SerieFourierDiscreto.ipynb

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   "id": "73eec230-c37c-4358-b303-90ec27411820",
   "metadata": {},
   "source": [
    "# Séries de Fourier de tempo discreto\n",
    "\n",
    "Renato Naville Watanabe"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3917775c-8bc3-4ce7-b6be-602cc006bdfc",
   "metadata": {},
   "source": [
    "## Preparação do ambiente\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "155bbc8a-3cdb-4678-9b73-113c9b5abda1",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "try:\n",
    "  from google.colab import output\n",
    "  output.enable_custom_widget_manager()\n",
    "  IN_COLAB = True\n",
    "except:\n",
    "  IN_COLAB = False\n",
    "\n",
    "if IN_COLAB: \n",
    "  !pip install ipympl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "8eccf5eb-0939-4900-bc7e-25f8b7fd9294",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sympy.plotting import PlotGrid\n",
    "%matplotlib widget"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca35c7f8-c949-403b-b775-a3822e26f21e",
   "metadata": {},
   "source": [
    "## Motivação\n",
    "\n",
    "Como visto anteriormente os sinais do tipo:\n",
    "\n",
    "$x[n] = e^{j\\omega n}$\n",
    "\n",
    "são autofunções de sistemas lineares e invariantes no tempo. Ou seja, a saída de um sistema linear e invariante no tempo para essa entrada é:\n",
    "\n",
    "$y[n] = H(e^{j\\omega})e^{j\\omega n}$\n",
    "\n",
    "em que $H(e^{j\\omega})$ é o valor da resposta em frequência do sistema para a frequência angular $\\omega$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c0b1344-d23b-485f-a0c1-8f6650b700f0",
   "metadata": {},
   "source": [
    "Isso faz com que seja interessante descrever um sinal qualquer como uma combinação linear de exponenciais complexas. \n",
    "\n",
    "Um tipo de sinal que já vimos ser uma combinação linear de exponenciais complexas é o cosseno:\n",
    "\n",
    "$\\cos(\\omega n) = \\frac{e^{j\\omega n}+ e^{-j\\omega n}}{2}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "315800f8-4dde-4dad-a97c-b792e694d6ee",
   "metadata": {},
   "source": [
    "Em 1807, Joseph Fourier apresentou um método para representar qualquer sinal periódico como uma combinação linear de exponenciais complexas harmonicamente relacionadas."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2d833ee-1f1a-49b5-9e98-1c5778426fee",
   "metadata": {},
   "source": [
    "## Exponenciais complexas harmonicamente relacionadas\n",
    "\n",
    "Exponenciais harmonicamente relacionadas $\\phi_k(t)$ são exponenciais complexas que têm um período $T$ em comum (o termo \"harmônico\" tem o mesmo significado do empregado em música). Ou seja, são sinais com frequências que são múltiplas da menor frequência encontrada entre os sinais.\n",
    "\n",
    "$\\phi_k[n]= A_ke^{jk\\omega_0 n}, k = 0,\\pm 1,\\pm 2 ... T_0$\n",
    "\n",
    "em que $T_0$ é o período fundamental do sinal. Diferentemente de sinais de tempo contínuo, existe um número finito exponenciais harmonicamente relacionadas quando o tempo é discreto.\n",
    "\n",
    "Para $k = 0$ o sinal é uma constante e para os outros valores de $k$ a frequência angular do sinal  é $|k|\\omega_0$. O período fundamental de um sinal que seja a soma dessas exponenciais harmônicas é:\n",
    "\n",
    "$T_0 = \\frac{2\\pi}{\\omega_0}$\n",
    "\n",
    "Note que o sinal discreto será periódico somente se existir um valor de $T_0$ inteiro. Para isso, $\\omega_0$ tem que ser múltiplo de $\\pi$.\n",
    "\n",
    "Os componentes para $k = N$ e $k = -N$ são chamados de N-ésima harmônica. Os componentes para $k=1$ e $k=-1$ são as harmônicas fundamentais.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d3dd219-e4f3-4f31-8cb2-19fd54b544de",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### Exemplo 1\n",
    "\n",
    "O sinal:\n",
    "\n",
    "$x[n] = e^{j0t} + e^{j\\frac{\\pi}{12}n} + e^{-j\\frac{\\pi}{12}n} + 2e^{j\\frac{\\pi}{4}n} + 2e^{-j\\frac{\\pi}{4}n} = 1 + 2\\cos\\left(\\frac{\\pi}{12}n\\right) + 4\\cos\\left(\\frac{\\pi}{4}n\\right)$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "63438710-aa0c-438f-830d-ff30ad0f27ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<StemContainer object of 3 artists>"
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     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = np.arange(-20,20)\n",
    "x = 1 + 2*np.cos(np.pi/12*n) + 4*np.cos(np.pi/4*n)\n",
    "plt.stem(n, x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81125c45-206f-404f-9c05-2573ed269f99",
   "metadata": {},
   "source": [
    "A frequência fundamental é $\\omega_0=\\frac{\\pi}{12}$. Com isso o período fundamental é $T_0=24$. De fato, pelo gráfico, o sinal se repete a cada $24$ amostras.\n",
    "\n",
    "---\n",
    "\n",
    "Repare também que os coeficientes que multiplicam as exponenciais complexas são números reais. Isso não é obrigatório. Os coeficientes podem ser números complexos também. Porém, para que seja possível reconstruir um cosseno, é necessário que os coeficientes que multiplicam as exponenciais conjugadas uma da outra sejam também complexos conjugados.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2efeae00-8b35-4733-86e4-745976346b0d",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### Exemplo 2\n",
    "\n",
    "Considere agora o seguinte sinal:\n",
    "\n",
    "$x[n] = e^{j0t} + e^{-j\\frac{\\pi}{3}}e^{j\\frac{\\pi}{12}n} +e^{j\\frac{\\pi}{3}}e^{-j\\frac{\\pi}{12}n}+2e^{-j\\frac{\\pi}{2}}e^{-j\\frac{\\pi}{4}n}+2e^{j\\frac{\\pi}{2}}e^{j\\frac{\\pi}{4}n}= 1 + 2\\cos\\left(\\frac{\\pi}{12}n-\\frac{\\pi}{3}\\right) + 4\\cos\\left(\\frac{\\pi}{4}n-\\frac{\\pi}{2}\\right)$\n",
    "\n",
    "Como é possível observar, quando os coeficientes de cada exponencial complexa são complexos, a fase do cosseno resultante se altera.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0b8fe07a-3aa4-46e8-a590-4b158a657717",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "412328dcacfc4c74a4657e36f8352632",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure 1\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = np.arange(-20,20)\n",
    "x = 1 + 2*np.cos(np.pi/12*n-np.pi/3) + 4*np.cos(np.pi/4*n-np.pi/2)\n",
    "plt.stem(n, x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f865e906-538d-4097-9b3c-8622c60ee062",
   "metadata": {},
   "source": [
    "Isso faz com que o sinal resultante da combinação linear das mesmas exponenenciais complexas seja diferente da do exemplo 1."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e567ee7-e213-4321-ae6d-2b47dee57afa",
   "metadata": {},
   "source": [
    "## Representação gráfica da magnitude e fase dos coeficientes "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "627f1e62-f33d-4654-b689-4c2436770f4e",
   "metadata": {},
   "source": [
    "Uma maneira muito comum de representar os coeficientes é de maneira gráfica, com o valor da harmônica na abscissa e o módulo do coeficiente em um gráfico e a fase do coeficiente em outro gráfico.\n",
    "\n",
    "---\n",
    "\n",
    "### Exemplo 3\n",
    "\n",
    "Vamos representar os coeficientes do exemplo 2 de forma gráfica. A harmônica fundamental é $\\omega = \\frac{\\pi}{12}$. Então seus coeficientes estarão em $k=\\pm 1$. A constante é $k=0$ e o cosseno de frequência angula $\\frac{\\pi}{4}$  é $k=\\pm 3$. Como a harmônica fundamental é $\\omega = \\frac{\\pi}{12}$, então o período fundamental é 24 amostras. Isso se reflete na decomposição do sinal em exponenciais harmônicas. Diferentemente da representação de sinais contínuos, existe um número finito de exponenciais complexas (nesse caso, 24). Isso faz com que após 24 exponenciais, as exponenciais começas a se repetir.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "7ee7283f-569d-4ee2-a305-8431411dd46d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6a91b835cdbb4082a50fbc2fe24394f8",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = np.arange(-30,31,1)\n",
    "cmod = np.zeros(len(k))\n",
    "cfase = np.zeros(len(k))\n",
    "\n",
    "cmod[6::24] = 1\n",
    "cfase[6::24] = 0\n",
    "\n",
    "cmod[7::24] = 1\n",
    "cfase[7::24] = -np.pi/3\n",
    "\n",
    "cmod[5::24] = 1\n",
    "cfase[5::24] = np.pi/3\n",
    "\n",
    "cmod[9::24] = 2\n",
    "cfase[9::24] = np.pi/2\n",
    "\n",
    "cmod[3::24] = 2\n",
    "cfase[3::24] = -np.pi/2\n",
    "\n",
    "\n",
    "plt.figure()\n",
    "plt.subplot(2,1,1)\n",
    "plt.stem(k, cmod)\n",
    "plt.xlabel('k')\n",
    "plt.title('|c|')\n",
    "plt.subplot(2,1,2)\n",
    "plt.stem(k, cfase)\n",
    "plt.xlabel('k')\n",
    "plt.title(r'$\\angle c$')\n",
    "plt.subplots_adjust(left=0.1,\n",
    "                    bottom=0.1,\n",
    "                    right=0.9,\n",
    "                    top=0.9,\n",
    "                    wspace=1,\n",
    "                    hspace=0.4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d05c7590-99e2-4c50-bd32-08eb225d360c",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "Repare que o gráfico do módulo dos coeficientes é uma função par e o gráfico da fase dos coeficientes é uma função ímpar. Isso sempre vai acontecer com sinais reais. Repare também que os coeficientes se repetem a cada 24 (o período do sinal) expoenciais harmônicas. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c88d95e-73ee-42db-b5fd-2a39ec0d1b9c",
   "metadata": {},
   "source": [
    "## Determinação dos coeficientes multiplicando cada harmônica\n",
    "\n",
    "Supondo que um sinal periódico qualquer possa ser decomposto em uma soma de exponenciais complexas, quais são os coeficientes que multiplicam cada exponencial complexa. É isso que o método desenvolvido por Joseph Fourier respondeu e hoje é conhecido como **série de Fourier**."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fddbead3-56c8-4745-9273-e346eb2453bf",
   "metadata": {},
   "source": [
    "Vamos supor que um sinal periódico $x[n]$ possa ser decomposto em soma de exponenciais complexas. Nesse caso, $x[n]$ pode escrito como:\n",
    "\n",
    "$\\boxed{x[n] = \\displaystyle\\sum_{k=<T_0>} c_ke^{jk\\frac{2\\pi}{T_0} n}}$\n",
    "\n",
    "A indicação do somatório $k=<T_0>$ indica que o valor de $k$ varia dentro de um período do sinal. Por exemplo, um sinal com período 4 , poderíamos pegar os valores de $c_k$ em $k=1, 2,3 $ e 4.\n",
    "\n",
    "A somatória é feita em apenas $T_0$ (período fundamental do sinal) frequências. Em tempo discreto existem apenas $T_0$ diferentes exponenciais harmonicamente relacionadas. A expressão acima é conhecida como **síntese** do sinal $x[n]$.\n",
    "\n",
    "O objetivo aqui é encontrar o valor de $c_k$, para todo $k$. Para isso, vamos multiplicar ambos os lados por $e^{-jw\\frac{2\\pi}{T_0} n}$:\n",
    "\n",
    "$x[n]e^{-jw\\frac{2\\pi}{T_0} n} = \\displaystyle\\sum_{k=<T_0>} c_ke^{jk2\\frac{\\pi}{T_0}n}e^{-jw\\frac{2\\pi}{T_0} n} \\rightarrow x[n]e^{-jw\\frac{2\\pi}{T_0} n} = \\displaystyle\\sum_{k=<T_0>} c_ke^{j(k-w)2\\frac{\\pi}{T_0}n}$\n",
    "\n",
    "Como $x[n]$ é periódico, com um período $T_0$, vamos somar ambos os lados da igualdade por um período $T_0$ do sinal:\n",
    "\n",
    "$\\displaystyle\\sum_{n=<T_0>}^{n_0+T_0-1} x[n]e^{-jw\\frac{2\\pi}{T_0} n} = \\displaystyle\\sum_{n=<T_0>}\\displaystyle\\sum_{k=<T_0>} c_ke^{j(k-w)2\\frac{\\pi}{T_0}n}$\n",
    "\n",
    "Como as variáveis das somatórias são  diferentes uma da outra, podemos mudar a ordem em que as somatória  aparecem:\n",
    "\n",
    "$\\displaystyle\\sum_{n=<T_0>} x[n]e^{-jw\\frac{2\\pi}{T_0} n} = \\displaystyle\\sum_{k=<T_0>} \\displaystyle\\sum_{n=<T_0>}c_ke^{j(k-w)2\\frac{\\pi}{T_0}n}$\n",
    "\n",
    "\n",
    "A segunda somatória do lado direito pode ser analisada em duas situações diferentes. A primeira, quando $k\\neq w$, utilizando a expressão de somatória de uma progressão geométrica com $T_0$ termos:\n",
    "\n",
    " $\\displaystyle\\sum_{n=n_0}^{n_0+T_0-1}c_ke^{j(k-w)2\\frac{\\pi}{T_0}n} = c_k\\displaystyle\\sum_{n=n_0}^{n_0+T_0-1}\\left(e^{j(k-w)2\\frac{\\pi}{T_0}}\\right)^n = c_k\\left(\\frac{1-(e^{j(k-w)2\\frac{\\pi}{T_0}})^{T_0}}{1-e^{j(k-w)2\\frac{\\pi}{T_0}}}\\right) = c_k\\left(\\frac{1-e^{j(k-w)2\\frac{\\pi}{T_0}T_0}}{1-e^{j(k-w)2\\frac{\\pi}{T_0}}}\\right) = c_k\\left(\\frac{1-e^{j(k-w)2\\pi}}{1-e^{j(k-w)2\\frac{\\pi}{T_0}}} \\right) = c_k\\left(\\frac{1-1}{1-e^{j(k-w)2\\frac{\\pi}{T_0}}} \\right) = 0$\n",
    "\n",
    "A segunda situação, quando $w = k$:\n",
    "\n",
    "$\\displaystyle\\sum_{n=<T_0>}c_ke^{j(0)2\\frac{\\pi}{T_0}n} = c_kT_0$\n",
    "\n",
    "Então, a segunda somatória do lado direito da igualdade só vai ser diferente de zero quando $k=w$. Então:\n",
    "\n",
    "$\\displaystyle\\sum_{n=<T_0>} x[n]e^{-jw\\frac{2\\pi}{T_0} n} = c_wT_0$\n",
    "\n",
    "Com isso, o coeficiente $c_n$ pode ser obtido por:\n",
    "\n",
    "$\\boxed{c_w = \\frac{1}{T_0}\\displaystyle\\sum_{n=<T_0>} x[n]e^{-jw\\frac{2\\pi}{T_0} n}}$\n",
    "\n",
    "Essa expressão é conhecida como **análise** do sinal $x[n]$.\n",
    "\n",
    "Perceba que o coeficiente $c_0$ corresponde à média do sinal $x[n]$. \n",
    "\n",
    "$c_0 = \\frac{1}{T_0}\\displaystyle\\sum_{n=<T_0>} x[n]$\n",
    "\n",
    "O valor de $c_0$ é comumente chamado de **valor DC** (direct current) ou **offset** do sinal.\n",
    "\n",
    "A série de Fourier é representada pelo operador $\\mathcal{SF}$:\n",
    "\n",
    "$\\mathcal{SF}(x[n]) = c_w$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ba662e5-941c-4976-993a-169028d1a7d1",
   "metadata": {},
   "source": [
    "### Exemplo 3\n",
    "\n",
    "Vamos calcular os coeficientes da série de Fourier da onda quadrada com período $T_0=10$  mostrada no gráfico abaixo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "17654d71-b6bf-4408-aab8-b6799bd0551b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
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       "model_id": "4dea5ec28e4944f3a5936281c78dc294",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = np.arange(-20,21)\n",
    "x = np.zeros(len(n))\n",
    "x[0:5] = 1\n",
    "x[10:15] = 1\n",
    "x[20:25] = 1\n",
    "x[30:35] = 1\n",
    "x[-1] = 1\n",
    "plt.figure()\n",
    "plt.stem(n,x)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89dbc0e0-1b52-4bca-a608-c94e6af50439",
   "metadata": {},
   "source": [
    "O período fundamental é $T_0=10$ instantes. Então, os coeficientes $c_n$ da série de Fourier são:\n",
    "\n",
