{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Interpolação trigonométrica: Séries de Fourier, DFT e FFT\n",
    "\n",
    " * Até agora usamos polinômios para aproximar e interpolar\n",
    " * Outra possibilidade: senos e cossenos\n",
    " * Extremamente versátil e poderoso\n",
    " * Usado em eqs. diferenciais, análise matemática, funções aleatórias, etc, etc, etc ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Polinômio trigonométrico\n",
    "\\begin{align}\n",
    "S_N(x) = \\frac{a_0}{2} +& a_1 \\cos\\left(\\frac{2\\pi x}{L_0}\\right) + a_2\\cos\\left(\\frac{4\\pi x}{L_0}\\right) + \\cdots + a_N\\cos\\left(\\frac{2\\pi n  x}{L_0}\\right) + \\\\ \n",
    "&b_1 \\sin\\left(\\frac{2\\pi x}{L_0}\\right) + b_2\\sin\\left(\\frac{4\\pi x}{L_0}\\right) + \\cdots + b_N\\sin\\left(\\frac{2\\pi N  x}{L_0}\\right)\n",
    "\\end{align}\n",
    "\n",
    "Nesta equação, $T_0$ é o período da função.\n",
    "\n",
    "O que temos é uma base $\\phi_n(t)$ com $2N+1$ termos:\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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Como calcular os coeficientes $a_i$ e $b_i$??? \n",
    "**Ortogonalidade de senos e cossenos**\n",
    "\n",
    "\\begin{align}\n",
    "\\int_{-L_0/2}^{L_0/2} \\cos\\left(\\frac{2\\pi n x}{L_0}\\right) \\cdot \\cos\\left(\\frac{2\\pi m x}{L_0}\\right) \\: dx &= \\left\\{\\begin{matrix}0 \\quad n\\neq m\\\\ \\frac{L_0}{2} \\quad n=m\\end{matrix}\\right.\\\\\n",
    "\\int_{-L_0/2}^{L_0/2} \\sin\\left(\\frac{2\\pi n x}{L_0}\\right) \\cdot \\sin\\left(\\frac{2\\pi m x}{L_0}\\right) \\: dx &= \\left\\{\\begin{matrix}0 \\quad n\\neq m\\\\ \\frac{L_0}{2} \\quad n=m\\end{matrix}\\right.\\\\\n",
    "\\int_{-L_0/2}^{L_0/2} \\cos\\left(\\frac{2\\pi n x}{L_0}\\right) \\cdot \\sin\\left(\\frac{2\\pi m x}{T_0}\\right) \\: dx &= 0\\\\\n",
    "\\end{align}\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Como calcular os coeficientes?\n",
    "\n",
    "\\begin{align}\n",
    "a_n &= \\frac{2}{L_0}\\int_{-L_0/2}^{L_0/2} y(x) \\cdot \\cos\\left(\\frac{2\\pi n x}{L_0}\\right)\\: dx \\\\\n",
    "b_m &= \\frac{2}{L_0}\\int_{-L_0/2}^{L_0} y(x) \\cdot \\sin\\left(\\frac{2\\pi m x}{L_0}\\right)\\: dx \\\\\n",
    "\\end{align}\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Exemplo: $y(x) = |x|, -1 \\le x \\le 1$ ($L_0 = 2$)\n",
    "\\begin{align}\n",
    "a_0 &= 2\\int_0^1 x\\:dx \\qquad a_0 = 1\\\\\n",
    "a_n &= 2\\int_0^1 \\cos\\left(\\frac{2\\pi n x}{2}\\right)\\:dx \\qquad a_n = \\frac{2}{\\pi^2 n^2}\\cdot\\left[(-1)^n - 1\\right] \\\\\n",
    "b_n &= 0\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Usando o SymPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{equation*}\\frac{2 \\left(-1\\right)^{n}}{\\pi^{2} n^{2}} - \\frac{2}{\\pi^{2} n^{2}}\\end{equation*}"
      ],
      "text/plain": [
       "      n        \n",
       "2⋅(-1)      2  \n",
       "─────── - ─────\n",
       "  2  2     2  2\n",
       " π ⋅n     π ⋅n "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using SymPy\n",
    "x = symbols(\"x\", real=true)\n",
    "n = symbols(\"n\", integer=true, positive=true)\n",
    "a0f  =  2 * integrate(x, (x, 0, 1))\n",
    "anf = 2 * integrate(x * cos(2PI*n*x/2), (x, 0, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "abst (generic function with 1 method)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function abst(t, n)\n",
    "    x = 1.0/2\n",
    "    for i in 1:2:n\n",
    "        ai = 2/(π*i)^2 * ((-1)^i - 1)\n",
    "        x += ai * cos(π*i*t)\n",
    "    end\n",
    "    return x\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "using PyPlot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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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 0x7fdcb5038160>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xx = -1:0.002:1; yy = abs.(xx); y1 = abst.(xx, 1); y3 = abst.(xx, 3); y5 = abst.(xx, 5); y7 = abst.(xx, 7);\n",
