{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Solução dos problemas propostos na aula 02 - Interpolação trigonométrica\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "metadata": {},
   "outputs": [],
   "source": [
    "using PyPlot\n",
    "using FFTW"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 339,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "nfftutil (generic function with 1 method)"
      ]
     },
     "execution_count": 339,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#nfftutil(N) = (N % 2 == 0) ? (div(N,2) + 1) : div(N+1,2)\n",
    "nfftutil(N) = div(N,2) + 1\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- TEASER_END -->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Problemas\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Problema 1\n",
    "\n",
    "Seja a seguinte função definida no domínio $-1 < x \\le 1$:\n",
    "\n",
    "$$\n",
    "y(x) = \\left\\{\\begin{matrix} -1 & x < 0 \\\\ 1 & x > 0\\\\ 0 & x=0\\end{matrix}\\right.\n",
    "$$\n",
    "\n",
    " 1. Ache os coeficientes $a_n$ e $b_n$ da série de Fourier\n",
    " 2. Plote a série de Fourier para diferentes números de termos da série de Fourier. Percebe algo estranho?\n",
    " 3. Qual a relação desta função com a função $y = |x|$ que estudamos anteriormente?\n",
    " 4. Escolha diferentes números de pontos e interpole esta função nestes pontos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Solução\n",
    "\n",
    "#### Ache os coeficientes $𝑎_n$ e $𝑏_𝑛$ da série de Fourier\n",
    "\n",
    "Esta é uma função ímpar, portanto os coeficientes $a_n$ são nulos!\n",
    "\n",
    "$$\n",
    "b_n = \\frac{2}{L_0}\\int_{-L_0/2}^{L_0/2} y(x) \\cdot \\sin\\left(\\frac{2\\pi n x}{L_0}\\right)\\:dx = 2\\int_0^1 \\sin\\left(\\pi n x\\right)\\:dx = \\frac{2}{n\\pi}\\left(1 - \\cos n\\pi\\right) = \\frac{2}{n\\pi}\\left[1 - (-1)^n\\right]\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = range(-1.0, 1.0, length=201);\n",
    "y0 = 1.0 .* sign.(x)\n",
    "bn = [2/(π*n) * (1.0 - cos(π*n)) for n in 1:500];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {},
   "outputs": [],
   "source": [
    "sinseries(x, b, N, L0) = sum(b[n]*sin(2π*n*x/L0) for n in 1:N);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Plote a série de Fourier para diferentes números de termos da série de Fourier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.legend.Legend object at 0x7f271df27af0>"
      ]
     },
     "execution_count": 278,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(x, y0, \"k:\")\n",
    "for n in 1:2:15\n",
    "    plot(x, sinseries.(x, Ref(bn), n, 2.0), label=\"n = $n\")\n",
    "end\n",
    "legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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1CtL7V3yPicElMzYEGTHB0vMBAEO72F/TXY4QF2fUwai3f8bKHd1iRr29s6bt5qhK6FDh5VLMnTsXtbW10k9xcfF/vxER+Syx20g8sALO6dNZcfbwIp7lD+0SDY1aJZXrHBOM/PRIt/ubmJeM5Igg6fJVXaIxPifJrczvRmRicOco6fKE3GTcM6KzdDkoQINHRnfDLXnJ0nW/GZ6BuddmIURnP+Anhukx/7oe+P3VXaQyj43tjj+N74XUSAMAoEeCEX++qReeuqEnVCpAq1bh2Qm98fwtvZHXKQIAMCQzCi9M7INFt+UgKECDEJ0Wr0zui0W35WB0T/uX+NjseLw2pS+W/DoPsaE6xIbqsOTXeVjy6zzc1j8FITotJuQm451p/bB0en90jglGenQw3pne397FNSQdMaE6TB6QivfuGoD37hqAXklGdIsLxfIZ/bFsen/cO7IzksKDcHu+vcwHM/ORmxqOHglGLL+zP96Z1g8PFHRBpygDfj0wFStm5uODWQPRPy0CPRONWDZjAN6e1g//96uu6BRlwOQBqVhxl7NMVnwo3pnWH29NtZdJjgjCLXnJWDEzH+/PGojc1HB0jgnGG3fk4a2peZhzTVfEhuowrncCVszMx4qZ+eiZaERSeBBem5KL16b0xX1XZ0rha9n0/nhnWn9kRAfDqNfi+Ym98cLE3pg1NB0qFZCTEo7Xf52H1x3PoVatwhPX98BfbuolhdlOUQYsmtQXL92aI73Os6/ugidv6IlfOYJiWFAA/nJTNv40vpf0XrwlLxnzr+shvaYatQqPjumOBwu6Su+N/PRIPH5dD3SKMkjXTR3UCbcP7CRdTokMwmNju8MQqJGu+1XPOIzKcjYCaNQqzHZ5zwFAn+RwdI93b9kY1iUagPOzFBOqQ7jB/hkTu1fFE4ZWC7uN3FxKt1FbcpqdiMj3fL6rBPev3IVBGVHYdNzZjK9Vq/B/o7vhr18dkq5bOr0f/vzvgzjuGCtwY04ipg7qhAmvb5LKHHx6DP6y+iDe+9k+tuX5W3rjhpxEXLPwBxRVN2JUVizemd4fO4rOYdo7WxBmCMDHvxmExPAgLP3pBD7eVowHCrpiTK941LdY8OJ/DiMsKACzR2ZCq1HjUJkJa/aVYUJuMlIiDRAEAesOVsCg02BwZ/sXhqm5FdtPncOgjCjoA+xfRKfONkCrUSMp3B6srDYBZxtaEBOig0pl/xJssVihggqBWud5qM0mQO0S2Eg+m02ASgXpebZYbbDYBOm1AeyLtxn1AdJzf7a+BVX1ZnRztP5ZrDZsPHYWWQmhiA3VAwD2ldTiWGU9xmYnIECjRk2jGSt+PoX+aZHIz4iCIAhYsbkI+07XYs6vuiLOqMeOonN4fNU+DO4chcfGdkej2YrJb9nH3rx8W1+MzU6QxkGF6rX4Zs5wFFU3YqJjb6LBnaPwwayBGPbcd1J357MTslFuasHCtfZB6WoV8J8Hh6Fg4Q/S47u+TyJOnW1wG+ieFR+KQ2V1uH9UFzx4jTNoXS5yvr871MaMgwYNwurVq92uW7t2LQYNGqRQjYiooxFbVbQaFfQBajQ7li4PNwQg3qh3K5sSYUBGTIgUXnokGJGdFI7oEB2q6ltQ0D0WQYEa3DeqCw6VmZAcYcD4vkkI0KjxyT2D8P2RSqm7ITc1Aj8/NgqBWjUCNPYvrDuvSsedV6VLfy9Ep8UT1/d0q0NWvBFZLme5KpUKBT3cu8eN+gCM7Bbrdl2nqGC3yxq1SvoSFOm0GrTF4PK/a/scajVqtH2qo0PcB8NGhegQ5XKdVqPGMEe3pahXUhh6JYVJl8MNgW6tIiqVCne4tKwA9vfdl/cNlS4H67RY9bshqDdbpNbHuddmoVeSEb2TwxFn1CM2VIffjeiM9Ycr8eQN9vfjtdnxeOP741CrgJHdYrGr2DnGJy06GJ2igqVB8ACQGK5HTZtZfGGOlhdbB5jF5tHwUl9fj8LCQunyiRMnsGvXLkRGRiI1NRVz585FSUkJ3n33XQDAPffcg9deew2PPPII7rzzTnz77bf4+OOP8eWXX3qymkTkQ6TwolbBEKhFc6v9ABtuCESs0f0LJTnCgKFdovHNQfs4g6FdYhCoVWPZ9P74ZHux1IUTE6rDJ/cMdrttnFGPW/u5j6EL1nWo8z3yU2q1yq3bVKtR46a+zi5LlUqFR8Zk4ZExWdJ1D4zqCgjAwIwoxBr16J/m7D4dkBaJAI0a8UY9zjjGtySGBeH0OfexpmJ4sXaAMS8e/SRu27YNI0eOlC7PmTMHADBt2jQsX74cpaWlKCpyjsBPT0/Hl19+iQcffBAvv/wykpOT8fbbb3OaNBFJxAOnRq1CkEszfnhQAOJcWl4igwMRFKjBpP4p2HqyGp1jQtAj0d4Ckp0chuzkMBD5i6BADeaO7S5djggOxLMTsrF6bxke+lU3APawL4aXhDC9FFZEfhNeRowYcdFFki60eu6IESOwc+dOD9aKiHyZ1XFMUatUbgMVww2BSHPpagnW2X+nD9DgtSm53q0kkQ+Y1D8Vk/qnSpczYoKx5aR9iYG+qRHY6dK1BACh+o4TXnx+thER+RebS8uLe3gJgEatwj3DO0OlAv5yU7ZSVSTySTOHZiAoQIMxPeMRE6pza3nRadXQBdgjg/VKH/NCRHS5iWd9arUKQYHu3UYA8PDobvjNsAxEBAcqUj8iX5UZG4KfHxsldceGu4SXEJ0WGsfsq46wrxfDCxH5FHFbFXHArkgMKxq1isGF6BK5tra4/j9Er5XWqekILS/sNiIin2J17KuiUbm3vLQdXEhE/xvXz1RwoEt4UX6NOra8EJFvEQ+carUKcQbn7KK2624Q0f8mOtT5mYoz6lzCi/LphS0vRORTxAWyNCoV0qOdS6eLK5sS0eXhOnvPEKiFWtVxWl4YXojIp7gO2HVtbRH3ByKiy8N124nokEA4FpbuECvsMrwQkU+xuKywe3X3WAztEo37RnVx24CRiC6PZydko29qOO4dmQmN2jFVmrONiIjkcV3nRafV4L278hWuEdGVy3UhO43j/ICzjYiIZHJdYZeIvEcasGtleCEiksXZ8qJwRYj8jJrrvBARXRrXAbtE5D0daYVdhhci8imuA3aJyHu4wi4R0SVyXeeFiLzHuUgdwwsRkSzsNiJShhheuM4LEZFMbHkhUoY4w8/C2UZERPKw5YVIGWx5ISK6RBywS6QMjnkhIrpErivsEpH3iF21HaDXiOGFiHyLeODkCrtE3iV1G7HlhYhIHra8EClDzW4jIqJLY2V4IVKEluGFiOjSWBheiBShVnGFXSKiS8J1XoiUwTEvRESXiOu8EClD3MmdLS9ERDJJLS88ehF5ldRtxJYXIiJ5nAN2efgi8iat4zPH8EJEJJM0YJdjXoi8SjxfYHghIpLJuc6LwhUh8jPc24iI6BKJgwW5wi6Rd2k45oWI6NJwhV0iZXCFXSKiSyS1vDC8EHmV2PLSAbILwwsR+Rabzf4vB+wSeRfHvBARXSIbx7wQKUL8yDG8EBHJJB432WtE5F1qdhsREV0accyLii0vRF4lhZcOkF4YXojIpzi7jRSuCJGfUbPbiIjo0ojHTU6VJvIutZrdRkREl8TGbiMiRbgOkhcUbn1heCEin8JuIyJluH7mlG59YXghIp8irvPCqdJE3uXa2qn0KrsML0TkU7jOC5EyXMeZKT1ol+GFiHyKFF549CLyKtduI6UnHPHjT0Q+xSYtUseWFyJvcv3MseWFiEgGgd1GRIpQuQ3YZXghImo3caAgZxsReZdby4tNwYqA4YWIfIzYbcR1Xoi8S8NuIyKiSyMeNLnCLpF3sduIiOgScVdpImWoVCopwHCROiIiGbjOC5FyxM8dtwcgIpJBHLDL7ELkfWKLp5XhhYio/QSu80KkGPFzx24jIiIZOGCXSDlSeOHeRkRE7SeGFza8EHmfeM7A7QGIiNpJEARuD0CkIGe3EVteiIjaxfV4yfBC5H0qDtglIpLH9WyPQ16IvE8ca8ap0kRE7eQ6RlDN9ELkdZxtREQkk3vLC8MLkbepOOaFiEgedhsRKUtapM4fpkovXrwYaWlp0Ov1yM/Px5YtW36x7PLlyx37Jzh/9Hq9N6pJRB2cjQN2iRTl3B5A4Xp4+g989NFHmDNnDp544gns2LEDffr0wejRo1FRUfGLtzEajSgtLZV+Tp065elqEpEPcG15YXYh8j5xwO4V3220cOFCzJo1CzNmzECPHj2wZMkSGAwGLF269Bdvo1KpEB8fL/3ExcV5uppE5AMEm/P/GqYXIq/zi12lzWYztm/fjoKCAucfVKtRUFCATZs2/eLt6uvr0alTJ6SkpODGG2/E/v37f7FsS0sLTCaT2w8RXZk4YJdIWX6xSF1VVRWsVut5LSdxcXEoKyu74G26deuGpUuX4vPPP8eKFStgs9kwePBgnD59+oLlFyxYgLCwMOknJSXlsj8OIuoYrOw2IlKUOGCXexu1MWjQIEydOhU5OTkYPnw4Pv30U8TExOCNN964YPm5c+eitrZW+ikuLvZyjYnIW1z3NVIxvRB5nVrdMdZ50XryzqOjo6HRaFBeXu52fXl5OeLj49t1HwEBAejbty8KCwsv+HudTgedTvc/15WIOj6B+xoRKcovuo0CAwORl5eHdevWSdfZbDasW7cOgwYNatd9WK1W7N27FwkJCZ6qJhH5CPGAycG6RMqQuo0UDi8ebXkBgDlz5mDatGno168fBgwYgEWLFqGhoQEzZswAAEydOhVJSUlYsGABAODpp5/GwIEDkZmZiZqaGjz//PM4deoUZs6c6emqElEHJy6MxexCpIyOss6Lx8PLpEmTUFlZifnz56OsrAw5OTlYs2aNNIi3qKgIarWzAejcuXOYNWsWysrKEBERgby8PGzcuBE9evTwdFWJqINjtxGRssSxZkqvsOvx8AIAs2fPxuzZsy/4u/Xr17tdfumll/DSSy95oVZE5GvEpmpuDUCkDI2jrUHpbqMON9uIiOiXiCd73FGaSBkdpduI4YWIfIaz5YXhhUgJ3FWaiEgmcWEsNrwQKUPtD9sDEBFdTjYO2CVSlLqDDNhleCEin+FcYZfhhUgJGmnMC8MLEVG7SIvU8chFpAi/2FWaiOhy4jovRMryi+0BiIguJ6uNs42IlKTmOi9ERPK47ipNRN7HlhciIpk424hIWVJ4sSlcD2X/PBFR+wnSgF2GFyIldJRdpRleiMhniC0vbHghUga3ByAikokDdomUJe0qzZYXIqL2EbirNJGi2G1ERCQTB+wSKUscb8ZF6oiI2om7ShMpS83tAYiI5BH72dU8chEpQtoegBszEhG1j8CWFyJFSbtKs9uIiKh9xIWxuKs0kTLEMS/sNiIiaicbZxsRKUrF2UZERPKI3ewatrwQKcK5t5HC9VD2zxMRtR9nGxEpi+u8EBHJxF2liZTl3JiR4YWIqF24SB2RstRcpI6ISB6B67wQKYrdRkREMnHMC5GyOGCXiEgmq2OdF4YXImVwewAiIpm4zguRssTzBisH7BIRtQ+3ByBSlobdRkRE8ogHTG4PQKQMNbcHICKSR+w20vDIRaQIbg9ARCSTuDAWu42IlMHZRkREMnGROiJlqTlgl4hIHm4PQKQsDadKExHJw5YXImWp2G1ERCSPOOZFw4VeiBThHPPClhcionZhtxGRsri3ERGRTOw2IlKWtKu0TeF6KPvniYjaj9sDECmL3UZERDJxewAiZTm7jRSuh7J/noio/aRdpdn0QqQI7ipNRCQTu42IlCXtKs3wQkTUPuw2IlKWuEwBu42IiNqJs42IlMUBu0REMnGdFyJliV22HPNCRNROYj+7humFSBHS9gBc54WIqH3Ekz3ONiJShthtxAG7RETtJO5txIYXImVoHKmB3UZERO3EAbtEyuKu0kREMnGdFyJlcbYREZFMNg7YJVIUtwcgIpLJOVWa4YVICVLLi8LpheGFiHwGx7wQKUutZrcREZEsAse8ECnK2W3E8EJE1C5WR9ML13khUoaas42IiORhtxGRsrg9ABGRTJwqTaQscbC8lQN2iYjaR2DLC5GiNOw2IiKSh7tKEylLze0BiIjkkQbsMr0QKcKvtgdYvNaDk4wAACAASURBVHgx0tLSoNfrkZ+fjy1btly0/CeffIKsrCzo9XpkZ2dj9erV3qgmEXVw4smehoNeiBSh9pcxLx999BHmzJmDJ554Ajt27ECfPn0wevRoVFRUXLD8xo0bMXnyZNx1113YuXMnxo8fj/Hjx2Pfvn2erioRdXAcsEukLI2/7G20cOFCzJo1CzNmzECPHj2wZMkSGAwGLF269ILlX375ZYwZMwYPP/wwunfvjj/96U/Izc3Fa6+95umqElEHx+0BiJTlnCqtcD08eedmsxnbt29HQUGB8w+q1SgoKMCmTZsueJtNmza5lQeA0aNH/2L5lpYWmEwmtx9PqKpvwVNf7Mdfvzrkkfsnov+O67wQKUvlDy0vVVVVsFqtiIuLc7s+Li4OZWVlF7xNWVmZrPILFixAWFiY9JOSknJ5Kt+GqakVyzacxAebT3nk/onov7PZ2G1EpCRuD3CZzJ07F7W1tdJPcXGxR/6OeKandFMZkT+TxrwwvRApIjE8CPeO7Iwp+Z0UrYfWk3ceHR0NjUaD8vJyt+vLy8sRHx9/wdvEx8fLKq/T6aDT6S5PhS9C3UGayoj8GbuNiJSVEmnAw6OzlK6GZ1teAgMDkZeXh3Xr1knX2Ww2rFu3DoMGDbrgbQYNGuRWHgDWrl37i+W9RTxWWhleiBTD2UZEBHi45QUA5syZg2nTpqFfv34YMGAAFi1ahIaGBsyYMQMAMHXqVCQlJWHBggUAgPvvvx/Dhw/Hiy++iHHjxmHlypXYtm0b3nzzTU9X9aLEdSWUXpiHyJ85wwvTC5E/83h4mTRpEiorKzF//nyUlZUhJycHa9askQblFhUVQa12NgANHjwYH3zwAebNm4fHHnsMXbp0wapVq9CrVy9PV/WinGNemF6IlGKz2f9ldiHybx4PLwAwe/ZszJ49+4K/W79+/XnXTZw4ERMnTvRwreRxjrBWth5E/kxseeEKu0T+zednG3lLR5nbTuTPuKs0EQEML+3muqogu46IlMEBu0QEMLy0m2szNbuOiJRh5fYARASGl3ZzPViy64hIGeKJg4bhhcivMby0k2szNcMLkTIEaYVdhStCRIriIaCdXAcIMrsQKYO7ShMRwPDSbq7hxcpBL0SKENd54WwjIv/G8NJOrs3U7DYiUgZnGxERwPDSbmoVZxsRKU1apI4tL0R+jeGlndzHvDC9EClBPHHgmBci/8bw0k6uzdQc80KkDHYbERHA8NJuKnYbESlO2h6A6YXIrzG8yCCusstuIyJliK2ezC5E/o3hRQbuLE2kLGe3EdMLkT9jeJGBO0sTKYu7ShMRwPAii9jywgG7RMpgywsRAQwvsohrS7DhhUgZ4okDswuRf2N4kUHNbiMiRdnYbUREYHiRRSUN2GV4IVKCONNPw+lGRH6N4UUGcW0JDnkhUgYXqSMigOFFFnYbESmL2wMQEcDwIgvDC5GybFykjojA8CKLtEidTdl6EPkrG8e8EBEYXmRhywuRsjjbiIgAhhdZxJM9ZhciZYgnDswuRP6N4UUGcZCglemFSBHcHoCIAIYXWTRqdhsRKcnK7QGICAwvsji7jRheiJQgrfPCIxeRX+MhQAbngF2FK0LkhwRBYLcREQFgeJFF2h6A6YXI61wbPBleiPwbw4sMag7YJVKM6+eOy7wQ+TeGFxnEAbvMLkTe5zpQntsDEPk3hhcZVFykjkgxrh87rrBL5N8YXmSQtgdgdiHyOhu7jYjIgeFFBmm2EdMLkdfZOGCXiBwYXmRwtrwwvBB5m9XmOuZFwYoQkeIYXmRQq7nOC5FSXBeH1DC9EPk1hhcZuKs0kXLYbUREIoYXGbg9AJFy3KdKK1gRIlIcw4sM0q7SNoUrQuSHxPCiUnGdFyJ/x/Aig4bdRkSKsTlOGthlREQMLzKIO9kyvBB5n/i542BdImJ4kUE842N2IfI+124jIvJvDC8ycHsAIuWIHzt2GxERw4sM4mwjKxd6IfI68aSBWwMQEcOLDBp2GxEpRjxpYMsLETG8yMBuIyLliA2eaja9EPk9hhcZuKs0kXIEdhsRkQPDiwzcHoBIOTYO2CUiB4YXGbjOC5FyxDEvXF2XiBheZJBaXthvROR1nG1ERCKGFxmc3UYKV4TID4kNnhqmFyK/x/Aig3PALtMLkbc5W14YXoj8HcOLDNwegEg53B6AiEQMLzKIAwWtTC9EXseWFyISMbzIoOFsIyLF2DjmhYgcGF5kYLcRkXJsNnYbEZEdw4sMKk6VJlIMF6kjIhHDiwzSrtJseiHyOm4PQEQihhcZuM4LkXKsHLBLRA4MLzKIAwUFtrwQeR27jYhI5NHwUl1djdtvvx1GoxHh4eG46667UF9ff9HbjBgxAiqVyu3nnnvu8WQ1203FReqIFCNNleYpF5Hf03ryzm+//XaUlpZi7dq1aG1txYwZM3D33Xfjgw8+uOjtZs2ahaefflq6bDAYPFnNdmO3EZFyBHYbEZGDx8LLwYMHsWbNGmzduhX9+vUDALz66qsYO3YsXnjhBSQmJv7ibQ0GA+Lj4z1VtUsmbQ/A9ELkdTab/V/uKk1EHmuA3bRpE8LDw6XgAgAFBQVQq9XYvHnzRW/7/vvvIzo6Gr169cLcuXPR2Nj4i2VbWlpgMpncfjxFrRZbXhheiLzNytlGROTgsZaXsrIyxMbGuv8xrRaRkZEoKyv7xdtNmTIFnTp1QmJiIvbs2YM//OEPOHz4MD799NMLll+wYAGeeuqpy1r3X8JuIyLliN1GGra8EPk92eHl0UcfxbPPPnvRMgcPHrzkCt19993S/7Ozs5GQkIBRo0bh2LFj6Ny583nl586dizlz5kiXTSYTUlJSLvnvXwx3lSZSDmcbEZFIdnh56KGHMH369IuWycjIQHx8PCoqKtyut1gsqK6uljWeJT8/HwBQWFh4wfCi0+mg0+nafX//C24PQKQc7ipNRCLZ4SUmJgYxMTH/tdygQYNQU1OD7du3Iy8vDwDw7bffwmazSYGkPXbt2gUASEhIkFvVy07aVZr9RkReJ37u2PJCRB4bsNu9e3eMGTMGs2bNwpYtW7BhwwbMnj0bt912mzTTqKSkBFlZWdiyZQsA4NixY/jTn/6E7du34+TJk/jXv/6FqVOnYtiwYejdu7enqtpuGhUH7BIpRfzYcZ0XIvLoYeD9999HVlYWRo0ahbFjx+Kqq67Cm2++Kf2+tbUVhw8flmYTBQYG4ptvvsGvfvUrZGVl4aGHHsKECRPwxRdfeLKa7eYc86JsPYj8kY3rvBCRg0cXqYuMjLzognRpaWluS+2npKTg+++/92SV/idqbg9ApBgO2CUiERtgZeD2AETKsXGdFyJyYHiRQS0N2FW4IkR+yMYBu0TkwPAig0bFbiMipUjdRmx6IfJ7DC8ysNuISDnsNiIiEcOLDNwegEg53FWaiEQMLzKIZ3xWtrwQeR1nGxGRiOFFBk6VJlKOuMIuswsRMbzIIHUbcbYRkdeJY140HPRC5PcYXmRQc3sAIsUI7DYiIgeGFxm4PQCRcrirNBGJGF5kYMsLkXI4YJeIRAwvMnCdFyLlcJ0XIhIxvMggDhRktxGR94nbA3DALhExvMig5vYARIoRTxpU7DYi8nsMLzKw24hIOew2IiIRw4sMzl2lGV6IvM3G7QGIyIHhRQaOeSFSDsMLEYkYXmQQm6s55oXI+zhVmohEDC8yqLirNJFiOOaFiEQMLzJwkToi5UjbAzC9EPk9hhcZpO0B2PRC5HXcVZqIRAwvMqg5YJdIMdKu0kwvRH6P4UUGdhsRKYe7ShORiOFFBu4qTaQcDtglIhHDiwzcHoBIOWJ44fYARMTwIoN4zOQKu0TeZ7XZ/2W3ERExvMggDhS0suWFyOucu0orXBEiUhwPAzJI2wOw5YXI68STBq7zQkQMLzKIB022vBB5n9Tywm4jIr/H8CKDeNC02RSuCJEfEk8aNGx5IfJ7DC8yiAdNDtgl8j6rjeGFiOwYXmQQD5oWhhcir2N4ISIRw4sM0oBdjnkh8joxvHCqNBExvMggHjTZbUTkfTaOeSEiB4YXGThVmkg57DYiIhHDiwxcpI5IOVbHx45TpYmI4UUGjYYDdomUYnWsUcCWFyJieJHBuc4LwwuRt0kDdhleiPwew4sMasezxW4jIu8TF4dktxERMbzIIB40BQEQGGCIvIor7BKRiOFFBteDJqdLE3kXZxsRkYjhRQa38MKWFyKvcq7zonBFiEhxPAzIwJYXIuVYrFxhl4jsGF5kcD1oMrwQeRdX2CUiEcOLDK4HTXHmAxF5B8e8EJGI4UUG1ymaHPNC5F3SbCN2GxH5PYYXGdQc80KkGBtbXojIgeFFJq2aO0sTKcHCFXaJyIHhRSbxwMluIyLvklpe2G1E5PcYXmRy3d/oyz2lKFj4PfafqVW4VkRXnoYWC2762wY8u+YQAK6wS0RODC8yaVy6je79YAcKK+rxh3/uUbhWRFeeL3afwc6iGry+/hgEQYBV3NuI4YXI7zG8yCQeN127jU5VNSpUG6IrV0Vdi9v/uc4LEYkYXmQSD5xNZqt0Hce/EF1+J882SP8/VlEvDZLnCrtExPAik0Ztf8oqXc4KiejyO1tvlv5fUdfCReqISMLwIpO4KVxdi0W6rtFsRYvF+gu3IKJLUdvUKv2/vsUihRctwwuR32N4kUmcbVTfbHG7vrbRfqCtbjCjrrn1vNsR0cWZLTaU1jZJl00u4aWhxSJ1z3KdFyJieJFJPHDWt7gHlJqmVlTVt2DkC+sx4fWN0poURNQ+T/xrPwb/9VtsKKwCYP9MiepbLFznhYgkDC8yif3tbVtezjWY8dW+MtQ2teJIeT22nTqnRPWIfFKj2YIPtxRBEIDnvj4MQRDcuo3qml1bXpSqJRF1FDwMyCSGF1Ob8FLT1Io9xTXS5Z1F9vDyzYFyXP/qT9hXwoXsiES1ja349dubseibIwCAQ2V10u9qGs1oMFvdtuCoa7ZAnNTHlhciYniRSRrz0nL+mJdylxlIxecaYbUJmPnuNuwtqcV9H+4EYF+Z94WvD2PZhhPeqzSRwn44UolH/7kH5xrsM4je/PEYfiqswqJvjuJkVQNKzjnHupTWNqOm0ex2e5PLODItm16I/J7HjgLPPPMMBg8eDIPBgPDw8HbdRhAEzJ8/HwkJCQgKCkJBQQGOHj3qqSpekl/sNmo0o8LULF0urm5yW6fieFUDmlut+Mf203jtu0I89cUBbDp2FgDw3qaTGLxgHdbsKwVgfx5W7y3F90cqpdsLgoCyWuf9Eymlqr4FreJytwCOlNfhvZ9PobnVPuOusKIOo15cj0f+sRs2m4CaRjOmLt2ClVuL8fS/DwAAfj5eLd1+47GzKKlxhhezxYYTVc7PDuA+84jZhYg8dhgwm82YOHEifvvb37b7Ns899xxeeeUVLFmyBJs3b0ZwcDBGjx6N5uaO86Wt/oWWl5qmVrcVQYvPNeJYRb1bmaPl9Vh7sFy6/PX+MlQ3mPH45/txprYZ96/cBYvVhn/uKMHv3t+BaUu34PsjlRAEAb//cCcGLliHJz7fBwAorW3ChNc34va3f8bZevvf/e5QBWa9u00a8NhqteHtH49j+YYTUhP8mZomLNtwwm1Wx7aT1dh60vll0txqxcbCKreF+KrqW9zWthEEARV1zW4Dk1ssVukLTNRqtUHgIn6/yNLm+Wm12tyedwA4W98Cs8UZFuqaW92+7G02AVtPVqOq3vn6nKhqwH/2l8HiCBlNZitW/HwKu126Nr85UI7nvz6EakdrSNHZRtz7wQ68/eNxx3L8Av742V5c/cJ6/HzcHrQ/31WCAc98g2tf/hGm5lZUmJox4W8b8fiqfXji8/0AgL+sPoRjlQ34eNtpfHe4QgrpALD2QDmsNgGHXbqJDpeZcPqc+yrVB0tNbpddZx5xnRci0nrqjp966ikAwPLly9tVXhAELFq0CPPmzcONN94IAHj33XcRFxeHVatW4bbbbvNUVWXRasQxL+6zjSpMLdKXAACcrm7C0Tbh5UBpLXa5fHlsOVEtBQ0AaLHYsO3UOXyw+ZR03YqfTyE8KAD/3mNvlfn7plOYMSQdi745gu2OQcEvfXME947MxG/e2w6z1Yafjlbhxz+MxLINJ7D4u2MA7OFqxpB0jF+8ARV1LVjy/TH858Hh+GL3GcxbZQ9Ef7qxJyb2S8H4xRtwqKwOXWJDsOreIfjxaCVmf7ATNkHAwltzMDY7AXcu34qfCquQmxqO92cOxI6ic7jnve1otdnw0q05uKZHHB78eDe+2H0GQ7tE462p/bD/jAm/XbEdLRYbXpzYB1dnxWLe5/vwz+2nMaxrDF6d3BeFFfW478OdaDBbsODmbIzsFou/rD6IT7afxuDOUVh4aw5Onm3AAyt3ocFswdM39MKIbjF44T+H8dHW08jPiMSLE/vg9LkmPPjRLpiaWzH/uh64OisWi745ig+2FGFAWiRemNgHZ2qbMOejXTjX2Ip547rjmh5xeGVdIVZsPoW+KeF4aVIOKupacP/KnThbb8Yfx3XHtb3i8cq6QizfeAJ9UsLxyuS+OFtvxm9XbEdVfQvmjeuB8X2TsHDtEbz943H0SgrDm3fkobrBjJl/34bS2mY8fl0PTMlPxV+/OoQ3fjiGrHgj3r1zAGqbWnHHO5tRbmrGH8Zk4TfDO+OJz/fh75tOISk8CJ/cMwim5lZMeuNn1Da14jfDM/DomCw89MlufLazBKF6LVbdOwT1zRZMfGMTzBYbxuck4qVJObhnxXZ8f6QSGrUKn9wzCE1mK2a+uw0AsPXEOay8eyB+98F27Csx4cs9pUiOCEKLxYb3NxcBAB7+x258M2c4nvnyIGwCUFhRj39sO41mi1Va8+jz3SV4aHRX/HjU2WK49kA5DIHOw0x9iwXfHqpwC/+HyupgCNS4fVYOl7l/dupcWjoZXohIJXj4tHj58uV44IEHUFNTc9Fyx48fR+fOnbFz507k5ORI1w8fPhw5OTl4+eWXL3i7lpYWtLQ4zzhNJhNSUlJQW1sLo9F4eR6Eiwmvb8T2U+eQFmXAybON0Aeo0dxqQ+/kMOw5XSvtfWQTgKsyo/GTSzgp6B6Hb1xaXlQqYEzPeHy1r0y67oY+ifjX7jPS5QCNCmN6JeALl+tu6puEf+85g1ar/aXTadUY3TPe7XY39EnEfw6UobnVfuYdFKDBqO6xUggCgGt7xePHo1XSF4khUIMR3WKweq+zPqOyYrH1ZLU0QNkQqMGQzGisPeB8HIM7R+FAqQk1jrVuggI06JcWgR+POh97Tko4iqobpYCnD1AjOykMW086Z2VlJ4WhpKZJKqPTqpGTEo7NJ5ytQr2SjCirbUaVY/XVQK0aeakR2HT8rFuZcpOzpShQo0b/9AhsKHSW6ZloRGVdi9RaFqBRIT89yu31yooPxblGM8pN9jJatQqDOke5Pa6s+FDUNLaizNFlqFGrMCjD/X66xIagrtkilVGrgGFdY7D+sPNLvnuCEfUtrSiutreoqFT218f1tchOCkOD2YLjlc4ulZv7JuHTnSXS5d7JYWhuteJIufPL/9Z+yfh422m3+2m12twGyU7ql4KPthW7PT+CABxwaQFpez89E42wWAUcLnfez/icRKza5XwfJoUHITokELtPOwesF3SPxTcHK6TLMaE6RBgCcKS8Xvo89UkJx+7iGhj1WpiaLdK/AHD8L2O51gvRFchkMiEsLKxd398dpve4rMx+kI6Li3O7Pi4uTvrdhSxYsABhYWHST0pKikfrKa7uKfbBJ4YFAXDOlkgIC0JiuP068Qvsmh72xyQGl15JRmREB0MQIAWXiXnJACAFkNzUcGTFh6LVKkjBZfrgNADAZztL0GoV0K9TBHonh6HFYpNuN2tounQ/za025KaGIzc1HE2tVim4/GZYBgD7365vsSAnJRz90yLQaLZKX5Yzr7Lfz7pDFTA1W5CdFIYBaZFoNFul4DJ9cBrUKvuYhZrGVvRIMGJAWiSaWq3SF/yU/FRo1CrsKq5BdYMZ3eJC0a9TBJpbbVJwmZCbjACNCntLalHdYEZGTDByU8PRYrFJwWVc7wQEatXYV2JCVb0Z6dH2MmaLTQou43onQOcoU1nXgk5RBvTrFAGz1SYFl3HZCdAHqLH/jAkVdS1IiQxC/7QItFoF6fUamx0PQ6AGh8rqUG5qQXJEEAakR8JiE6THNbpnHIIdZcpMzUgKD8LgzlGw2pz3c13vBITotDhaUS+VGdEtBjYBUnC5OTcJITotDpaaUFzdhHijHmN6xkMQIL0Wk/qlIFSnxd6SWhyvbEBMqA439EkEACm4TB6QghCdFntO1+JIeT0igwMxIdf+nhIDx5T8VIQ47udQWR1C9VpM6mf/vIjBZUp+KoICNNh/xoQDpSYEBWhwS577/UwekIoAjQr7z5hwuLwOARqV9P4Vg4tYpqSmSQou1zvqLAaXgu72z0VlXYsUtvqmRAAACh2BKD5MD