    "$c_w = \\frac{1}{10}\\displaystyle\\sum_{n=-5}^{4}x[n]e^{-jw\\frac{2\\pi}{10}n} =  \\frac{1}{10}\\displaystyle\\sum_{n=0}^{4}e^{-jw\\frac{2\\pi}{10}n} = \\frac{1}{10}\\left(\\frac{1-e^{-jw\\frac{2\\pi}{10}5}}{1-e^{-jw\\frac{2\\pi}{10}}}\\right) = \\left(\\frac{1-e^{-jw\\pi}}{1-e^{-jw\\frac{\\pi}{5}}}\\right)=\\frac{1}{10}\\left(\\frac{e^{j\\frac{w\\pi}{2}}-e^{-j\\frac{w\\pi}{2}}}{e^{j\\frac{w\\pi}{10}}-e^{-jw\\frac{\\pi}{10}}}\\right)\\frac{e^{j\\frac{-w\\pi}{2}}}{e^{j\\frac{-w\\pi}{10}}}= \\frac{1}{10}\\left(\\frac{\\mathrm{sen}(\\frac{w\\pi}{2})}{\\mathrm{sen}(\\frac{w\\pi}{10})}\\right)e^{j\\frac{-2w\\pi}{5}}$\n",
    "\n",
    "\n",
    "Para $w=0, \\pm 10, \\pm 20, ...$ a expressão acima não é válida, para esses valores de $w$, $c_w$ é definido como:\n",
    "\n",
    "$c_w = 0.5$, para $w=0, \\pm 10, \\pm 20, ...$\n",
    "\n",
    "\n",
    "O gráfico do módulo e fase dos coeficientes da série quadrada é:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1df790d9-3bd6-4b9a-9683-98ea402b451e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_79945/2443482382.py:2: RuntimeWarning: invalid value encountered in divide\n",
      "  c = np.sin(w*np.pi/2)/np.sin(w*np.pi/10)*np.exp(-1j*2*w*np.pi/5)/10\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d5e0147678424e9d901557f9485224e8",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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4o1h5MVt4cVaw4nK24PK9aM/iEAIiAlwR3S9SLBijWHkxW3hxVrDicrbg8r1hxOVtweVqwZ/UMAREB2RpLSPG51d7K/S2fOBsvOSOrX9/H5DVUePK7X9hxR5cHj/XpPSaRqtgpmaH2R2B6hnJ/EDL+JGcIKuAwMAmJjXCouyNSiLdVySUFvBu74T6G4ILNf14MK9SUGIlGzlTBD6wv39gjHZT6YYTBmCCvgCCCC5Gelaf2cyUpJjA9anupxa/2cyf26DlS4LjEQzpqtiBlaX7i2Rzgv88EMgzFDRDuOAKKT/Kw0XXNxsi5b/qYkafP8KzX1kmH9+svv2y4x4NKZSwz8IDO1T98nHDVbGTO0vlBvj3DPLxw1Wx0zRDTjCCC6dPbOHoqPAYrEJQZCXbPVMUPrC+X2iNRlPphhMGaIaEUARERwiQHrY4bWxvysjxkilAiAiAguMWB9zNDamJ/1MUOEEgEQEcElBqyPGVob87M+ZohQIgAiIjouMSCp039eXGLAGpihtTE/62OGCCUCICKGSwxYHzO0NuZnfcwQocJlYBBRXGLA+pihtTE/62OGCAWOACLiuMSA9TFDa2N+1scM0V8EQAAAAIchAAIAADgMARAAAMBhCIAAAAAOQwAEAABwGAIgAACAwxAAAQAAHIYACAAA4DAEQAAAAIchAAIAADgMARAAAMBhCIAAAAAOQwAEAABwGAIgAACAwxAAAQAAHOY8swsIpXXr1mnVqlWqr6/XxIkTtXbtWmVnZ3e7/ssvv6xHH31Uhw4d0iWXXKLf/OY3+pd/+ZcIVhxZPr+hqtomNba0KiXBreyMJMXGuKL6ua1YczixncP/vOFmxe1hxZrDhe0cuedGeNkmAG7btk1FRUXasGGDcnJy9PTTTysvL0/79+9XSkpKp/Xfffdd3XrrrSotLdW//uu/auvWrZo1a5aqq6uVlZVlQgfhVVZTp5Lte1XnbQ0sS/O4VVyQqfystKh8bivWHE5s58jUHE5W3B5WrDlc2M6Re26En21eAn7qqae0cOFCzZ8/X5mZmdqwYYMGDRqkjRs3drn+M888o/z8fN1///269NJL9fjjj2vy5Mn6t3/7twhXHn5lNXVatKU6aCeVpHpvqxZtqVZZTV3UPbcVaw4ntnNkag4nK24PK9YcLmznyD03IsMWRwDb29u1e/duLV26NLAsJiZGM2bMUGVlZZdfU1lZqaKioqBleXl5evXVV8NZao8YhqH4L9skSf4vvpD/y+7H5G//8pzr+vyGSv/zA8V9tc43uSSV/ucHun5MYtBh+2973nA+txVrPltv1u3J+tG2ne1aczjXjbbtYdeazxbKGbKvRH6GZ69rGEa366HvXIYNtuzRo0c1cuRIvfvuu8rNzQ0sf+CBB7Rz507t2rWr09fExcXphRde0K233hpY9uyzz6qkpEQNDQ1dfp+2tja1tX39A9/c3Kz09HR5vV4lJiaGrJ+TJ5r16VU5IXs+AACsKv29XRo8JHS/Y6Uzv789Hk/If39biW1eAo6E0tJSeTyewC09PT0s32dQnC0OzAIA0G/8TgwPW2zV5ORkxcbGdjpy19DQoNTU1C6/JjU1tVfrS9LSpUuDXjbuOAIYaq6BAzWuendInmtXbZPmbar61vU2z89WTkZSVDy3FWsOJ7Zz+J833Ky4PaxYc7iwnSP33F1xDRzY7+dAZ7YIgHFxcZoyZYrKy8s1a9YsSZLf71d5ebkWL17c5dfk5uaqvLxc99xzT2DZjh07gl5C/qb4+HjFx8eHsvQuuVwuuQYNCslzZV86UEkXeFTvbVVXr/W7JKV63Mq+dKRiennqfrie24o1hxPbOTI1h5MVt4cVaw4XtnPknhuRY5uXgIuKivT888/rhRde0Mcff6xFixbp1KlTmj9/viTp9ttvDzpJ5P/9v/+nsrIy/fa3v9W+ffu0fPly/e1vf+s2MFpVbIxLxQWZks7slGfruF9ckNmn6zaF67mtWHM4sZ3D/7zhZsXtYcWaw4XtHLnnRuTYJgDOnj1bq1ev1rJlyzRp0iTt2bNHZWVlGj58uCTp8OHDqqv7+rT0q6++Wlu3btXvf/97TZw4UX/605/06quv2vIagPlZaVo/Z7JSPe6g5aket9bPmdyv6zWF67mtWHM4sZ0jU3M4WXF7WLHmcGE7R+65ERm2OAvYLF6vV0OGDNGnn35qibOIfH5Duw99rmMnWzVssFtTxgwN6dXgw/HcVqw5nNjO4X/ecLPi9rBizeHCdo7cc4dTx3v4T5w4IY/HY3Y5prDFewDN0tLSIklhOxsYAACET0tLi2MDIEcA+8Hv9+vo0aNKSEiQyxXav3g6/jqxytHF3qI/67N7j/RnfXbvkf76zjAMtbS0aMSIEYqJsc274XqFI4D9EBMTo1GjRoX1eyQmJtpyx+5Af9Zn9x7pz/rs3iP99Y1Tj/x1cGbsBQAAcDACIAAAgMMQAKNUfHy8iouLI3LhaTPQn/XZvUf6sz6790h/6A9OAgEAAHAYjgACAAA4DAEQAADAYQiAAAAADkMABAAAcBgCYBQ5dOiQFixYoIyMDA0cOFAXXXSRiouL1d7eHrTe3//+d02dOlVut1vp6elauXKlSRX3zRNPPKGrr75agwYN0pAhQ7pcx+Vydbq99NJLkS20j3rS3+HDh3XjjTdq0KBBSklJ0f33368vv/wysoWG0JgxYzrNa8WKFWaX1Wfr1q3TmDFj5Ha7lZOTo6qqKrNLCpnly5d3mtX48ePNLqvP3n77bRUUFGjEiBFyuVx69dVXgx43DEPLli1TWlqaBg4cqBkzZuiTTz4xp9g++rYe582b12mm+fn55hTbB6WlpbryyiuVkJCglJQUzZo1S/v37w9ap7W1VYWFhbrgggs0ePBg3XzzzWpoaDCpYnsgAEaRffv2ye/367nnntNHH32kNWvWaMOGDXr44YcD6zQ3N2vmzJkaPXq0du/erVWrVmn58uX6/e9/b2LlvdPe3q5bbrlFixYtOud6mzZtUl1dXeA2a9asyBTYT9/Wn8/n04033qj29na9++67euGFF7R582YtW7YswpWG1mOPPRY0r7vuusvskvpk27ZtKioqUnFxsaqrqzVx4kTl5eWpsbHR7NJC5rvf/W7QrN555x2zS+qzU6dOaeLEiVq3bl2Xj69cuVK/+93vtGHDBu3atUvnn3++8vLy1NraGuFK++7bepSk/Pz8oJm++OKLEaywf3bu3KnCwkK999572rFjh06fPq2ZM2fq1KlTgXWWLFmi7du36+WXX9bOnTt19OhR3XTTTSZWbQMGotrKlSuNjIyMwP1nn33WGDp0qNHW1hZY9uCDDxrjxo0zo7x+2bRpk+HxeLp8TJLxyiuvRLSeUOuuvzfeeMOIiYkx6uvrA8vWr19vJCYmBs3VSkaPHm2sWbPG7DJCIjs72ygsLAzc9/l8xogRI4zS0lITqwqd4uJiY+LEiWaXERbf/H/D7/cbqampxqpVqwLLTpw4YcTHxxsvvviiCRX2X1f/N86dO9f40Y9+ZEo94dDY2GhIMnbu3GkYxpmZDRgwwHj55ZcD63z88ceGJKOystKsMi2PI4BRzuv1KikpKXC/srJS1157reLi4gLL8vLytH//fn3++edmlBg2hYWFSk5OVnZ2tjZu3CjDJpesrKys1GWXXabhw4cHluXl5am5uVkfffSRiZX1z4oVK3TBBRfo8ssv16pVqyz5knZ7e7t2796tGTNmBJbFxMRoxowZqqysNLGy0Prkk080YsQIjR07Vj//+c91+PBhs0sKi9raWtXX1wfN0+PxKCcnx1bzlKSKigqlpKRo3LhxWrRokY4fP252SX3m9XolKfC7b/fu3Tp9+nTQHMePH68LL7zQdnOMpPPMLgDdO3DggNauXavVq1cHltXX1ysjIyNovY4gUV9fr6FDh0a0xnB57LHH9P3vf1+DBg3Sm2++qTvvvFMnT57U3XffbXZp/VZfXx8U/qTgGVrR3XffrcmTJyspKUnvvvuuli5dqrq6Oj311FNml9Yrn332mXw+X5fz2bdvn0lVhVZOTo42b96scePGqa6uTiUlJZo6dapqamqUkJBgdnkh1bE/dTVPq+5rXcnPz9dNN92kjIwMHTx4UA8//LBuuOEGVVZWKjY21uzyesXv9+uee+7RNddco6ysLEln5hgXF9fpPdV2m2OkcQQwAh566KEuT2o4+/bNXy5HjhxRfn6+brnlFi1cuNCkynuuLz2ey6OPPqprrrlGl19+uR588EE98MADWrVqVRg7OLdQ92cFvem5qKhI06ZN04QJE/TLX/5Sv/3tb7V27Vq1tbWZ3AW+6YYbbtAtt9yiCRMmKC8vT2+88YZOnDihP/7xj2aXhj766U9/qh/+8Ie67LLLNGvWLL3++ut6//33VVFRYXZpvVZYWKiamhrLnPRnZRwBjIB7771X8+bNO+c6Y8eODfz76NGjmj59uq6++upOJ3ekpqZ2OvOp435qampoCu6D3vbYWzk5OXr88cfV1tZmyudChrK/1NTUTmeVRsMMv6k/Pefk5OjLL7/UoUOHNG7cuDBUFx7JycmKjY3tch+LptmE0pAhQ/Sd73xHBw4cMLuUkOuYWUNDg9LS0gLLGxoaNGnSJJOqCr+xY8cqOTlZBw4c0PXXX292OT22ePFivf7663r77bc1atSowPLU1FS1t7frxIkTQUcB7bxfRgIBMAKGDRumYcOG9WjdI0eOaPr06ZoyZYo2bdqkmJjgg7S5ubl65JFHdPr0aQ0YMECStGPHDo0bN87Ul39702Nf7NmzR0OHDjXtQ8FD2V9ubq6eeOIJNTY2KiUlRdKZGSYmJiozMzMk3yMU+tPznj17FBMTE+jPKuLi4jRlyhSVl5cHzjr3+/0qLy/X4sWLzS0uTE6ePKmDBw/qtttuM7uUkMvIyFBqaqrKy8sDga+5uVm7du361qsQWNn//d//6fjx40GhN5oZhqG77rpLr7zyiioqKjq9zWnKlCkaMGCAysvLdfPNN0uS9u/fr8OHDys3N9eMkm2BABhFjhw5omnTpmn06NFavXq1jh07Fnis46+cn/3sZyopKdGCBQv04IMPqqamRs8884zWrFljVtm9dvjwYTU1Nenw4cPy+Xzas2ePJOniiy/W4MGDtX37djU0NOiqq66S2+3Wjh079OSTT+q+++4zt/Ae+rb+Zs6cqczMTN12221auXKl6uvr9atf/UqFhYWmBdz+qKys1K5duzR9+nQlJCSosrJSS5Ys0Zw5cyz5ntSioiLNnTtXV1xxhbKzs/X000/r1KlTmj9/vtmlhcR9992ngoICjR49WkePHlVxcbFiY2N16623ml1an5w8eTLo6GVtba327NmjpKQkXXjhhbrnnnv061//WpdccokyMjL06KOPasSIEZa5rJR07h6TkpJUUlKim2++WampqTp48KAeeOABXXzxxcrLyzOx6p4rLCzU1q1b9dprrykhISHwvj6Px6OBAwfK4/FowYIFKioqUlJSkhITE3XXXXcpNzdXV111lcnVW5jZpyHja5s2bTIkdXk724cffmh873vfM+Lj442RI0caK1asMKnivpk7d26XPb711luGYRjGn//8Z2PSpEnG4MGDjfPPP9+YOHGisWHDBsPn85lbeA99W3+GYRiHDh0ybrjhBmPgwIFGcnKyce+99xqnT582r+h+2L17t5GTk2N4PB7D7XYbl156qfHkk08ara2tZpfWZ2vXrjUuvPBCIy4uzsjOzjbee+89s0sKmdmzZxtpaWlGXFycMXLkSGP27NnGgQMHzC6rz956660u97e5c+cahnHmUjCPPvqoMXz4cCM+Pt64/vrrjf3795tbdC+dq8cvvvjCmDlzpjFs2DBjwIABxujRo42FCxcGXWYq2nX3e2/Tpk2Bdf75z38ad955pzF06FBj0KBBxo9//GOjrq7OvKJtwGUYNrm2BgAAAHqEs4ABAAAchgAIAADgMARAAAAAhyEAAgAAOAwBEAAAwGEIgAAAAA5DAAQAAHAYAiAAAIDDEAABAAAchgAIAADgMARAAAAAhyEAAoCk119/XUOGDJHP55Mk7dmzRy6XSw899FBgnTvuuENz5swxq0QACBkCIABImjp1qlpaWvTBBx9Iknbu3Knk5GRVVFQE1tm5c6emTZtmToEAEEIEQACQ5PF4NGnSpEDgq6io0JIlS/TBBx/o5MmTOnLkiA4cOKDrrrvO3EIBIAQIgADwleuuu04VFRUyDEN//etfddNNN+nSSy/VO++8o507d2rEiBG65JJLzC4TAPrtPLMLAIBoMW3aNG3cuFEffvihBgwYoPHjx2vatGmqqKjQ559/ztE/ALbBEUAA+ErH+wDXrFkTCHsdAbCiooL3/wGwDQIgAHxl6NChmjBhgv7whz8Ewt61116r6upq/eMf/+AIIADbIAACwFmuu+46+Xy+QABMSkpSZmamUlNTNW7cOHOLA4AQcRmGYZhdBAAAACKHI4AAAAAOQwAEAABwGAIgAACAwxAAAQAAHIYACAAA4DAEQAAAAIchAAIAADgMARAAAMBhCIAAAAAOQwAEAABwGAIgAACAwxAAAeArbW1teuCBB/TII4/I5/OZXQ4AhA0BEAC+UlpaqlWrVsnj8Sg2NtbscgAgbFyGYRhmFwEAZvvkk0902WWX6Tvf+Y6qq6t13nnnmV0SAIQNRwABQFJhYaHa29v13HPPnTP87d69Wz/5yU+UkpIit9ut8ePH67HHHotgpQDQf/yJC8DxXnzxRe3YsUO/+MUvlJub2+16r7zyin76059q7Nixuv/++zV48GC9//77evfddyNYLQD0Hy8BA3A0r9er8ePHyzAM7du3T0OGDOlyvX/84x+6/PLLlZeXp61bt8rtdgcea2trU3x8fIQqBoD+4wggAEd75JFHVF9fr61bt3Yb/iRp2bJlcrvd2rx5c1D4k0T4A2A5HAEE4Fh/+9vflJOToxkzZui///u/u12vra1NSUlJuuOOO/TMM89EsEIACA9OAgHgSH6/X7/85S8VFxenZ5999pzr/u///q+++OILTZkyJULVAUB4EQABONK6deu0e/du/epXv9JFF110znX/+c9/SpJcLlckSgOAsOMlYACOU1dXp/Hjx2vkyJHas2eP4uLizrl+c3OzPB6Pbr/9dr3wwgtBj50+fVoDBgwIZ7kAEHKcBALAcZYsWaLm5mYNGDBAEyZMOOe677//vhITEzVv3jxt3rxZbW1tmjZtmlpaWvTWW2/pxhtvVGFhYYQqB4DQIAACcJQdO3Zo27ZtkqTjx4/r+PHj51y/4zOB161bp5EjR+qPf/yjXn31VSUlJenqq69Wfn5+2GsGgFDjJWAAAACH4SQQAAAAhyEAAgAAOAwBEAAAwGEIgAAAAA5DAAQAAHAYAiAAAIDDcB3AfvD7/Tp69KgSEhL4iCgAACzCMAy1tLRoxIgRiolx5rEwAmA/HD16VOnp6WaXAQAA+uDTTz/VqFGjzC7DFATAfkhISJB05gcoMTHR5GoAAEBPNDc3Kz09PfB73IkIgP3Q8bJvYmIiAdCCfH5DVbVNamxpVUqCW9kZSYqN4aV8q2B+APrLyW/fIgDCkcpq6lSyfa/qvK2BZWket4oLMpWflWZiZegJ5gcA/ePMdz7C0cpq6rRoS3VQeJCkem+rFm2pVllNnUmVoSeYHwD0HwEQjuLzGyrZvldGF491LCvZvlc+f1drwGzMDwBCgwAIR6mqbep05OhshqQ6b6uqapsiVxR6jPkBQGgQAOEojS3dh4e+rIfIYn4AEBoEQDhKSoI7pOshspgfAIQGARCOkp2RpDSPW92d+O/SmbNJszOSIlkWeoj5AUBoEADhKLExLhUXZEpSpxDRcb+4IJPryUUp5gcAoUEAhOPkZ6Vp/ZzJSkmMD1qe6nFr/ZzJXEcuyjE/AOg/l2EYXC+hj5qbm+XxeOT1evkkEAtqaT2ty5a/KUnaPP9KTb1kGEeOLIT5Aegrfn9zBBAOdnZY4GPErIf5AUDfEQABAAAchgAIAADgMI4OgKWlpbryyiuVkJCglJQUzZo1S/v37ze7LAAAgLBydADcuXOnCgsL9d5772nHjh06ffq0Zs6cqVOnTpldGgAAQNicZ3YBZiorKwu6v3nzZqWkpGj37t269tprTaoKAAAgvBwdAL/J6/VKkpKS+BSBaOHzG6qqbVJjS6tSEtyc7WlBzBAAog8B8Ct+v1/33HOPrrnmGmVlZXW5Tltbm9ra2gL3m5ubI1WeI5XV1Klk+17VeVsDy9I8bhUXZHKxX4tghgAQnRz9HsCzFRYWqqamRi+99FK365SWlsrj8QRu6enpEazQWcpq6rRoS3VQcJCkem+rFm2pVllNnUmVoaeYIQBELwKgpMWLF+v111/XW2+9pVGjRnW73tKlS+X1egO3Tz/9NIJVOofPb6hk+1519RE1HctKtu+Vz8+H2EQrZggA0c3RAdAwDC1evFivvPKK/vKXvygjI+Oc68fHxysxMTHohtCrqm3qdNTobIakOm+rqmqbIlcUeoUZAkB0c/R7AAsLC7V161a99tprSkhIUH19vSTJ4/Fo4MCBJlfnXI0t3QeHvqyHyGOGABDdHH0EcP369fJ6vZo2bZrS0tICt23btpldmqOlJLhDuh4ijxkCQHRz9BFAw+D9R9EoOyNJaR636r2tXb6HzCUp1XPmciKITswQAKKbo48AIjrFxrhUXJAp6UxQOFvH/eKCTK4lF8WYIQBENwIgolJ+VprWz5mslMT4oOWpHrfWz5nMNeQsgBkCQPRy9EvAiG75WWm65uJkXbb8TUnS5vlXauolwzhqZCHMEACiE0cAEdXODgp8hJg1MUMAiD4EQAAAAIchAAIAADgMARAAAMBhCIAAAAAOQwAEAABwGC4Dg5Dw+Q1V1TapsaVVKQlu253tSX/W54Qe7Yz5WR8zjC4EQPRbWU2dSrbvVZ23NbAszeNWcUGmLS72S3/W54Qe7Yz5WR8zjD68BIx+Kaup06It1UE7tSTVe1u1aEu1ymrqTKosNOjP2v1JzujRzpif9THD6EQARJ/5/IZKtu+V0cVjHctKtu+Vz9/VGtGP/qzdn+SMHu2M+VkfM4xeBED0WVVtU6e/6M5mSKrztqqqtilyRYUQ/Vm7P8kZPdoZ87M+Zhi9CIDos8aW7nfqvqwXbeivd+tFIyf0aGfMz/qYYfQiAKLPUhLcIV0v2tBf79aLRk7o0c6Yn/Uxw+hFAESfZWckKc3jVncn8bt05iyv7IykSJYVMvRn7f4kZ/RoZ8zP+phh9CIAos9iY1wqLsiUpE47d8f94oJMy17nif6s3Z/kjB7tjPlZHzOMXgRA9Et+VprWz5mslMT4oOWpHrfWz5ls+es70Z+1+5Oc0aOdMT/rY4bRiQtBo9/ys9J0zcXJumz5m5KkzfOv1NRLhtnmLzr6sz4n9GhnzM/6mGH04QggQuLsndiOH+9Df9bnhB7tjPlZHzOMLgRAAAAAhyEAAgAAOAwBEAAAwGEIgAAAAA7DWcAO4vMbqqptUmNLq1IS3LZ7E67d+5Ps36Pd+3MCZmh9zNAZCIAOUVZTp5Lte4M+lDvN41ZxQaYtrsFk9/4k+/do9/6cgBlaHzN0Dl4CdoCymjot2lIdtENLUr23VYu2VKusps6kykLD7v1J9u/R7v05ATO0PmboLARAm/P5DZVs3yuji8c6lpVs3yufv6s1op/d+5Ps36Pd+3MCZmh9zNB5CIA2V1Xb1OmvubMZkuq8raqqbYpcUSFk9/4k+/do9/6cgBlaHzN0HgKgzTW2dL9D92W9aGP3/iT792j3/pyAGVofM3QeAqDNpSS4Q7petLF7f5L9e7R7f07ADK2PGToPAdDmsjOSlOZxq7sT+F06c4ZXdkZSJMsKGbv3J9m/R7v35wTM0PqYofMQAG0uNsal4oJMSeq0Y3fcLy7ItOw1nuzen2T/Hu3enxMwQ+tjhs5DAHSA/Kw0rZ8zWSmJ8UHLUz1urZ8z2fLXdrJ7f5L9e7R7f07ADK2PGToLF4J2iPysNF1zcbIuW/6mJGnz/Cs19ZJhtvlrzu79Sfbv0e79OQEztD5m6BwcAXSQs3dgO360j937k+zfo937cwJmaH3M0BkIgAAAAA5DAAQAAHAYAiAAAIDDEAABAAAchgAIAADgMFwGJgr5/IaqapvU2NKqlAS37c7Coj/rs3uP9Gd9du+R/tBfjg+A69at06pVq1RfX6+JEydq7dq1ys7ONq2espo6lWzfqzrv1x+4neZxq7gg0xYX4aQ/67N7j/RnfXbvkf4QCo5+CXjbtm0qKipScXGxqqurNXHiROXl5amxsdGUespq6rRoS3XQD70k1XtbtWhLtcpq6kypK1Toz9r9Sfbvkf6s3Z9k/x7pz9r9RRNHHwF86qmntHDhQs2fP1+StGHDBv3Xf/2XNm7cqIceeiiitfj8hkq275UhSYaheF970OMuSaX/+YGuH5PY58Pg/vYvFf9l25l/f/GF/F+Gbvzf9tw+v6HS//xAcV+t803d9debmnvbXyifu6/99Va4ZtiT5422GYZ63pGaoVn4GWWGPWXWDLvrry02TobLJZekku179YPMVEvOL9q4DMMwzC7CDO3t7Ro0aJD+9Kc/adasWYHlc+fO1YkTJ/Taa691+pq2tja1tX39g9nc3Kz09HR5vV4lJib2q57Kg8d16/PvSZLiv2zTq68/0q/nAwDADmb96xNqO+/rzyd+ceFVyr3ogn49Z3NzszweT0h+f1uVY18C/uyzz+Tz+TR8+PCg5cOHD1d9fX2XX1NaWiqPxxO4paenh6yexpbWb18JAACH4/dlaDj6JeDeWrp0qYqKigL3O44AhkJKgjvw77bYOM361ye6XG/z/GzlZCQF7n/R/qWm/Pr/kyTt/tUMDYoLzUhD/by7aps0b1PVt673zf6soj/9McPo0Nf+erude7N+KNflZ/Rr/ZmhmfOO1M9ob4Tyubvrry02Luj+2b8v0XeODYDJycmKjY1VQ0ND0PKGhgalpqZ2+TXx8fGKj4/v8rH+ys5IUprHrXpvqwyXK+hwt3TmvR2pHreyLx2pmLPe+xBz3peBdWMGDVJMiHbsUD9v9qUDlXSB50x/XTzeXX9W0Z/+mGF06Gt/vd3OvVk/lOvyMxqaGZo570j9jPZGKJ+7x/1Z8A/MaOTYl4Dj4uI0ZcoUlZeXB5b5/X6Vl5crNzc34vXExrhUXJAp6cwP+dk67hcXZFr2ja/0Z+3+JPv3SH/W7k+yf4/0Z+3+oo1jA6AkFRUV6fnnn9cLL7ygjz/+WIsWLdKpU6cCZwVHWn5WmtbPmaxUT/Dh7VSPW+vnTLb89Y/oz9r9Sfbvkf6s3Z9k/x7pz9r9RRPHvgQsSbNnz9axY8e0bNky1dfXa9KkSSorK+t0Ykgk5Wel6QeZqba9Ajr9WZ/de6Q/67N7j/SHUHB0AJSkxYsXa/HixWaXESQ2xtXvU9yjGf1Zn917pD/rs3uP9If+cvRLwAAAAE5EAAQAAHAYAiAAAIDDEAABAAAchgAIAADgMARAdMnn//o67FW1TUH3YQ3M0PrsPkO79yfZv0e792dnBEB0UlZTpxlP7Qzcn7fpfX3vN39RWU2diVWhN5ih9dl9hnbvT7J/j3bvz+4IgAhSVlOnRVuq1dDcFrS83tuqRVuq2bEtgBlan91naPf+JPv3aPf+nIAAiACf31DJ9r1dfgh3x7KS7Xs5xB/FmKH12X2Gdu9Psn+Pdu/PKQiACKiqbVKdt7Xbxw1Jdd5WVdU2Ra4o9AoztD67z9Du/Un279Hu/TkFARABjS3d79B9WQ+Rxwytz+4ztHt/kv17tHt/TkEAREBKgjuk6yHymKH12X2Gdu9Psn+Pdu/PKQiACMjOSFKaxy1XN4+7JKV53MrOSIpkWegFZmh9dp+h3fuT7N+j3ftzCgIgAmJjXCouyJSkTjt2x/3igkzFxnS328NszND67D5Du/cn2b9Hu/fnFARABMnPStP6OZOV6gk+dJ/qcWv9nMnKz0ozqTL0FDO0PrvP0O79Sfbv0e79OcF5ZheA6JOflaYfZKaqqrZJjS2tSkk4cyifv+asgxlan91naPf+JPv3aPf+7I4AiC7FxriUe9EFZpeBfmCG1mf3Gdq9P8n+Pdq9PzvjJWAAAACHIQACAAA4DAEQAADAYQiAAAAADkMABAAAcBgCoMX5/Ebg31W1TUH3YQ3M0NqcMD+790h/cCICoIWV1dRpxlM7A/fnbXpf3/vNX1RWU2diVegNZmhtTpif3XukPzgVAdCiymrqtGhLtRqa24KW13tbtWhLNTu3BTBDa3PC/OzeI/1Zuz/0DwHQgnx+QyXb96qrg/gdy0q27+UwfxRjhtbmhPnZvUf6s3Z/6D8CoAVV1Tapztva7eOGpDpvq6pqmyJXFHqFGVqbE+Zn9x7pz9r9of8IgBbU2NL9Tt2X9RB5zNDanDA/u/dIf71bD/ZDALSglAR3SNdD5DFDa3PC/OzeI/31bj3YDwHQgrIzkpTmccvVzeMuSWket7IzkiJZFnqBGVqbE+Zn9x7pz9r9of8IgBYUG+NScUGmJHXauTvuFxdkKjamu10fZmOG1uaE+dm9R/qzdn/oPwKgReVnpWn9nMlK9QQfvk/1uLV+zmTlZ6WZVBl6ihlamxPmZ/ce6c/a/aF/zjO7APRdflaafpCZqqraJjW2tCol4czhfP6isw5maG1OmJ/de6Q/OBUB0OJiY1zKvegCs8tAPzBDa3PC/OzeI/3BiXgJGAAAwGEIgAAAAA5DAAQAAHAYAiAAAIDDEAABAAAchgAIADbg8xuBf1fVNgXdhzUwQ0QSARAALK6spk4zntoZuD9v0/v63m/+orKaOhOrQm8wQ0QaARAALKyspk6LtlSrobktaHm9t1WLtlQTICyAGcIMjgyAhw4d0oIFC5SRkaGBAwfqoosuUnFxsdrb280uDQB6zOc3VLJ9r7p6obBjWcn2vbyUGMWYIcziyAC4b98++f1+Pffcc/roo4+0Zs0abdiwQQ8//LDZpQFAj1XVNqnO29rt44akOm+rqmqbIlcUeoUZwiyO/Ci4/Px85efnB+6PHTtW+/fv1/r167V69WoTKwOAnmts6T449GU9RB4zhFkceQSwK16vV0lJSWaXAQA9lpLgDul6iDxmCLMQACUdOHBAa9eu1S9+8YtzrtfW1qbm5uagGwCYJTsjSWket1zdPO6SlOZxKzuDP26jFTOEWWwVAB966CG5XK5z3vbt2xf0NUeOHFF+fr5uueUWLVy48JzPX1paKo/HE7ilp6eHsx0AOKfYGJeKCzIlqVOA6LhfXJCp2Jju4gXMxgxhFpdhGLY5tejYsWM6fvz4OdcZO3as4uLiJElHjx7VtGnTdNVVV2nz5s2KiTl3Hm5ra1Nb29en6Tc3Nys9PV1er1eJiYn9bwCA7X3R/qUyl/23JGnvY3kaFNf/t2KX1dSpZPveoJMJ0jxuFRdkKj8rrd/Pj6+FY34SM4y05uZmeTweR//+ttVJIMOGDdOwYcN6tO6RI0c0ffp0TZkyRZs2bfrW8CdJ8fHxio+P72+ZABBS+Vlp+kFmqqpqm9TY0qqUhDMvGXLUyDqYISLNVgGwp44cOaJp06Zp9OjRWr16tY4dOxZ4LDU11cTKAKBvYmNcyr3oArPLQD8wQ0SSIwPgjh07dODAAR04cECjRo0KesxGr4gDAAB0yVYngfTUvHnzZBhGlzcAAAC7c2QABAAAcDICIAAAgMMQAAEggnz+r99qUlXbFHQf0Y/5wS4IgAAQIWU1dZrx1M7A/Xmb3tf3fvMXldXUmVgVeor5wU4IgAAQAWU1dVq0pVoNzW1By+u9rVq0pZoQEeWYH+yGAAgAYebzGyrZvlddvVjYsaxk+15eToxSzA92RAAEgDCrqm0K+oivbzIk1XlbVVXbFLmi0GPMD3ZEAASAMGts6T489GU9RBbzgx0RAAEgzFIS3CFdD5HF/GBHBEAACLPsjCSledxydfO4S1Kax63sjKRIloUeYn6wIwIgAIRZbIxLxQWZktQpRHTcLy7IVGxMdxEDZmJ+sCMCIABEQH5WmtbPmaxUT/DLhKket9bPmaz8rDSTKkNPMD/YjcswDM5b76Pm5mZ5PB55vV4lJiaaXQ4AC/D5DVXVNqmxpVUpCWdeNuTIkXUwP3vg97d0ntkFWFlHdm5ubja5EgBW8t1hA/TdYQMkSadOtphcDXqL+Vlfx+9tJx8DIwD2Q0vLmR0/PT3d5EoAAEBvtbS0yOPxmF2GKXgJuB/8fr+OHj2qhIQEuVyhfQmgublZ6enp+vTTT215eJr+rM/uPdKf9dm9R/rrO8Mw1NLSohEjRigmxpmnQ3AEsB9iYmI0atSosH6PxMREW+7YHejP+uzeI/1Zn917pL++ceqRvw7OjL0AAAAORgAEAABwGAJglIqPj1dxcbHi4+PNLiUs6M/67N4j/Vmf3XukP/QHJ4EAAAA4DEcAAQAAHIYACAAA4DAEQAAAAIchAAIAADgMATCKHDp0SAsWLFBGRoYGDhyoiy66SMXFxWpvbw9a7+9//7umTp0qt9ut9PR0rVy50qSK++aJJ57Q1VdfrUGDBmnIkCFdruNyuTrdXnrppcgW2kc96e/w4cO68cYbNWjQIKWkpOj+++/Xl19+GdlCQ2jMmDGd5rVixQqzy+qzdevWacyYMXK73crJyVFVVZXZJYXM8uXLO81q/PjxZpfVZ2+//bYKCgo0YsQIuVwuvfrqq0GPG4ahZcuWKS0tTQMHDtSMGTP0ySefmFNsH31bj/Pmzes00/z8fHOK7YPS0lJdeeWVSkhIUEpKimbNmqX9+/cHrdPa2qrCwkJdcMEFGjx4sG6++WY1NDSYVLE9EACjyL59++T3+/Xcc8/po48+0po1a7RhwwY9/PDDgXWam5s1c+ZMjR49Wrt379aqVau0fPly/f73vzex8t5pb2/XLbfcokWLFp1zvU2bNqmuri5wmzVrVmQK7Kdv68/n8+nGG29Ue3u73n33Xb3wwgvavHmzli1bFuFKQ+uxxx4Lmtddd91ldkl9sm3bNhUVFam4uFjV1dWaOHGi8vLy1NjYaHZpIfPd7343aFbvvPOO2SX12alTpzRx4kStW7euy8dXrlyp3/3ud9qwYYN27dql888/X3l5eWptbY1wpX33bT1KUn5+ftBMX3zxxQhW2D87d+5UYWGh3nvvPe3YsUOnT5/WzJkzderUqcA6S5Ys0fbt2/Xyyy9r586dOnr0qG666SYTq7YBA1Ft5cqVRkZGRuD+s88+awwdOtRoa2sLLHvwwQeNcePGmVFev2zatMnweDxdPibJeOWVVyJaT6h1198bb7xhxMTEGPX19YFl69evNxITE4PmaiWjR4821qxZY3YZIZGdnW0UFhYG7vt8PmPEiBFGaWmpiVWFTnFxsTFx4kSzywiLb/6/4ff7jdTUVGPVqlWBZSdOnDDi4+ONF1980YQK+6+r/xvnzp1r/OhHPzKlnnBobGw0JBk7d+40DOPMzAYMGGC8/PLLgXU+/vhjQ5JRWVlpVpmWxxHAKOf1epWUlBS4X1lZqWuvvVZxcXGBZXl5edq/f78+//xzM0oMm8LCQiUnJys7O1sbN26UYZNLVlZWVuqyyy7T8OHDA8vy8vLU3Nysjz76yMTK+mfFihW64IILdPnll2vVqlWWfEm7vb1du3fv1owZMwLLYmJiNGPGDFVWVppYWWh98sknGjFihMaOHauf//znOnz4sNklhUVtba3q6+uD5unxeJSTk2OreUpSRUWFUlJSNG7cOC1atEjHjx83u6Q+83q9khT43bd7926dPn06aI7jx4/XhRdeaLs5RtJ5ZheA7h04cEBr167V6tWrA8vq6+uVkZERtF5HkKivr9fQoUMjWmO4PPbYY/r+97+vQYMG6c0339Sdd96pkydP6u677za7tH6rr68PCn9S8Ayt6O6779bkyZOVlJSkd999V0uXLlVdXZ2eeuops0vrlc8++0w+n6/L+ezbt8+kqkIrJydHmzdv1rhx41RXV6eSkhJNnTpVNTU1SkhIMLu8kOrYn7qap1X3ta7k5+frpptuUkZGhg4ePKiHH35YN9xwgyorKxUbG2t2eb3i9/t1zz336JprrlFWVpakM3OMi4vr9J5qu80x0jgCGAEPPfRQlyc1nH375i+XI0eOKD8/X7fccosWLlxoUuU915cez+XRRx/VNddco8svv1wPPvigHnjgAa1atSqMHZxbqPuzgt70XFRUpGnTpmnChAn65S9/qd/+9rdau3at2traTO4C33TDDTfolltu0YQJE5SXl6c33nhDJ06c0B//+EezS0Mf/fSnP9UPf/hDXXbZZZo1a5Zef/11vf/++6qoqDC7tF4rLCxUTU2NZU76szKOAEbAvffeq3nz5p1znbFjxwb+ffToUU2fPl1XX311p5M7UlNTO5351HE/NTU1NAX3QW977K2cnBw9/vjjamtrM+VzIUPZX2pqaqezSqNhht/Un55zcnL05Zdf6tChQxo3blwYqguP5ORkxcbGdrmPRdNsQmnIkCH6zne+owMHDphdSsh1zKyhoUFpaWmB5Q0NDZo0aZJJVYXf2LFjlZycrAMHDuj66683u5weW7x4sV5//XW9/fbbGjVqVGB5amqq2tvbdeLEiaCjgHbeLyOBABgBw4YN07Bhw3q07pEjRzR9+nRNmTJFmzZtUkxM8EHa3NxcPfLIIzp9+rQGDBggSdqxY4fGjRtn6su/vemxL/bs2aOhQ4ea9qHgoewvNzdXTzzxhBobG5WSkiLpzAwTExOVmZkZku8RCv3pec+ePYqJiQn0ZxVxcXGaMmWKysvLA2ed+/1+lZeXa/HixeYWFyYnT57UwYMHddttt5ldSshlZGQoNTVV5eXlgcDX3NysXbt2fetVCKzs//7v/3T8+PGg0BvNDMPQXXfdpVdeeUUVFRWd3uY0ZcoUDRgwQOXl5br55pslSfv379fhw4eVm5trRsm2QACMIkeOHNG0adM0evRorV69WseOHQs81vFXzs9+9jOVlJRowYIFevDBB1VTU6NnnnlGa9asMavsXjt8+LCampp0+PBh+Xw+7dmzR5J08cUXa/Dgwdq+fbsaGhp01VVXye12a8eOHXryySd13333mVt4D31bfzNnzlRmZqZuu+02rVy5UvX19frVr36lwsJC0wJuf1RWVmrXrl2aPn26EhISVFlZqSVLlmjOnDmWfE9qUVGR5s6dqyuuuELZ2dl6+umnderUKc2fP9/s0kLivvvuU0FBgUaPHq2jR4+quLhYsbGxuvXWW80urU9OnjwZdPSytrZWe/bsUVJSki688ELdc889+vWvf61LLrlEGRkZevTRRzVixAjLXFZKOnePSUlJKikp0c0336zU1FQdPHhQDzzwgC6++GLl5eWZWHXPFRYWauvWrXrttdeUkJAQeF+fx+PRwIED5fF4tGDBAhUVFSkpKUmJiYm66667lJubq6uuusrk6i3M7NOQ8bVNmzYZkrq8ne3DDz80vve97xnx8fHGyJEjjRUrVphUcd/MnTu3yx7feustwzAM489//rMxadIkY/Dgwcb5559vTJw40diwYYPh8/nMLbyHvq0/wzCMQ4cOGTfccIMxcOBAIzk52bj33nuN06dPm1d0P+zevdvIyckxPB6P4Xa7jUsvvdR48sknjdbWVrNL67O1a9caF154oREXF2dkZ2cb7733ntklhczs2bONtLQ0Iy4uzhg5cqQxe/Zs48CBA2aX1WdvvfVWl/vb3LlzDcM4cymYRx991Bg+fLgRHx9vXH/99cb+/fvNLbqXztXjF198YcycOdMYNmyYMWDAAGP06NHGwoULgy4zFe26+723adOmwDr//Oc/jTvvvNMYOnSoMWjQIOPHP/6xUVdXZ17RNuAyDJtcWwMAAAA9wlnAAAAADkMABAAAcBgCIAAAgMMQAAEAAByGAAgAAOAwBEAAAACHIQACAAA4DAEQAADAYQiAAAAADkMABAAAcBgCIABIev311zVkyBD5fD5J0p49e+RyufTQQw8F1rnjjjs0Z84cs0oEgJAhAAKApKlTp6qlpUUffPCBJGnnzp1KTk5WRUVFYJ2dO3dq2rRp5hQIACFEAAQASR6PR5MmTQoEvoqKCi1ZskQffPCBTp48qSNHjujAgQO67rrrzC0UAEKAAAgAX7nuuutUUVEhwzD017/+VTfddJMuvfRSvfPOO9q5c6dGjBihSy65xOwyAaDfzjO7AACIFtOmTdPGjRv14YcfasCAARo/frymTZumiooKff755xz9A2AbHAEEgK90vA9wzZo1gbDXEQArKip4/x8A2yAAAsBXhg4dqgkTJugPf/hDIOxde+21qq6u1j/+8Q+OAAKwDQIgAJzluuuuk8/nCwTApKQkZWZmKjU1VePGjTO3OAAIEZdhGIbZRQAAACByOAIIAADgMARAAAAAhyEAAgAAOAwBEAAAwGEIgAAAAA5DAAQAAHAYAiAAAIDDEAABAAAchgAIAADgMARAAAAAhyEAAgAAOAwBEAAAwGH+f67C8Y+YDRATAAAAAElFTkSuQmCC' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w = np.arange(-20,21)\n",
