frac{1-(-1)^n}{\\pi n} \\text{ dla }n\\geq 1.\n",
|
|
"$$\n",
|
|
"\n",
|
|
"Zatem \n",
|
|
"$$\n",
|
|
"c_0=\\frac{1}{2}\n",
|
|
"$$\n",
|
|
"oraz\n",
|
|
"\n",
|
|
"$$\n",
|
|
"c_n=\\begin{cases}\n",
|
|
"i\\frac{(-1)^n-1}{2\\pi n}, & n>0\\\\\n",
|
|
"i\\frac{(-1)^n-1}{2\\pi n}, & n<0\n",
|
|
"\\end{cases}\n",
|
|
"$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "81b0a878-4faa-479b-bb85-842fcd0870b1",
|
|
"metadata": {},
|
|
"source": [
|
|
"##### Rozwiązanie II\n",
|
|
"Mamy\n",
|
|
"\n",
|
|
"$$\n",
|
|
"c_0=\\frac{1}{2\\pi}\\int_{-\\pi}^\\pi f(x)dx=\\frac{1}{2\\pi}\\int_{0}^\\pi1dx=\\frac{1}{2}.\n",
|
|
"$$\n",
|
|
"\n",
|
|
"Dla całkowitych $n\\not=0$ mamy\n",
|
|
"\n",
|
|
"$$\n",
|
|
"c_n=\\frac{1}{2\\pi}\\int_{-\\pi}^\\pi f(x)e^{-inx}dx=\\frac{1}{2\\pi}\\int_{0}^\\pi e^{-inx}dx=\n",
|
|
"\\frac{e^{-inx}}{-2in\\pi}\\big|_0^\\pi=\\frac{(-1)^n-1}{-2in\\pi}=i\\frac{(-1)^n-1}{2n\\pi}.\n",
|
|
"$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "0e920dd6",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Zastosowanie: sumowanie pewnych szeregów"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "1bb51ff4",
|
|
"metadata": {},
|
|
"source": [
|
|
"#### Zadanie 6\n",
|
|
"Rozwiniemy w szereg Fouriera $2\\pi$ okresową funkcję $f$ taką, że $f(x)=x^2$ dla $x\\in[-\\pi,\\pi]$.\n",
|
|
"Następnie na dwa sposoby policzymy wartość tej funkcji dla $x=\\pi$. Na końcu sprawdzimy co dla tej funkcji oznacza tożsamość Parservala."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "25e6e515-f309-45fd-b285-28cdfe99dbfe",
|
|
"metadata": {},
|
|
"source": [
|
|
"##### Rozwiązanie:\n",
|
|
" Wszystkie współczynniki $b_n=0$, bo funkcja $f$ jest parzysta.\n",
|
|
"Łatwo jest policzyć, że \n",
|
|
"\n",
|
|
"$$\n",
|
|
"a_0=\\frac{2}{3}\\pi^2.\n",
|
|
"$$\n",
|
|
"Ponadto dwukrotne całkowanie przez części daje, że dla $n\\geq 1$ mamy\n",
|
|
"\n",
|
|
"$$\n",
|
|
"a_n=4\\frac{(-1)^n}{n^2}.\n",
|
|
"$$\n",
|
|
"\n",
|
|
"Stąd \n",
|
|
"\n",
|
|
"$$\n",
|
|
"f(x)=\\frac{\\pi^2}{3}+4\\sum_{n=1}^\\infty \\frac{(-1)^n}{n^2}\\cos(nx).\n",
|
|
"$$\n",
|
|
"\n",
|
|
"Podstawiając $x=\\pi$\n",
|
|
"otrzymujemy, że \n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\pi^2=\\frac{\\pi^2}{3}+4\\sum_{n=1}^\\infty\\frac{1}{n^2}.\n",
|
|
"$$\n",
|
|
"\n",
|
|
"Stąd\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\sum_{n=1}^\\infty\\frac{1}{n^2}=\\frac{\\pi^2}{6}.\n",
|
|
"$$\n",
|
|
"\n",
|
|
"Przypomnijmy teraz, że tożsamość Parservala mówi, że dla odpowiednio \"dobrych\" funkcji mamy:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "cbfb72bc-39e7-44b4-acca-455deebea3fd",
|
|
"metadata": {},
|
|
"source": [
|
|
"***Twierdzenie***\n",
|
|
"$$\n",
|
|
"\\frac{a_0^2}{2}+\\sum_{n=1}^{\\infty}(a_n^2+b_n^2)=\\frac{1}{\\pi}\\Vert f \\Vert_2^2.\n",
|
|
"$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "d7e4ffb0-afe2-499c-9f11-160ec7b5967f",
|
|
"metadata": {},
|
|
"source": [
|
|
"Mamy\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\frac{1}{\\pi}\\Vert f \\Vert_2^2=\\frac{1}{\\pi}\\int_{-\\pi}^\\pi x^4dx=\\frac{2\\pi^4}{5}.\n",
|
|
"$$\n",
|
|
"\n",
|
|
"Podstawiając to do wzoru otrzymujemy po prostych przekształceniach, że \n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\sum_{n=1}^\\infty\\frac{1}{n^4}=\\frac{\\pi^4}{90}.\n",
|
|
"$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "e6763551-2bc9-46c4-9fb0-29efd59afb86",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3 (ipykernel)",
|
|
"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": "3.12.4"
|
|
},
|
|
"toc": {
|
|
"base_numbering": 1,
|
|
"nav_menu": {},
|
|
"number_sections": false,
|
|
"sideBar": true,
|
|
"skip_h1_title": false,
|
|
"title_cell": "Table of Contents",
|
|
"title_sidebar": "Contents",
|
|
"toc_cell": false,
|
|
"toc_position": {},
|
|
"toc_section_display": true,
|
|
"toc_window_display": true
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|