8A5u0+jVjG4EJG88PLoo49CpVJd9OfQoUOequsFzZ07F7W1tdJPcXHxf7/R/yBQa3/KxIOpGFTEMQlxRh1SIgxutxEP2qKclHAMSI903qdGjYdHd3NrDh+bnYAbc5Kky0nhQXhsbHckOA7mADBjSDrudgQR8X4fG9sd/TpFSNc9em13zLuuh3Tfo3vGYe7Y7ripr/2+gwI0WHBzNp6d0BthQQEAgNvzUzHvuh64d2RnAEB0iA4v35aDVyb3RVqU/bHNHpmJJ2/oicev64EAjQrp0cF44448LLkjD31TwxEUoMEjY7rhLzdl47kJvREVHIjspDAsm9EfS2f0x/CuMYgJ1WHeuO548dY+eOW2vkiNNGBAWiTen5mPFTPzMS47ASmRQXjy+h5YPCUXS36di65xIRiSGYUPZuXj/ZkDcVPfJGREB+OpG3pi8ZRcvDW1H3okGDG0SzRW3j0QK2bmY2JeMjrHBNvv5/ZcvDOtP3omGnFVZjRW3j0IK2bm47b+KciICca8cd3xt9vz8PY0+/0MzIjEBzMHYsVd+ZjULwWdogx4eHQ3vHFHP7w1rR+6xoUgNzUc7901AMtnDMDNuUmIM+rw+6sz8erkvnjjjjx0ijIgKz4US6f3x5t39MO43gkI1WkxY0gaXpzYB69N6Yuo4EAkhunxxh15eHlyDkZ0iwFgb8lYcHM2Xri1D3RaNUJ0Wrx8Ww6eu6U3+qbaB8IP7hyFp2/shadv7AmVyt6y8+fx9svp0cEAgM4xwZh/XQ88UNBFem88UNAVj43tjnCD/XU36rV4ZHQ3/HpgqlRmUv8U3D/KeRsAuGd4hhTIAWB41xjcNsD9pGFcdoIURMT375ie8W5lBqRHIDpE53ZdnxT7Y2pwjPuJM+rdfh+gYXAhIpndRpWVlTh79uxFy2RkZCAwMFC67Oluo7bkNDtdihnLtuA7l+b+iXnJ+GS7syn92l7xMOoDpDNZjVqFvU/+CjlPrYXZMXjyhYl9oFEDD360GwAwKCMKH949ELPe3Ya1B8oRqFVj/f+NgE6rxrhXfkKZqRnPTeiNW/unYP3hCjz8jz0Y1iUGz93SG2oV8Lf1x7DndA3+OLYHUqMMqKpvwTs/nUC/ThEY5Ti73V1cgwOlJtzUNwn6AA2sNgHfH6lAl9hQpETaA8m5BjOKqhvROzkMKsfA5KKzjYgODZTGLVisNpitNrdxDFabALUK0m3o8rDaBLdA29xqhUoF6LQa6fcnquqRER0itUYcr6yHRq1Cpyh7aDE1t2Jj4VkMyYxCqD4AgiDgPwfKIQj2IKtSqXCozIR/bj+Nm/omo0eiEY1mC5758iCsNgHzruuBEJ0WyzacwKvfFmLm0HT8bkQm9pXUYuKSTbDaBKyYmY9+nSJwzUvf45ijZeinP4zE6+uPYdE39tmCt/VPwb0jMzH0ue+kx7Py7oFYuPYItjha1xLD9PjdyExpDBZwfldVqE6LvU+N9tAzTkRKkvP9LWvAbkxMDGJiYv6nyv2S9PR0xMfHY926dVJ4MZlM2Lx5s6wZS54WoHFvrBJbXkRxRj2iQ5zhLTXSAEOgFhkxwVLXUr9OEYg16tA5phAnzzbid44Wjr/enI3USANGZcVK9/ufOcNQYWpGZmwoAGBEt1hseWyUW1C4d2SmWx2iQ3T4w5gst+v6pIRLZ7WAPVRdneXeRRcRHIiI4EC361Kj3FuRtBo1tG2eAw6g9Iy2z6s+QHPe78X3hSgjJsTtslEfgDG9nC0eKpUKo9u0gGTFG/HHcT2ky4ZALZ65KdutzIwh6Zg+OE163/VKCsP3D49Aq01AkuO9+s60/li+8SRu7ZcCnVaDyQNS8d6mU2g0W3HXVelIjnD/rPRKCkNGdLAUXtJjghET6t4Sk9ymFTNA22F6uolIQR6bbVRUVITq6moUFRXBarVi165dAIDMzEyEhNgPsFlZWViwYAFuuukmqFQqPPDAA/jzn/+MLl26ID09HY8//jgSExMxfvx4T1VTtvPDi3uzdkyoTmrJAIDOji+TuWO7487lWzEhNwlpjqb8z+4dgpqGVikgRIXo8Ph1Pdzuz6gPgFEf4HYdWzhICW3fd7FtunTSooPx5A09pctxRj2+fnAYWq02JDjGhj13S2888o89uH9UF4To7KFelB59fnhJanNywB2liQjwYHiZP38+/v73v0uX+/btCwD47rvvMGLECADA4cOHUVvrnIXwyCOPoKGhAXfffTdqampw1VVXYc2aNdDr3Q+SSmrb5x4TqoNWrYLFsd5JnFGPqzKjpd8Pd4xdGN41BjvmXYNQvfMpv1AwIbqStB3Tcmu/FFzTPU4aZzOqexz+svqQ9P/YNuGlbctm25MHIvJPHgsvy5cv/69rvLQdbqNSqfD000/j6aef9lS1/mdtu0wMgVqEGwKkqbtxRh0igwOx4OZs7Cupxa39kqWyYQYGFSLXAvp4rwAAEBVJREFUrsnOMSF4bGwWKutaMKxLjNvKvQAQHRKIoAANmhyLH3LALhEBHgwvV6q2Z36GQA3CDYEu4cXeSjR5QOp5tyWi8909rLP0f41a49aSGROqQ1Cga3hhywsRdaB1XnxFYJszP0Ogxq0fXpyaSkSXxuKy5US4wd7yImrb8klE/olHApnaHjyDArW4Pd/eytInOYxnhkT/o99fbZ89Jy5ipw9wfqbYbUREALuNZDuv2yhAg9vzOyEyWOe28BwRXZr7R3VBl7hQDO9qH+we5LLvEU8OiAhgeJGt7ZlfUKAGarUK43onKFQjoiuLVqOWtj8A4N5txKnSRAR2G8nmeuanVtk3DyQiz3FdnC+QnzciAsOLbFqXlhdDoJYLxhF5mCGQLS9E5I7hRaZAl5YX1754IvIM124jjnkhIoDhRTbXMz8DwwuRx3HALhG1xSOBTK4bwwUFMLwQeZrereWF3UZExPAiW4Da+ZSx5YXI87hIHRG1xSOBTAFa9wG7RORZHPNCRG3xSCCT64GUA3aJPM/1c+a62i4R+S8eCWQKC3LuiMtuIyLPcx3zEmEIvEhJIvIXDC8yhRsCpP9HBesUrAmRf4gKdgYW188fEfkvhheZXA+e0aE8CyTytJhQ50lCWBDDCxExvMgW7tptxKnSRB4XHeIML+HsNiIiMLzI5jpgMID7rBB5nGvLSyBnGxERGF5kc93LKCveqGBNiPxDsM65JEF8mF7BmhBRR8GFSi7BqnuH4GRVA/I6RShdFSK/8PFvBqGyrgXp0cFKV4WIOgCGl0uQkxKOnJRwpatB5DcGpEcqXQUi6kDYbUREREQ+heGFiIiIfArDCxEREfkUhhciIiLyKQwvRERE5FMYXoiIiMinMLwQERGRT2F4ISIiIp/C8EJEREQ+heGFiIiIfArDCxEREfkUhhciIiLyKQwvRERE5FOuuF2lBUEAAJhMJoVrQkRERO0lfm+L3+MXc8WFl7q6OgBASkqKwjUhIiIiuerq6hAWFnbRMiqhPRHHh9hsNpw5cwahoaFQqVSX9b5NJhNSUlJQXFwMo9F4We+7I7jSHx9w5T9GPj7fd6U/Rj4+3+epxygIAurq6pCYmAi1+uKjWq64lhe1Wo3k5GSP/g2j0XjFvimBK//xAVf+Y+Tj831X+mPk4/N9nniM/63FRcQBu0RERORTGF6IiIjIp2iefPLJJ5WuhC/RaDQYMWIEtNorrscNwJX/+IAr/zHy8fm+K/0x8vH5PqUf4xU3YJeIiIiubOw2IiIiIp/C8EJEREQ+heGFiIiIfArDCxEREfkUhhcXzzzzDAYPHgyDwYDw8PB23UYQBMyfPx8JCQkICgpCQUEBjh496lamuroat99+O4xGI8LDw3HXXXehvr7eEw/hv5Jbl5MnT0KlUl3w55NPPpHKXej3K1eu9MZDcnMpz/WIESPOq/s999zjVqaoqAjjxo2DwWBAbGwsHn74YVgsFk8+lAuS+/iqq6vx+9//Ht26dUNQUBBSU1Nx3333oba21q2ckq/f4sWLkZaWBr1ej/z8fGzZsuWi5T/55BNkZWVBr9cjOzsbq1evdvt9ez6T3iTn8b311lsYOnQoIiIiEBERgYKCgvPKT58+/bzXasyYMZ5+GBcl5zEuX778vPrr9Xq3Mr78Gl7oeKJSqTBu3DipTEd6DX/44Qdcf/31SExMhEqlwqpVq/7rbdavX4/c3FzodDpkZmZi+fLl55WR+7mWTSDJ/PnzhYULFwpz5swRwsLC2nWbv/71r0JYWJiwatUqYffu3cINN9wgpKenC01NTVKZMWPGCH369BF+/vln4ccffxQyMzOFyZMne+phXJTculgsFqG0tNTt56mnnhJCQkKEuro6qRwAYdmyZW7lXJ8Db7mU53r48OHCrFmz3OpeW1sr/d5isQi9evUSCgoKhJ07dwqrV68WoqOjhblz53r64ZxH7uPbu3evcPPNNwv/+te/hMLCQmHdunVCly5dhAkTJriVU+r1W7lypRAYGCgsXbpU2L9/vzBr1iwhPDxcKC8vv2D5DRs2CBqNRnjuueeEAwcOCPPmzRMCAgKEvXv3SmXa85n0FrmPb8qUKcLixYuFnTt3CgcPHhSmT58uhIWFCadPn5bKTJs2TRgzZozba1VdXe2th3QeuY9x2bJlgtFodKt/WVmZWxlffg3Pnj3r9tj27dsnaDQaYdmyZVKZjvQarl69WvjjH/8ofPrppwIA4bPPPrto+ePHjwsGg0GYM2eOcODAAeHVV18VNBqNsGbNGqmM3OfsUjC8XMCyZcvaFV5sNpsQHx8vPP/889J1NTU1gk6nEz788ENBEAThwIEDAgBh69atUpmvvvpKUKlUQklJyeWv/EVcrrrk5OQId955p9t17XnTe9qlPr7h/9/evYY09f4BAP962/K2TOa1TNJsmc40YksJByleMhB6kRqYRWSU0QUzNTBJgyZJvYguEpN60Q8RMQzKFEFfGMvQNMtUnCyrFxpazMvMdH1/L37/nb/HednlNJ18PxC053zP2fM93z07D/Q8SybDCxcuLHn85cuXaG9vz/qCffDgAQoEApyZmeGm80bgqn7V1dXI4/FwdnaWaVut+kkkEszJyWFe63Q69Pf3x5s3by4af+TIEUxJSWG1SaVSPH36NCIaNyatydT8Fpqbm0N3d3d88uQJ05aVlYWpqamc99Vcpua40vfreqvhnTt30N3dHScnJ5m2tVZDPWO+B65cuYJhYWGstrS0NExMTGReW3rPjEH/bGQBtVoNw8PDEB8fz7Rt3LgRpFIpKJVKAABQKpXg4eEBe/fuZWLi4+PB3t4e2trarNpfLvrS0dEBXV1dcPLkSYNjOTk5IBQKQSKRQGVlpVH/rTmXLMnv6dOnIBQKITw8HAoLC0Gr1bKuKxaLwcfHh2lLTEyE8fFx6Onp4T6RJXD1WdJoNCAQCAx+XMra9fv9+zd0dHSwxo+9vT3Ex8cz42chpVLJigf4rxb6eGPGpLWYk99CWq0WZmdnwdPTk9Xe0tIC3t7eIBKJ4MyZMzA2NsZp341lbo6Tk5MQGBgIAQEBkJqayhpH662GCoUC0tPTwdXVldW+VmpoqpXGIBf3zBjr9+f/rGB4eBgAgPVQ07/WHxseHgZvb2/WcUdHR/D09GRirIWLvigUCggNDYWYmBhWe0lJCRw4cABcXFygsbERzp49C5OTk3D+/HnO+r8Sc/M7evQoBAYGgr+/P3R3d0N+fj709/dDbW0tc93Faqw/Zi1c1G90dBRKS0shOzub1b4a9RsdHQWdTrfove3r61v0nKVqMX+86duWirEWc/JbKD8/H/z9/VkPgqSkJDh8+DBs27YNBgcH4erVq5CcnAxKpRIcHBw4zWEl5uQoEomgsrISIiIiQKPRQHl5OcTExEBPTw9s2bJlXdXw7du38PHjR1AoFKz2tVRDUy01BsfHx2F6ehp+/vxp8efeGOt+8lJQUABlZWXLxvT29sLOnTut1CPuGZujpaanp+Gff/6BoqIig2Pz26KiomBqagpu3brFycPvb+c3/0EuFovBz88P4uLiYHBwEIKDg82+rrGsVb/x8XFISUmBXbt2wcL/FeRv1o+YRy6XQ1VVFbS0tLAWtKanpzN/F4vFEBERAcHBwdDS0gJxcXGr0VWTREdHQ3R0NPM6JiYGQkNDoaKiAkpLS1exZ9xTKBQgFotBIpGw2m29hmvBup+85ObmwvHjx5eNCQoKMuvavr6+AAAwMjICfn5+TPvIyAhERkYyMd+/f2edNzc3Bz9+/GDOt5SxOVral5qaGtBqtXDs2LEVY6VSKZSWlsLMzAzw+fwV45djrfz0pFIpAACoVCoIDg4GX19fg5XyIyMjAACc1NAa+U1MTEBSUhK4u7vDs2fPwMnJadl4Luu3FKFQCA4ODsy91BsZGVkyH19f32XjjRmT1mJOfnrl5eUgl8uhqakJIiIilo0NCgoCoVAIKpXK6g8+S3LUc3JygqioKFCpVACwfmo4NTUFVVVVUFJSsuL7rGYNTbXUGBQIBODs7AwODg4WfyaMwtnqmXXE1AW75eXlTJtGo1l0wW57ezsT09DQsKoLds3ti0wmM9ilspQbN27gpk2bzO6rObi6162trQgA+P79e0T8/4Ld+SvlKyoqUCAQ4K9fv7hLYAXm5qfRaHDfvn0ok8lwamrKqPeyVv0kEgmeO3eOea3T6XDz5s3LLtg9dOgQqy06Otpgwe5yY9KaTM0PEbGsrAwFAgEqlUqj3uPr169oZ2eHdXV1FvfXHObkON/c3ByKRCK8dOkSIq6PGiL+9xzh8/k4Ojq64nusdg31wMgFu+Hh4ay2jIwMgwW7lnwmjOorZ1daB4aGhrCzs5PZCtzZ2YmdnZ2sLcEikQhra2uZ13K5HD08PLCurg67u7sxNTV10a3SUVFR2NbWhq2trRgSErKqW6WX68u3b99QJBJhW1sb67yBgQG0s7PD+vp6g2s+f/4cHz16hB8+fMCBgQG8f/8+uri44LVr1/56PguZmp9KpcKSkhJsb29HtVqNdXV1GBQUhLGxscw5+q3SCQkJ2NXVha9evUIvL69V2yptSn4ajQalUimKxWJUqVSsrZlzc3OIuLr1q6qqQj6fj48fP8ZPnz5hdnY2enh4MDu7MjMzsaCggIl//fo1Ojo6Ynl5Ofb29mJxcfGiW6VXGpPWYmp+crkceTwe1tTUsGql/w6amJjAy5cvo1KpRLVajU1NTbhnzx4MCQmx6kTakhyvX7+ODQ0NODg4iB0dHZieno4bNmzAnp4eJsaWa6i3f/9+TEtLM2hfazWcmJhgnnUAgLdv38bOzk4cGhpCRMSCggLMzMxk4vVbpfPy8rC3txfv3bu36Fbp5e4ZF2jyMk9WVhYCgMGf5uZmJgb+93sYen/+/MGioiL08fFBPp+PcXFx2N/fz7ru2NgYZmRkoJubGwoEAjxx4gRrQmRNK/VFrVYb5IyIWFhYiAEBAajT6QyuWV9fj5GRkejm5oaurq64e/dufPjw4aKxf5up+X358gVjY2PR09MT+Xw+bt++HfPy8li/84KI+PnzZ0xOTkZnZ2cUCoWYm5vL2mpsLabm19zcvOhnGgBQrVYj4urX7+7du7h161bk8XgokUjwzZs3zDGZTIZZWVms+OrqatyxYwfyeDwMCwvDFy9esI4bMyatyZT8AgMDF61VcXExIiJqtVpMSEhALy8vdHJywsDAQDx16hSnDwVzmJLjxYsXmVgfHx88ePAgvnv3jnU9W64hImJfXx8CADY2Nhpca63VcKnvCH1OWVlZKJPJDM6JjIxEHo+HQUFBrGei3nL3jAt2iFbez0oIIYQQYgH6nRdCCCGE2BSavBBCCCHEptDkhRBCCCE2hSYvhBBCCLEpNHkhhBBCiE2hyQshhBBCbApNXgghhBBiU2jyQgghhBCbQpMXQgghhNgUmrwQQgghxKbQ5IUQQgghNoUmL4QQQgixKf8CTVETd2DG45QAAAAASUVORK5CYII=",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{PyCall.PyObject,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x7f271de32e20>"
      ]
     },
     "execution_count": 280,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1 = range(-1, 1, length=1001)\n",
    "plot(x1, sinseries.(x1, Ref(bn), 100, 2.0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Qual a relação desta função com a função $y = |x|$ que estudamos anteriormente?\n",
    "\n",
    "Esta função é a derivada da função $y = |x|$!\n",
    "\n",
    "E a série de $dy/dx$ é formada pelas derivadas da série original!\n",
    "\n",
    "Existem condições específicas onde se pode derivar a série termo a termo. Mas se as funções forem suaves, derive e integre a vontade! Funciona até para algumas descontinuidades.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Escolha diferentes números de pontos e interpole esta função nestes pontos\n",
    "\n",
    "\n",
    "Lembram da função `myresample`? Do jeito que foi implementada originalmente, só funcionava para N ímpar! Vamos primeiro entender isso."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "qpoints (generic function with 3 methods)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qpoints(Q, a=-1.0, b=1.0) = range(a, b, length=Q+1)[1:Q]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9×3 Array{Float64,2}:\n",
       "  0.0   0.0   0.0\n",
       "  1.0   0.0   0.0\n",
       "  2.0   0.0   0.0\n",
       "  3.0  -0.0   0.0\n",
       "  4.0   0.5   1.0\n",
       " -4.0   0.5  -1.0\n",
       " -3.0  -0.0  -0.0\n",
       " -2.0   0.0  -0.0\n",
       " -1.0   0.0  -0.0"
      ]
     },
     "execution_count": 289,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q = 9\n",
    "x = qpoints(Q, 0.0, 1.0)\n",
    "dx  = x[2]-x[1]\n",
    "f = \n",
    "y = cos.(2π*f.*x) .+ 2*sin.(2π*f.*x);\n",
    "Y = fft(y)./Q\n",
    "freq = fftfreq(Q, 1/dx)\n",
    "\n",
    "hcat(freq, round.(real.(Y), digits=2), round.(imag.(Y), digits=2))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 293,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5×3 Array{Float64,2}:\n",
       " 0.0  0.0  0.0\n",
       " 1.0  0.0  0.0\n",
       " 2.0  0.0  0.0\n",
       " 3.0  0.0  0.0\n",
       " 4.0  1.0  0.0"
      ]
     },
     "execution_count": 293,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q = 8\n",
    "x = qpoints(Q, 0.0, 1.0)\n",
    "dx  = x[2]-x[1]\n",
    "f = 4\n",
    "y = cos.(2π*f.*x) .+ 2*sin.(2π*f.*x);\n",
    "Y = rfft(y)./Q\n",
    "freq = rfftfreq(Q, 1/dx)\n",
    "\n",
    "hcat(freq, round.(real.(Y), digits=2), round.(imag.(Y), digits=2))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "myresample (generic function with 1 method)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Resample\n",
    "\n",
    "function myresample(y, Qout)\n",
    "    Qin = length(y)\n",
    "    Nin = Qin ÷ 2 + 1 \n",
    "    Nout = Qout ÷ 2 + 1\n",
    "    \n",
    "    Yin = rfft(y)\n",
    "    Yout = zeros(ComplexF64, Nout)\n",
    "    nmin = min(Nout, Nin)\n",
    "    for i in 1:nmin\n",
    "        Yout[i] = Qout/Qin * Yin[i]\n",
    "    end\n",
    "    \n",
    "    \n",
    "    if Qout > Qin  # interpolação\n",
    "        if iseven(Qin)\n",
    "            Yout[Nin] /= 2\n",
    "        end\n",
    "    elseif Qout < Qin\n",
    "        if iseven(Qin)\n",
    "            Yout[Nout] = 2*real(Yout[Nout])\n",
    "        end\n",
    "    end\n",
    "    \n",
    "    return irfft(Yout, Qout)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 299,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "Q0 = 32\n",