    "plot(xx, yy, \"b:\", label=\"Exato\"); plot(xx, y1, label=\"n = 1\"); plot(xx, y3, label=\"n = 3\"); \n",
    "plot(xx, y5, label=\"n = 5\"); plot(xx, y7, label=\"n = 7\"); legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Vamos generalizar?\n",
    "\n",
    "Imagine que queremos aproximar $u(x)$ usando uma base ortogonal $\\phi_n(x)$ com $1 \\le n \\le N$ no domínio $a \\le x \\le b$:\n",
    "$$\n",
    "u(x) \\approx u^\\delta(x) = \\sum_{n=1}^N \\hat{u}_n \\phi_n(x)\n",
    "$$\n",
    "O erro da aproximação vale:\n",
    "$$\n",
    "\\varepsilon(x) = u^\\delta(x) - (x) \\quad\\longrightarrow\\quad \\varepsilon^2 = \\int_a^b w(x)\\left[ u^\\delta(x) - u(x) \\right]^2\\:dx\n",
    "$$\n",
    "\n",
    "Nesta equação, $w(x)$ é uma função de peso que agora vamos considerar constante e igual a 1.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Mínimos quadrados.\n",
    "$$\n",
    "\\varepsilon^2 = f(\\hat{u}_1, \\ldots, \\hat{u}_N)\n",
    "$$\n",
    "Para minimizar o erro, fazemos como fizemos na aula anterior:\n",
    "$$\n",
    "\\frac{\\partial \\varepsilon^2}{\\partial \\hat{u}_k} = 0 \\quad 1 \\le k \\le N\n",
    "$$\n",
    "\n",
    "Com isso chegamos ao seguinte sistema de equações lineares:\n",
    "$$\n",
    "\\sum_{j=1}^N \\hat{u}_j \\int_a^b w(x)\\phi_n(x)\\phi_k(x)\\:dx = \\int_a^b w(x)\\hat{u}_k u(x)\\:dx \\qquad 1\\le k \\le N\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Base ortogonal:\n",
    "\n",
    "$$\n",
    "\\int_a^b w(x) \\phi_j(x) \\phi_k(x) \\:dx = \n",
    "\\left\\{\\begin{matrix} 0 & \\quad &  se\\: j\\ne k \\\\ \\gamma(k) & \\quad & se\\: j=k\\end{matrix}\\right.\n",
    "$$\n",
    "Quando $\\gamma(k) = 1$ para $1\\le k \\le N$, a base é ortonormal.\n",
    "\n",
    "Para a função de peso $w(x)=1$ e a base formada com senos e cossenos, recuperamos as equações para $a_n$ e $b_n$ acima.\n",
    "\n",
    "**Sempre que possível, use bases ortogonais**\n",
    "\n",
    "Quando não for possível, ainda ajuda usar bases parcialmente ortogonais."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Mínimos quadrados discreto\n",
    "\n",
    "Neste caso, com uma base $\\phi_n(x)$ com $1\\le n \\le N$ e com a função $u(x)$ conhecida nos pontos $x_k$, $1 \\le k \\le Q$, podemos usar o método dos mínimos quadrados:\n",
    "$$\n",
    "\\varepsilon^2 = \\sum_{k=1}^Q w_k\\left[u^\\delta(x_k) - u(x_k)\\right]^2 = \\sum_{k=1}^Q w_k\\left[\\left(\\sum_{n=1}^N \\hat{u}_n \\phi_n(x)\\right) - u_k\\right]^2\n",
    "$$\n",
    "\n",
    "Chegamos ao sistema apresentado na aula anterior:\n",
    "\n",
    "$$\n",
    "\\left(\n",
    "\\begin{matrix}\n",
    "\\sum_{k=1}^Q w_k\\phi_1(x_k)\\cdot\\phi_1(x_k) & \n",
    "\\cdots &\n",
    "\\sum_{k=1}^Q w_k\\phi_1(x_k)\\cdot\\phi_N(x_k) \\\\\n",
    "\\sum_{k=1}^Q w_k\\phi_2(x_k)\\cdot\\phi_1(x_k) & \n",
    "\\cdots &\n",
    "\\sum_{k=1}^Q w_k\\phi_2(x_k)\\cdot\\phi_N(x_k) \\\\\n",
    "\\vdots & \\ddots & \\vdots \\\\\n",
    "\\sum_{k=1}^Q w_k\\phi_N(x_k)\\cdot\\phi_1(x_k) & \n",
    "\\cdots &\n",
    "\\sum_{k=1}^Q w_k\\phi_N(x_k)\\cdot\\phi_N(x_k) \\\\\n",
    "\\end{matrix}\\right)\n",
    "\\cdot\n",
    "\\left(\\begin{matrix} \\hat{u}_1 \\\\ \\hat{u}_2 \\\\ \\vdots \\\\ \\hat{u}_N \\end{matrix}\\right)\n",
    "= \n",
    "\\left(\\begin{matrix} \\sum_{k=1}^Q w_k u_k \\phi_1(x_k) \\\\ \\sum_{k=1}^Q w_k u_k \\phi_2(x_k) \\\\  \\vdots \\\\ \\sum_{k=1}^Q w_k u_k \\phi_N(x_k)\\end{matrix}\\right)\n",
    "$$\n",
    "\n",
    "Aqui introduzimos a possibilidade de haver um peso $w_k$ para cada ponto."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Voltando para os polinômios trigonométricos...\n",
    "\n",
    "### Ortogonalidade discreta\n",
    "Já vimos que a base dos polinômios trigonométricos é ortogonal, de modo que para $k\\ne n$, \n",
    "$$\n",
    "\\int_{-L_0/2}^{L_0/2} \\phi_n(x) \\cdot \\phi_k(x) \\: dx = 0\n",
    "$$\n",
    "Mas podemos aproximar esta integral, chamando $\\Delta x = L_0 / Q$\n",
    "$$\n",
    "\\int_{-L_0/2}^{L_0/2} \\phi_n(x) \\cdot \\phi_k(x) \\: dx \\approx \\Delta x\\cdot \\sum_{i=0}^Q \\phi_n(x_i)\\cdot \\phi_k(x_i)  \\approx 0 \\qquad x_i = -\\frac{L_0}{2} + i\\cdot\\Delta x\\quad i = 0, \\ldots, Q-1\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Ortogonalidade discreta\n",
    "Admitindo que temos $Q$ pontos $x_j = j\\cdot \\Delta x$ para $0\\le j\\le Q$ e $\\Delta x = L_0/Q$, demonstra-se que\n",
    "\n",
    "$$\n",
    "\\sum_{j=0}^{Q-1} \\cos\\left(\\frac{2\\pi n x_j}{L_0}\\right) = 0 \\qquad\n",
    "\\sum_{j=0}^{Q-1} \\sin\\left(\\frac{2\\pi n x_j}{L_0}\\right) = 0\n",
    "$$\n",
    "quando $n$ é multiplo de $Q$. Por outro lado\n",
    "\n",
    "$$\n",
    "\\sum_{j=0}^{Q-1} \\left[\\cos\\left(\\frac{2\\pi n x_j}{L_0}\\right)\\right]^2 = \\frac{Q}{2} \\qquad\n",
    "\\sum_{j=0}^{Q-1} \\left[\\sin\\left(\\frac{2\\pi n x_j}{L_0}\\right)\\right]^2 = \\frac{Q}{2}\n",
    "$$\n",
    "quando $n$ não é múltiplo de $Q/2$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Ortogonalidade discreta\n",
    "Lembrando que \n",
    "\\begin{align}\n",
    "    2\\cos\\theta\\cos\\phi &= \\cos(\\theta-\\phi) + \\cos(\\theta+\\phi)\\\\\n",
    "    2\\cos\\theta\\sin\\phi &= \\sin(\\theta+\\phi) - \\sin(\\theta-\\phi)\\\\\n",
    "\\end{align}\n",
    "\n",
    "Chega-se à relação de ortogonalidade desejada:\n",
    "$$\n",
    "\\sum_{i=0}^Q \\phi_n(x_i)\\cdot \\phi_k(x_i)=0 \\qquad k\\ne n,k+n \\text{ e } k-n \\text{ não são múltiplos de}\\: Q/2\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Transformada de Fourier real discreta\n",
    "\n",
    "Com as relações de ortogonalidade, chega-se à seguinte relação para os coeficientes $a_n$ e $b_n$:\n",
    "\n",
    "\\begin{align}\n",
    "a_n &= \\frac{2}{Q}\\cdot\\sum_{j=0}^{Q-1} y_j\\cos\\left(\\frac{2\\pi n x_j}{L_0}\\right) \\qquad n=0, 1, \\ldots, N\\\\\n",
    "b_n &= \\frac{2}{Q}\\cdot\\sum_{j=0}^{Q-1} y_j\\sin\\left(\\frac{2\\pi n x_j}{L_0}\\right) \\qquad n=1, \\ldots, N\n",
    "\\end{align}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Outra abordagem para a transformada de Fourier real discreta\n",
    "\\begin{align}\n",
    "a_n &= \\frac{2}{L_0}\\int_{-L_0/2}^{L_0/2} y(x) \\cdot \\cos\\left(\\frac{2\\pi n x}{L_0}\\right)\\: dx \\\\\n",
    "b_m &= \\frac{2}{L_0}\\int_{-L_0/2}^{L_0} y(x) \\cdot \\sin\\left(\\frac{2\\pi m x}{L_0}\\right)\\: dx \\\\\n",
    "\\end{align}\n",
    "\n",
    "Aproximando as integrais:\n",
    "\\begin{align}\n",
    "a_n &= \\frac{2}{L_0}\\int_{-L_0/2}^{L_0/2} y(x) \\cdot \\cos\\left(\\frac{2\\pi n x}{L_0}\\right)\\: dx \\approx \\frac{2}{Q\\cdot \\Delta x} \\sum_{j=0}^{Q-1} y(x_j) \\cos\\left(\\frac{2\\pi n x_j}{L_0}\\right) \\cdot \\Delta x =\\\\\n",
    " & =  \\frac{2}{Q} \\sum_{j=0}^{Q-1} y_j \\cos\\left(\\frac{2\\pi n x_j}{L_0}\\right)\n",
    "\\end{align}\n",
    "\n",
    "Onde $\\Delta x = L_0 / Q$\n",
    "\n",
    "E assim obtemos o mesmo resultado que no slide anterior!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Exemplo: $y(x) = |x|, -1 \\le x \\le 1$ ($L_0 = 2$)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fourierseries (generic function with 1 method)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function fourierseries(x, L0, a0, a, b)\n",
    "    y = a0/2\n",
    "    N = length(a)\n",
    "    for i = 1:N\n",
    "        y += a[i] * cos(2π*i*x/L0)\n",
    "        y += b[i] * sin(2π*i*x/L0)\n",
    "    end\n",
    "    return y\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "L0 = 2.0\n",