    "x0 = range(-1, 1, length=Q0+1)[1:Q0]\n",
    "y0 = 1.0 * sign.(x0);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 301,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{PyCall.PyObject,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x7f271db629a0>"
      ]
     },
     "execution_count": 301,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q1 =  256\n",
    "x1 = qpoints(Q1, -1, 1)\n",
    "y1 = myresample(y0, Q1)\n",
    "plot(x1, y1)\n",
    "plot(x0, y0, \"r.\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Problema 2\n",
    "\n",
    "Verifique a ortogonalidade discreta da base trigonométrica, ou seja, \n",
    "\n",
    "$$\n",
    "\\sum_{i=1}^Q \\phi_n(x_i)\\cdot \\phi_k(x_i)=0 \\qquad k\\ne n, k+n \\text{ e } k-n \\text{ não são múltiplos de}\\: Q/2\n",
    "$$\n",
    "\n",
    "para \n",
    "\n",
    "\\begin{align}\n",
    "\\phi_0(x) &= \\frac{1}{2}\\\\\n",
    "\\phi_n(x) &= \\cos\\left(\\frac{2\\pi n x}{L_0}\\right) \\qquad 0\\le n \\le N \\\\\n",
    "\\phi_{n+N}(x) &= \\sin\\left(\\frac{2\\pi n x}{L_0}\\right) \\qquad 1\\le n \\le N \n",
    "\\end{align}\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 307,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.0:0.2:0.8"
      ]
     },
     "execution_count": 307,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q = 10\n",
    "x = qpoints(Q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 314,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.9999999999999964"
      ]
     },
     "execution_count": 314,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L0 = 2.0\n",
    "n = 3; k = 13\n",
    "sum(sin.((2π*n/L0)*x) .* sin.((2π*k/L0)*x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Problema 3\n",
    "\n",
    "Nos exemplos iniciais usando a DFT, ao se escolher os pontos, foi utilizado o seguinte código:\n",
    "```julia\n",
    "L₀ = 1.0; Q = 16; freq=1\n",
    "x = range(0.0, L₀, length=Q+1)[1:Q]\n",
    "```\n",
    "O que acontece se utilzarmos a expressão mais simples a seguir?\n",
    "```julia\n",
    "x = range(0.0, L₀, length=Q)\n",
    "```\n",
    "O que está acontecendo? Você consegue explicar?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 318,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{PyCall.PyObject,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x7f26c2843f10>"
      ]
     },
     "execution_count": 318,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L₀ = 1.0; Q = 16; freq=1; \n",
    "x = range(0.0, L₀, length=Q+1)[1:Q]\n",
    "y = sin.(freq.*2π.*x); f = (0:Q-1) / L₀\n",
    "Y = 1/Q * fft(y);\n",
    "plot(f, imag.(Y), \"ro\")\n",
    "plot(f, real.(Y), \"xb\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{PyCall.PyObject,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x7f2722bfc4f0>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L₀ = 1.0; Q = 16; freq=1; \n",
    "x = range(0.0, L₀, length=Q)\n",
    "y = sin.(freq.*2π.*x); f = (0:Q-1) / L₀\n",
    "Y = 1/Q * fft(y);\n",
    "plot(f, imag.(Y), \"ro\")\n",
    "plot(f, real.(Y), \"xb\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**O que está acontecendo?**\n",
    "\n",
    "O que a gente quer?  Interpolar a função $\\sin2\\pi x$ para $0\\le x\\le 1$ \n",
    "\n",
    "Visualmente o que ocorre pode ser visto no gráfico a seguir:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 2 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q = 4; x1 = range(0, 1, length=Q+1)[1:Q]; dx1 = x1[2]-x1[1];\n",
    "x2 = range(0, 1, length=Q); dx2 = x2[2]-x2[1]\n",
    "subplot(121); plot(x1, zeros(Q), \"r.\")\n",
    "for i in 1:Q\n",
    "    plot([x1[i], x1[i]+dx1], [0, 0], \"k-\")\n",
    "end\n",
    "subplot(122); plot(x2, zeros(Q), \"r.\")\n",
    "for i in 1:Q\n",
    "    plot([x2[i], x2[i]+dx2], [0, 0], \"k-\")\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Temos uma inconsistência!\n",
    "\n",
    "Como só passamos o número de pontos, na verdade estamos aproximando a função mais um trecho reto:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{PyCall.PyObject,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x7f2722b675e0>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q = 4; x1 = range(0, 1, length=Q+1)[1:Q]; dx1 = x1[2]-x1[1]\n",
    "dx1 = 1.0 / Q; xx1 = 0:0.01:1; yy1 = sin.(2π.*xx1)\n",
    "xx = [xx1; 1.0 + dx1]; yy = [yy1; 0.0]\n",
    "plot(xx, yy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Problema 4\n",
    "\n",
    "Implemente a DFT usando a definição. Verifique como aumenta o custo computacional quando o número de pontos aumenta. \n",
    "\n",
    "Como foi mostrado, esta operação é uma multiplicação de matriz por vetor. Verifique se invertendo a ordem dos loops afeta o desempenho. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### DFT - Discrete Fourier Transform (transformada de Fourier discreta)\n",
    "\n",
    "$$\n",
    "c_n = X_n = \\frac{1}{N}\\sum_{k=0}^{N-1} x_k \\exp\\left(-\\frac{2\\pi i n k}{N} \\right)\n",
    "$$\n",
    "\n",
    "Chamando \n",
    "$$\n",
    "w_k = w^k = \\exp\\left(-\\frac{2\\pi i k}{N}\\right)\n",
    "$$\n",
    "Repare que isto pode ser escrito como uma multiplicação de matrizes:\n",
    "\n",
    "$$\n",
    "\\left(\\begin{matrix} X_0 \\\\ X_1 \\\\ \\vdots \\\\ X_{N-1}\\end{matrix} \\right)\n",
    "= \n",
    "\\left(\\begin{matrix} 1 & 1 & \\cdots & 1\\\\\n",
    "1 & w & \\cdots & w^{N-1} \\\\\n",
    "\\vdots & \\vdots & \\ddots &\\vdots \\\\\n",
    "1 & w^N & \\cdots & w^{(N-1)^2}\\\\\n",
    "\\end{matrix}\\right) \n",
    "\\cdot \n",
    "\\left(\\begin{matrix} x_0 \\\\ x_1 \\\\ \\vdots \\\\ x_{N-1}\\end{matrix} \\right) \n",
    "$$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 319,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mydft (generic function with 1 method)"