    "Q = 20\n",
    "N = 8\n",
    "\n",
    "x = range(-1.0, 1.0, length=Q+1)[1:Q]\n",
    "y = abs.(x)\n",
    "\n",
    "a0 = 2/Q * sum(y)\n",
    "a = 2/Q * [sum(y .* cos.(2π .* n .* x ./ L0)) for n = 1:N]\n",
    "b = 2/Q * [sum(y .* sin.(2π .* n .* x ./ L0)) for n = 1:N];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# y(x) = |x|, -1 \\le x \\le 1$ ($L_0 = 2$)\n",
    "xx = -1:0.005:1\n",
    "yy = abs.(xx)\n",
    "yy1 = fourierseries.(xx, L0, a0, Ref(a), Ref(b))\n",
    "plot(xx, yy)\n",
    "plot(xx, yy1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Problemas digitais:\n",
    "\n",
    "O que nós temos: \n",
    "$$\n",
    "y_j, \\Delta x, \\quad\\longrightarrow\\quad x_{j+1}-x_j = \\Delta x =\\frac{L_0}{Q} \\qquad 0\\le j < Q\n",
    "$$\n",
    "não temos os valores de $x_n$ exatos. Então podemos assumir $x_j = j \\Delta x$:\n",
    "\\begin{align}\n",
    " a_n &= \\frac{2}{Q} \\sum_{j=0}^{Q-1} y_j \\cos\\left(\\frac{2\\pi n x_j}{L_0}\\right) = \n",
    " \\frac{2}{Q} \\sum_{j=0}^{Q-1} y_j \\cos\\left(\\frac{2\\pi n j \\Delta x}{Q\\cdot\\Delta x}\\right) = \n",
    " \\frac{2}{Q} \\sum_{j=0}^{Q-1} y_j \\cos\\left(\\frac{2\\pi n j}{Q}\\right) \\\\\n",
    " b_n &= \\frac{2}{Q} \\sum_{j=0}^{Q-1} y_j \\sin\\left(\\frac{2\\pi n x_j}{L_0}\\right) = \n",
    " \\frac{2}{Q} \\sum_{j=0}^{Q-1} y_j \\sin\\left(\\frac{2\\pi n j}{Q}\\right) \n",
    "\\end{align}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Forma complexa da série de Fourier\n",
    "\n",
    "$$\n",
    "c_n = \\left\\{ \\begin{matrix}\n",
    "\\frac{a_0}{2} & n = 0 \\\\\n",
    "\\frac{1}{2}\\left(a_n - i b_n\\right) & n > 0\\\\\n",
    "\\frac{1}{2}\\left(a_n + i b_n\\right) & n < 0\n",
    "\\end{matrix}\\right.\n",
    "$$\n",
    "$$\n",
    "f(x) = \\sum_{n=-N}^N c_n \\exp\\left(\\frac{2\\pi i n x}{L_0} \\right) \\qquad \n",
    "c_n = \\frac{1}{L_0}\\int_0^{L_0} f(x) \\exp\\left(-\\frac{2\\pi i n x}{L_0} \\right)\\:dx\n",
    "$$\n",
    "Se $f(x)$ for uma função real, para $n$ positivo:\n",
    "$$\n",
    "\\begin{matrix}\n",
    "c_n + c_{-n} = a_n\\\\\n",
    "c_n - c_{-n} = -i b_n\n",
    "\\end{matrix}\n",
    "\\longrightarrow\n",
    "c_n = c^*_{-n}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## DFT - Transformada de Fourier discreta\n",
    "\n",
    "$$\n",
    "c_n = \\frac{1}{L_0}\\int_0^{L_0} f(x) \\exp\\left(-\\frac{2\\pi i\\cdot n x}{L_0} \\right)\\:dx \\approx \\frac{1}{\\Delta x \\cdot Q}\\sum_{j=0}^{Q-1} y_j \\exp\\left(-\\frac{2\\pi i \\cdot n j\\Delta x}{Q\\cdot \\Delta x} \\right)\\cdot\\Delta x\n",
    "$$\n",
    "\n",
    "Portanto, \n",
    "$$\n",
    "c_n = \\frac{1}{Q}\\sum_{j=0}^{Q-1} y_j \\exp\\left(-\\frac{2\\pi i\\cdot n j}{Q} \\right)\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# DFT - Discrete Fourier Transform\n",
    "\n",
    "$$\n",
    "c_n = X_n = \\frac{1}{N}\\sum_{k=0}^{N-1} x_k \\exp\\left(-\\frac{2\\pi n k}{N} \\right)\n",
    "$$\n",
    "\n",
    "Chamando \n",
    "$$\n",
    "w_k = w^k = \\exp\\left(-\\frac{2\\pi k}{N}\\right)\n",
    "$$\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": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## FFT - Transformada Rápida de Fourier\n",
    "\n",
    "\n",
    "Um algorítmo rápido para\n",
    "$$\n",
    "\\sum_{j=0}^{Q-1} y_j \\exp\\left(-\\frac{2\\pi i\\cdot n j}{Q} \\right)\n",
    "$$\n",
    "\n",
    "Se $0\\le n\\le Q$, o custo computacional é $\\mathcal{O}(Q^2)$.\n",
    "\n",
    "FFT: custo cai para $\\mathcal{O}(Q\\cdot\\log Q)$\n",
    "\n",
    "Originalmente, só funcionava com $Q$ igual a potências de 2.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": [
       "PyObject <matplotlib.legend.Legend object at 0x7fdca5b24ee0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q = [2, 3, 5, 10, 15, 20, 40, 60, 80, 100, 150, 200, 300, 500, 700, 1000, 2000, 5000, 10000,\n",
    "20000, 30000, 50000, 100000, 200000, 500000, 1000000]\n",
    "t1 = Q\n",
    "t2 = Q.^2\n",
    "tlog = Q .* log2.(Q);\n",
    "loglog(Q, t1, label=\"\\$\\\\mathcal{O}(Q)\\$\")\n",
    "plot(Q, t2, label=\"\\$\\\\mathcal{O}(Q^2)\\$\")\n",
    "plot(Q, tlog, label=\"\\$\\\\mathcal{O}(Q\\\\cdot\\\\log_2 Q)\\$\")\n",
    "legend()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## FFTW - Fastest Fourier Transform of the West"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Pkg.add(\"FFTW\")\n",
    "using FFTW"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Complex{Float64},1}:\n",
       "  3.061616997868383e-17 + 0.0im\n",
       " -3.061616997868383e-17 - 0.5im\n",
       "  3.061616997868383e-17 + 0.0im\n",
       " -3.061616997868383e-17 + 0.5im"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L₀ = 1.0; Q = 4; 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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Exemplos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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": [
       "PyObject <matplotlib.legend.Legend object at 0x7fdc9eb40b50>"
      ]
     },
     "execution_count": 11,
     "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\", label=\"Parte Imaginária\")\n",
    "plot(f, real.(Y), \"bx\", label=\"Parte Real\")\n",
    "xlabel(\"Frequência (Hz)\"); axvline(freq, linestyle=\":\")\n",
    "annotate(\"???\", (f[Q], imag(Y[Q])))\n",
    "legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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": [
       "PyObject <matplotlib.legend.Legend object at 0x7fdc9eaff5b0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L₀ = 1.0; Q = 8; freq=1\n",
    "x = range(0.0, L₀, length=Q+1)[1:Q]; f = (0:Q-1) / L₀\n",
    "\n",
    "y = cos.(freq.*2π.*x) + 2*sin.(2*freq.*2π.*x)\n",
    "\n",
    "Y = 1/Q * fft(y)\n",
    "plot(f, imag.(Y), \"ro\", label=\"Parte Imaginária\")\n",
    "plot(f, real.(Y), \"bx\", label=\"Parte Real\")\n",
    "xlabel(\"Frequência (Hz)\"); axvline(freq, linestyle=\":\")\n",
    "legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8-element Array{Float64,1}:\n",
       "  0.0\n",
       "  1.0\n",
       "  2.0\n",
       "  3.0\n",
       " -4.0\n",
       " -3.0\n",
       " -2.0\n",
       " -1.0"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fftfreq(Q) * Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## A DFT é periódica (aliasing)!\n",
    "\n",
    "Sejam os pontos $y_j$, $0 \\le j < N$:\n",
    "\n",
    "$$\n",
    "Y_k = \\frac{1}{N}\\sum_{j=0}^{N-1} y_j\\exp\\left(-\\frac{2\\pi i j k}{N}\\right)\n",
    "$$\n",
    "$$\n",
    "Y_{N+k} = \\frac{1}{N}\\sum_{j=0}^{N-1} y_j\\exp\\left[-\\frac{2\\pi i j (k+N)}{N}\\right] = \n",
    "\\frac{1}{N}\\sum_{j=0}^{N-1} y_je^{-2\\pi i j}\\exp\\left(-\\frac{2\\pi i j k}{N}\\right)\n",
    "$$\n",
    "$$\n",
    "Y_{N+k} = \\frac{1}{N}\\sum_{j=0}^{N-1} y_j\\exp\\left(-\\frac{2\\pi i j k}{N}\\right) = Y_k\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Exemplo de Aliasing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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 0x7fdc9ea9c370>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ncyc = 4; Q = 13; T₀ = 1; g(t) = sin(3*2π * t)\n",
    "t = range(0, ncyc, length=Q+1); x = g.(t)\n",
    "t0 = 0:0.01:ncyc; x0 = g.(t0)\n",
    "plot(t0, x0); plot(t, x, \"ro-\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## O que acontece com frequências negativas (quando $y_j$ é real)?\n",
    "\n",
    "E se o $y_j$ forem reais?\n",
    "$$\n",
    "Y_{-k} = \\frac{1}{N}\\sum_{j=0}^{N-1} y_j\\exp\\left(\\frac{2\\pi i j k}{N}\\right) = Y^*_k\n",
    "$$\n",
    "\n",
    "Mas lembre-se que $Y$ também é periódico:\n",
    "\n",
    "$$\n",