      ]
     },
     "execution_count": 319,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function mydft(x)\n",
    "    N = length(x)\n",
    "    X = zeros(ComplexF64,N)\n",
    "    w = exp(-2π*im/N)\n",
    "\n",
    "    for i in 1:N\n",
    "        for k in 1:N\n",
    "            X[i] += x[k] * w^((i-1)*(k-1))\n",
    "        end\n",
    "    end\n",
    "    \n",
    "    return X\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 321,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.504777312823609e-15"
      ]
     },
     "execution_count": 321,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = rand(10)\n",
    "X1 = mydft(x)\n",
    "X2 = fft(x)\n",
    "maximum(abs, X1 - X2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mydft (generic function with 1 method)"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function mydft!(x, X)\n",
    "    N = length(x)\n",
    "    w = exp(-2π*im/N)\n",
    "    for i in 1:N\n",
    "        Xi = 0.0 + 0.0im\n",
    "        wi = w^(i-1)\n",
    "        wk = 1.0 + 0.0im\n",
    "        for k in 1:N\n",
    "            Xi += x[k] * wk\n",
    "            wk *= wi\n",
    "        end\n",
    "        X[i] = Xi\n",
    "    end\n",
    "    return X\n",
    "end\n",
    "mydft(x) = mydft!(x, zeros(ComplexF64, length(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 322,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.907503795392484e-14"
      ]
     },
     "execution_count": 322,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = randn(20)\n",
    "X1 = mydft(x)\n",
    "X2 = fft(x)\n",
    "maximum(abs, X1-X2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Problema 5\n",
    "\n",
    "(Desafio) procure na net ou em algum livro como implementar a FFT. Tente!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Com $N$ divísível por 2:\n",
    "\\begin{align}\n",
    "X[k] &= \\sum_{r=0}^N x[r] W_N^{rk} \\qquad W_N = \\exp\\left(-\\frac{2\\pi i}{N}\\right)\\\\\n",
    "X[k] &= \\sum_{r=0}^{N/2-1} x[2r] W_N^{2rk} + \\sum_{r=0}^{N/2-1} x[2r+1] W_N^{(2r+1)k} \\\\\n",
    "X[k] &= \\sum_{r=0}^{N/2-1} x[2r] W_{N/2}^{rk} + W_N^k\\sum_{r=0}^{N/2-1} x[2r+1] W_{N/2}^{rk} \\\\\n",
    "X[k] &= X_{par}[k] + W_N^k\\cdot X_{ímpar}[k]\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 323,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "myfft_rec (generic function with 1 method)"
      ]
     },
     "execution_count": 323,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function myfft_rec(x)\n",
    "    N = length(x)\n",
    "    n1 = div(N,2)\n",
    "    if N==1\n",
    "        return [x[1]]\n",
    "    elseif N % 2 != 0\n",
    "        error(\"O tamanho deve ter potência de 2\")\n",
    "    else\n",
    "        Xe = myfft_rec(x[1:2:end])\n",
    "        Xo = myfft_rec(x[2:2:end])\n",
    "        factor = exp.(-2π*im .* (0:N-1) ./ N)\n",
    "        return[Xe .+ factor[1:n1] .* Xo; \n",
    "            Xe .+ factor[(n1+1):end] .* Xo]\n",
    "        \n",
    "    end\n",
    "end    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 324,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.532931148469529e-14"
      ]
     },
     "execution_count": 324,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = randn(2^10)\n",
    "X1 = myfft_rec(x)\n",
    "X2 = fft(x)\n",
    "maximum(abs, X1 - X2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 326,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.005355 seconds (17.39 k allocations: 1.628 MiB)\n",
      "  0.000071 seconds (51 allocations: 35.109 KiB)\n"
     ]
    }
   ],
   "source": [
    "@time myfft(x);\n",
    "@time fft(x);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Jeito mais inteligente\n",
    "(retirado do livro Random Vibratrions, Spectral & Wavelet Analysis de D. E. Newland)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 328,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "swaparr! (generic function with 1 method)"
      ]
     },
     "execution_count": 328,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function bitrev(n, bits)\n",
    "    nrev = zero(n)\n",
    "    N = 1 << bits\n",
    "    nrev = n\n",
    "    \n",
    "    for i in 1:bits-1\n",
    "        n >>= 1\n",
    "        nrev <<= 1\n",
    "        nrev |= n & 1\n",
    "    end\n",
    "    nrev &= N-1\n",
    "    return nrev\n",
    "end\n",
    "function swaparr!(x)\n",
    "    N = length(x)\n",
    "    n = Int(log2(N))\n",
    "    \n",
    "    for i in 1:N\n",
    "        ir = bitrev(i-1, n)+1\n",
    "        if ir > i\n",
    "            tmp = x[i]\n",
    "            x[i] = x[ir]\n",
    "            x[ir] = tmp\n",
    "        end\n",
    "    end\n",
    "end\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 329,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "myfft! (generic function with 1 method)"
      ]
     },
     "execution_count": 329,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function myfft!(x)\n",
    "    N = length(x)\n",
    "    n = Int(log2(N))\n",
    "    swaparr!(x)  \n",
    "    m = 1\n",
    "    while true\n",
    "        U = 1.0+0.0im\n",
    "        j = 1\n",
    "        k = 2^(m-1)\n",
    "        W = exp(-π*im/k)\n",
    "        while true\n",
    "            l = j\n",
    "            while true\n",
    "                t = x[l+k] * U\n",
    "                x[l+k] = x[l] - t\n",
    "                x[l] = x[l] + t\n",
    "                \n",
    "                l = l + 2^m\n",
    "                if l > 2^n\n",
    "                    break\n",
    "                end\n",
    "            end\n",
    "            U = U * W\n",
    "            j = j + 1\n",
    "            if j > k\n",