    "Y_{-k} = Y_{N-k} = Y^*_k\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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": [
       "PyObject <matplotlib.legend.Legend object at 0x7fdcb4fd2100>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L₀ = 1.0; Q = 8; freq=5\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\", label=\"Parte Imaginária\")\n",
    "plot(f, real.(Y), \"bx\", label=\"Parte Real\")\n",
    "xlabel(\"Frequência (Hz)\"); axvline(freq, linestyle=\":\")\n",
    "annotate(\"???\", (f[Q], imag(Y[Q])))\n",
    "legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Qual o número de frequencias relevantes?\n",
    "\n",
    " * Q números reais\n",
    " * `fft` gera Q números complexos - 2 $\\times$ vezes mais informação\n",
    " * A frequência 0 sempre vai corresponder a um número real (a média)!\n",
    " \n",
    "### Q é um número ímpar\n",
    "  * $a_0$\n",
    "  * $(Q-1)/2\\:\\longrightarrow\\:a_n$\n",
    "  * $(Q-1)/2\\:\\longrightarrow\\:b_n$\n",
    "\n",
    "### N é um número par\n",
    " * $a_0$\n",
    " * $Q/2\\:\\longrightarrow\\:a_n$\n",
    " * $Q/2\\:\\longrightarrow\\:b_n$ mas $b_{1+Q/2} = 0$\n",
    "\n",
    "$$\n",
    "N_\\text{relevante} = \\frac{Q}{2} + 1\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "nfftutil (generic function with 1 method)"
      ]
     },
     "execution_count": 16,
     "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": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "div(3,2)\n",
    "3 % 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nfftutil(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nfftutil(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nfftutil(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nfftutil(6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## `rfft`: especializado para números reais"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "64.32486796593503\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "4-element Array{Complex{Float64},1}:\n",
       "    64.32486796593503 + 0.0im\n",
       " -0.05102229399856828 + 0.6832587292617861im\n",
       " 0.023004050822528654 - 0.3227015418884201im\n",
       "  -0.8993776580689623 + 0.0im"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q = 6\n",
    "x = rand(Q) .+ 10\n",
    "println(sum(x))\n",
    "X = rfft(x)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6-element Array{Complex{Float64},1}:\n",
       "    64.32486796593503 + 0.0im\n",
       " -0.05102229399856828 + 0.6832587292617861im\n",
       " 0.023004050822528654 - 0.3227015418884201im\n",
       "  -0.8993776580689623 + 0.0im\n",
       " 0.023004050822528654 + 0.3227015418884201im\n",
       " -0.05102229399856828 - 0.6832587292617861im"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = fft(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Interpolação trigonométrica"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "struct TrigInterp\n",
    "    Q::Int\n",
    "    dx::Float64\n",
    "    c::Vector{ComplexF64}\n",
    "end\n",
    "TrigInterp(x::Vector{Float64}, dx) = TrigInterp(length(x), dx, rfft(x))\n",
    "\n",
    "function interp(f::TrigInterp, x)\n",
    "    y = real(f.c[1])/2\n",
    "    Q = f.Q\n",
    "    P = Q * f.dx\n",
    "    N = length(f.c)\n",
    "    for k in 1:N-1\n",
    "        c = f.c[k+1]\n",
    "        y += real(c) * cos(2π*k*x/P) - imag(c) * sin(2π*k*x)\n",
    "    end\n",
    "    \n",
    "    return 2y/Q\n",
    "end\n",
    "\n",
    "(f::TrigInterp)(x) = interp(f, x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Exemplo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "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": [
       "PyObject <matplotlib.legend.Legend object at 0x7fdc9eb1b1c0>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q = 7; L₀ = 1.0; \n",
    "x0 = range(0, L₀, length=Q+1)[1:Q]\n",
    "f = x->(2*(sin(2π*x)) + 1.0 + cos(2π*x))\n",
    "y0 = f.(x0)\n",
    "Y = TrigInterp(y0, L₀/Q)\n",
    "x = 0:0.01:L₀; y = Y.(x);\n",
    "plot(x, f.(x), label=\"Exato\")\n",
    "plot(x, y, \"k:\", label=\"Interpolado\")\n",
    "plot(x0, y0, \"ro\", label=\"Pontos\")\n",
    "legend()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## E usando fft (não rfft)?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "struct TrigInterp0\n",
    "    Q::Int\n",
    "    dx::Float64\n",
    "    c::Vector{ComplexF64}\n",
    "end\n",
    "TrigInterp0(x::Vector{Float64}, dx) = TrigInterp0(length(x), dx, fft(x))\n",
    "\n",
    "function interp(f::TrigInterp0, x)\n",
    "    y = real(f.c[1])/2\n",
    "    Q = f.Q\n",
    "    P = Q * f.dx\n",
    "    N = nfftutil(length(f.c))\n",
    "    for k in 1:N-1\n",
    "        c = f.c[k+1]\n",
    "        y += real(c) * cos(2π*k*x/P) - imag(c) * sin(2π*k*x)\n",
    "    end\n",
    "    \n",
    "    return 2y/Q\n",
    "end\n",
    "\n",
    "(f::TrigInterp0)(x) = interp(f, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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": [
       "PyObject <matplotlib.legend.Legend object at 0x7fdc9bccb6d0>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y = TrigInterp0(y0, L₀/Q)\n",
    "x = 0:0.01:L₀; y = Y.(x);\n",
    "plot(x, f.(x), label=\"Exato\")\n",
    "plot(x, y, \"k:\", label=\"Interpolado\")\n",
    "plot(x0, y0, \"ro\", label=\"Pontos\")\n",
    "legend()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Transformação inversa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Complex{Float64},1}:\n",
       " 0.0 + 0.0im\n",
       " 0.0 + 0.0im\n",
       " 0.0 + 0.0im\n",
       " 0.0 + 0.0im"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = rand(4)\n",
    "X = fft(x)\n",
    "x1 = ifft(X)\n",
    "x1 .- x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Float64,1}:\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y = rfft(x)\n",
    "x2 = irfft(Y, 4)\n",
    "x2 .- x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Resample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "myresample (generic function with 1 method)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\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\n",
    "   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Usando `myresample`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "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": [
       "PyObject <matplotlib.legend.Legend object at 0x7fdc9bca8be0>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q = 8; L₀ = 1.0; \n",
    "x0 = range(0, L₀, length=Q+1)[1:Q]; x = 0:0.01:L₀\n",
    "f = x->(2*sin(2π*x) + 1.0 + cos(2π*x))\n",
    "y0 = f.(x0)\n",
    "Qout = 10\n",
    "y1 = myresample(y0, Qout);\n",
    "x1 = range(0, L₀, length=Qout+1)[1:Qout]\n",
    "plot(x, f.(x), label=\"Exato\")\n",
    "plot(x1, y1, \"k:\", label=\"Interpolado\")\n",
    "plot(x0, y0, \"ro\", label=\"Pontos\")\n",
    "legend()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Outros formatos\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Complex{Float64},1}:\n",
       "  2.696840093674516 + 0.0im\n",
       " 0.6096228197517748 + 0.0im\n",
       " 2.0509948408906125 + 0.0im\n",
       "  2.618050977379867 + 0.0im"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = rand(4)\n",
    "X1 = fft(x)\n",
    "X2 = copy(X)\n",
    "fft!(X2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O mesmo para `ifft`, `rfft`, etc!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Lembra que a DFT era uma multiplicação de matrizes?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Complex{Float64},1}:\n",
       "  2.2606423628078156 + 0.0im\n",