    "                break\n",
    "            end\n",
    "        end\n",
    "        m = m + 1\n",
    "        if m > n\n",
    "            break\n",
    "        end\n",
    "    end\n",
    "    return x\n",
    "end\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 336,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.042963 seconds (51 allocations: 16.003 MiB)\n",
      "  0.392928 seconds (2 allocations: 16.000 MiB)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2.055062868211651e-8"
      ]
     },
     "execution_count": 336,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 20\n",
    "N = 2^n\n",
    "\n",
    "x = rand(N) + rand(N) .* im\n",
    "@time X1 = fft(x)\n",
    "@time X2 = myfft!(copy(x))\n",
    "\n",
    "maximum(abs,X1-X2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Problema 6\n",
    "\n",
    "A transformada de Fourier está diretamente relacionada com a série de Fourier e é dada por:\n",
    "$$\n",
    "X(\\omega) = \\frac{1}{2\\pi} \\int_{-\\infty}^\\infty x(t)e^{-i\\omega t}\\: dt\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ### 6.1 Calcula a transformada de Fourier para a função \n",
    "  $$\n",
    "  x(t) = \\left\\{\\begin{matrix} 1 & -1 < x < 1 \\\\ 0 & x \\ge 1\\end{matrix}\\right.\n",
    "  $$\n",
    "$$\n",
    "X(\\omega) = \\frac{1}{2\\pi}\\int_{-\\infty}^\\infty x(t)e^{-i\\omega t}\\: dt = \n",
    "\\frac{1}{2\\pi}\\int_{-1}^1 e^{-i\\omega t}\\: dt = \\frac{1}{2\\pi}\\left.\\frac{i e^{-i\\omega}}{\\omega}\\right|_{-1}^1 = \n",
    "\\frac{\\sin\\omega}{\\pi\\omega}\n",
    "$$\n",
    "$$\n",
    "\\text{sinc} = \\frac{\\sin\\pi x}{\\pi x}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{PyCall.PyObject,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x7f2722e57160>"
      ]
     },
     "execution_count": 207,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = -15:0.01:15\n",
    "y = 1/π .* sinc.(x./π)\n",
    "plot(x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### 6.2 Discretize a função e use a FFT para calcular a transformada.\n",
    "\n",
    "$$\n",
    "X(\\omega) = \\frac{1}{2\\pi}\\int_{-\\infty}^\\infty x(t)e^{-i\\omega t}\\: dt = \n",
    "\\frac{1}{2\\pi}\\int_{-T_0/2}^{T_0/2} e^{-i\\omega t}\\: dt \\approx \\frac{1}{2\\pi} \\sum_{k=0}^{N-1} x(t_k) e^{-i\\omega t_k}\\Delta t \\qquad \\Delta t = \\frac{T_0}{N} \\qquad t_k = -\\frac{T_0}{2} + k\\cdot \\Delta t\n",
    "$$\n",
    "\n",
    "Ou seja, \n",
    "\n",
    "$$\n",
    "X(\\omega) \\approx \\frac{1}{2\\pi} \\sum_{k=0}^{N-1} x(t_k) e^{-i\\omega t_k}\\Delta t = \n",
    "\\frac{\\Delta t}{2\\pi} \\sum_{k=0}^{N-1} x_k e^{-i\\omega(-T_0/2 + k\\Delta t)} = \n",
    "\\frac{\\Delta t}{2\\pi}\\cdot e^{\\frac{i\\omega T_0}{2}}\\cdot \\sum_{k=0}^{N-1} x_k e^{-i\\omega k\\Delta t} = \n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "\n",
    "Discretizando $\\omega = \\omega_j = j\\cdot \\omega_0 = \\frac{2\\pi j}{T_0}$, $0 \\le j < N$\n",
    "\n",
    "$$\n",
    "X_j = X(\\omega_j) = \\frac{\\Delta t}{2\\pi}\\cdot e^{\\frac{2\\pi j T_0}{2{T_0}}}\\cdot \\sum_{k=0}^{N-1} x_k e^{-\\frac{2\\pi i j\\omega k\\Delta t}{N\\cdot \\Delta t}} = \n",
    " \\frac{\\Delta t}{2\\pi}\\cdot e^{\\pi i j}\\cdot \\sum_{k=0}^{N-1} x_k \\exp\\left(-\\frac{2\\pi i j k}{N}\\right)\n",
    "$$\n",
    "ou seja\n",
    "$$\n",
    "X_j = X(\\omega_j) =\n",
    "\\frac{\\Delta t}{2\\pi}\\cdot e^{\\pi i j}\\cdot \\sum_{i=0}^{N-1} x_k \\exp\\left(-\\frac{2\\pi i j k}{N}\\right)\n",
    "$$\n",
    "A somatória no ultimo termo é a DFT. O termo $e^{\\pi i j}$ é corresponde à translação."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "Q = 32\n",
    "Δt = 2.0 / Q\n",
    "x = ones(Q)\n",
    "X0 = rfft(x)\n",
    "N = length(X)\n",
    "for j in 0:N-1\n",
    "    X0[j+1] = X0[j+1] * Δt/(2π) * exp(π*j*im) \n",
    "end\n",
    "freq0 = rfftfreq(Q, 1/Δt)\n",
    "w = 2π*freq0;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 267,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{PyCall.PyObject,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x7f271e0f9ca0>"
      ]
     },
     "execution_count": 267,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ww = range(0, maximum(w), length=1001)\n",
    "yy = 1/π .* sinc.(ww./π)\n",
    "plot(ww./(2π), yy)\n",
    "plot(freq0, real.(X0), \"ro\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### 6.3 Tente verificar o que acontece se você adiciona zeros à esquerda e à direita da função discretizada.\n",
    " \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 337,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q1 = 32; nn = 1; x = [zeros(nn*Q1); ones(Q1); zeros(nn*Q1-1)]\n",
    "Q = length(x); Δt = 2.0 / Q1\n",
    "X = rfft(x); N = length(X)\n",
    "for j in 0:N-1\n",
    "    X[j+1] = X[j+1] * Δt/(2π) * exp(π*j*im) \n",
    "end\n",
    "freq = rfftfreq(Q, 1/Δt); w = 2π*freq;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 338,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{PyCall.PyObject,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x7f27202d40d0>"
      ]
     },
     "execution_count": 338,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(ww./(2π), yy); plot(freq, real.(X), \"r.\")\n",
    "plot(freq0, real.(X0), \"b+\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Problema 7\n",
    "\n",
    "Faça alguns exemplos do pacote `ApproxFun` (<https://github.com/JuliaApproximation/ApproxFun.jl>)\n"
   ]
  }
 ],
 "metadata": {
  "@webio": {
   "lastCommId": null,
   "lastKernelId": null
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  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Julia 1.4.1",
   "language": "julia",
   "name": "julia-1.4"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.4.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