       " -0.8363595278420679 - 0.1408644287536589im\n",
       "  -0.577655517107104 + 0.0im\n",
       " -0.8363595278420679 + 0.1408644287536589im"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = rand(4)\n",
    "P = plan_fft(x, flags=FFTW.ESTIMATE)\n",
    "\n",
    "X1 = P * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Complex{Float64},1}:\n",
       "  2.2606423628078156 + 0.0im\n",
       " -0.8363595278420679 - 0.1408644287536589im\n",
       "  -0.577655517107104 + 0.0im\n",
       " -0.8363595278420679 + 0.1408644287536589im"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fft(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Transformada inversa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Complex{Float64},1}:\n",
       " 0.002566947504143935 + 0.0im\n",
       "   0.7800066843555593 + 0.0im\n",
       "   0.8389264753462118 + 0.0im\n",
       "   0.6391422556019004 + 0.0im"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P \\ X1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Complex{Float64},1}:\n",
       " 0.002566947504143935 + 0.0im\n",
       "   0.7800066843555593 + 0.0im\n",
       "   0.8389264753462118 + 0.0im\n",
       "   0.6391422556019004 + 0.0im"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ifft(X1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Outros tipos de transformadas\n",
    "\n",
    " * Cosseno: `dct`, `idct`\n",
    " * Mais genérica: `r2r` (ver <www.fftw.org>)\n",
    " * Tudo o que foi feito até aqui, vale para problemas multidimensionais!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Conclusões\n",
    "\n",
    "Algumas questões\n",
    " \n",
    " * Será que esta série converge para a função original?\n",
    " * Em que condições esta série converge?\n",
    " * Quão rápido se dá esta convergência?\n",
    " * O que acontece quando $N\\longrightarrow\\infty$?\n",
    " \n",
    "Respostas genéricas\n",
    " * A série converge para condições bem amplas, inclusive se houver discontinuidades na função.\n",
    " * Esta convergência se dá para $N\\longrightarrow\\infty$. Para valor de $N$ finito, as coisas são mais complicadas (como veremos adiante).\n",
    " * Para funções periódicas e suaves, não existe aproximação melhor!!!"
   ]
  },
  {
   "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": [
    "## Problema 2\n",
    "\n",
    "Verifique a ortogonalidade discreta da base trigonométrica, ou seja, \n",
    "\n",
    "$$\n",
    "\\sum_{i=0}^Q \\phi_n(x_i)\\cdot \\phi_k(x_i)=0 \\qquad k\\ne n, k+n \\text{ e } k-n \\text{ não são múltiplos de}\\: Q/2\n",
    "$$\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": "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": null,
   "metadata": {},
   "outputs": [],
   "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, real.(Y), \"xb\")\n",
    "#plot(f, imag.(Y), \"ro\")"
   ]
  },
  {
   "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"
   ]
  },
  {
   "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": [
    "## Problema 6\n",
    "\n",
    "A transformada de Fourier está diretamente relacionada com a série de Fourier e é dada por:\n",
    "\n",
    "$$\n",
    "X(\\omega) = \\frac{1}{2\\pi} \\int_{-\\infty}^\\infty x(t)e^{-i\\omega t}\\: dt\n",
    "$$\n",
    "\n",
    " 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",
    " 2. Discretize a função e use a FFT para calcular a transformada.\n",
    " 3. Tente verificar o que acontece se você adiciona zeros à esquerda e à direita da função discretizada.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problema 7\n",
    "\n",
    "Faça alguns exemplos do pacote `ApproxFun` (<https://github.com/JuliaApproximation/ApproxFun.jl>)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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