    "c = np.sin(w*np.pi/2)/np.sin(w*np.pi/10)*np.exp(-1j*2*w*np.pi/5)/10\n",
    "c[0::10] = 0.5\n",
    "plt.figure()\n",
    "plt.subplot(2,1,1)\n",
    "plt.stem(w, np.abs(c))\n",
    "plt.xlabel('w')\n",
    "plt.title('|c|')\n",
    "plt.subplot(2,1,2)\n",
    "plt.stem(w, np.angle(c))\n",
    "plt.xlabel('w')\n",
    "plt.title(r'$\\angle c$')\n",
    "plt.subplots_adjust(hspace=0.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4272193-5897-440b-8009-b20315d31d12",
   "metadata": {},
   "source": [
    "## Propriedades da série de Fourier"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cf47a47-6fdc-4cc9-a13b-5757018a771e",
   "metadata": {},
   "source": [
    "- **Linearidade**\n",
    "\n",
    "  Se $\\mathcal{SF}(x_1[n]) = a_w$ e $\\mathcal{SF}(x_2[n]) = b_w$\n",
    "\n",
    "  Então:\n",
    "\n",
    "  $\\boxed{\\mathcal{SF}(Ax_1[n]+Bx_2[n]) = Aa_w+Bb_w}$\n",
    "\n",
    "- **Deslocamento no tempo**\n",
    "\n",
    "  Se $\\mathcal{SF}(x[n]) = a_w$\n",
    "\n",
    "  Então:\n",
    "\n",
    "  $\\boxed{\\mathcal{SF}(x[n-n_0]) = e^{-jw\\omega_0 n_0}a_n}$\n",
    "\n",
    "- **Primeira diferença**\n",
    "\n",
    "  Se $\\mathcal{SF}(x[n]) = a_w$\n",
    "\n",
    "  Então:\n",
    "\n",
    "  $\\boxed{\\mathcal{SF}(x[n]-x[n-1]) = (1-e^{-jw\\frac{2\\pi}{T_0}})a_w}$\n",
    "\n",
    "- **Multiplicação**\n",
    "\n",
    "  Se $\\mathcal{SF}(x[n]) = a_w$ e $\\mathcal{SF}(y[n]) = b_w$\n",
    "\n",
    "   Então:\n",
    "\n",
    "  $\\boxed{\\mathcal{SF}(x[n]y[n]) = \\displaystyle\\sum_{k=<T_0>}a_kb_{w-k}}$\n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc6f631d-0c81-4657-bccb-309a3da27dad",
   "metadata": {},
   "source": [
    "---\n",
    "### Exemplo  4\n",
    "\n",
    "\n",
    "Considere agora o seguinte sinal de período $T_0=10$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f8b372c6-406e-46ab-804d-ddd679b2b909",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a7d5507710664e499767d7bcac797094",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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crNzW3zudLSUq/HTz31lJ566qkO5wsICNCKFSu0YsWKnioRAADA79niM4AAAADoOQRAAAAAwxAAAQAADEMABAAAMAwBEAAAwDAEQAAAAMMQAAEAAAxDAAQAADAMARAAAMAwBEAAAADDEAABAAAMQwAEAAAwDAEQAADAMARAAAAAwxAAAQAADEMABAAAMAwBEAAAwDAEQAAAAMMQAAEAAAxDAAQAADAMARAAAMAwBEAAAADDEAABAAAMQwAEAAAwDAEQAADAMARAAAAAwxAAAQAADEMABAAAMAwBEAAAwDAEQAAAAMMQAAEAAAxjqwC4adMmDR06VCEhIUpLS9OuXbvaHfvCCy/o5ptv1uDBgzV48GBlZGScN3727NkKCAjw2rKysnp7GQAAAD5lmwD4+uuvKy8vTwUFBdq9e7fGjRunzMxM1dTUtDm+tLRUP/zhD/Xhhx+qrKxMCQkJmjx5so4ePeo1LisrS1VVVZ7tV7/6VV8sBwAAwGdsEwDXr1+vnJwcZWdnKykpSYWFhQoNDdXmzZvbHP/KK6/ovvvuU3JyskaNGqX//M//VGtrq0pKSrzGORwOOZ1OzzZ48OC+WA4AAIDP2CIANjU1qaKiQhkZGZ59gYGBysjIUFlZWafmOH36tJqbmxUZGem1v7S0VDExMRo5cqTmzZunEydOtDtHY2Oj3G631wYAAGA3tgiAx48fV0tLi2JjY732x8bGyuVydWqORYsWKT4+3itEZmVl6aWXXlJJSYmefPJJ7dy5U7fddptaWlranGP16tUKDw/3bAkJCd1fFAAAgI/083UBfeGJJ57Qa6+9ptLSUoWEhHj2T58+3fPnMWPGaOzYsRo+fLhKS0s1adKk8+bJz89XXl6e57Hb7SYEAgAA27HFGcCoqCgFBQWpurraa391dbWcTmeHx65bt05PPPGEduzYobFjx3Y4dtiwYYqKitKBAwfafN7hcCgsLMxrAwAAsBtbBMDg4GClpKR4XcBx7oKO9PT0do9bs2aNVq5cqaKiIo0fP/6CX+err77SiRMnFBcX1yN1AwAA+CNbBEBJysvL0wsvvKBt27Zp7969mjdvnk6dOqXs7GxJ0syZM5Wfn+8Z/+STT2rJkiXavHmzhg4dKpfLJZfLpYaGBklSQ0ODHn74YX3yySc6dOiQSkpKdOedd2rEiBHKzMz0yRoBAAD6gm0+A3j33Xfr66+/1tKlS+VyuZScnKyioiLPhSGHDx9WYOD/5dnnnntOTU1N+rd/+zeveQoKCrRs2TIFBQXps88+07Zt21RXV6f4+HhNnjxZK1eulMPh6NO1AQAA9CXbBEBJys3NVW5ubpvPlZaWej0+dOhQh3MNGDBA77//fg9VBgAAYB+2eQsYAAAAPYMACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGCYfr4uABenpdXSroO1qjl5RjGDQpSaGKmgwIA+Hdud8b5eX2/P7Q9rZH19s0Z/ed1d6j204/r8ZY3+UnNv9hBdZ6sAuGnTJq1du1Yul0vjxo3Txo0blZqa2u74N954Q0uWLNGhQ4d09dVX68knn9Ttt9/ued6yLBUUFOiFF15QXV2dbrzxRj333HO6+uqr+2I5F61oT5WWb/+LqurPePbFhYeo4I4kZV0T1ydjuzPe1+vr7bn9YY2sr/t19Nb6enONl3oP7bg+f1mjv9Tcmz1E99jmLeDXX39deXl5Kigo0O7duzVu3DhlZmaqpqamzfEff/yxfvjDH2rOnDn64x//qKlTp2rq1Knas2ePZ8yaNWu0YcMGFRYWqry8XAMHDlRmZqbOnDnT5pz+pGhPlea9vNvrm0mSXPVnNO/l3SraU9XrY7sz3tfr6+25/WGNrM//XqO9ucZLvYd2XJ+/rNFfau7NHqL7AizLsnxdRGekpaXp+uuv1zPPPCNJam1tVUJCgu6//34tXrz4vPF33323Tp06pXfffdezb8KECUpOTlZhYaEsy1J8fLwWLlyohx56SJJUX1+v2NhYbd26VdOnT79gTW63W+Hh4aqvr1dYWFgPrVQ61dis6362XZJU8WiGQoO9T9S2tFrKWL9TLnfbQTVAUmxYiH6X9z1J6pWxQYEBXaqjK6f5e2t9Xa25q3Ofc7rprFIe+52ktvvXm2vsrbFdfZvGH9Z3Ma/RC/Wwq/P6y99HV/hDzV0Z+8/r68kedrWOvvh35kLs/hr9dv92P36HBjr6X3jRXdBbP7/txBYBsKmpSaGhoXrzzTc1depUz/5Zs2aprq5Ov/3tb8875qqrrlJeXp4WLFjg2VdQUKDf/OY3+tOf/qS//vWvGj58uP74xz8qOTnZM+Z73/uekpOT9Ytf/OK8ORsbG9XY2Oh57Ha7lZCQ0OMvoIY6t45MSOux+QAAsKuET8p1WUTPhjQCoE3eAj5+/LhaWloUGxvrtT82NlYul6vNY1wuV4fjz/23K3OuXr1a4eHhni0hIaFb67mQts4YAQBgIn4m9g7+VrsgPz9feXl5nsfnzgD2tIABAzRyd0W7z5cfrNXsLbsuOM/W7G8ukOmNsWmJkV2qIy0x0vP4Qm/N9Nb6ulpzV+fuCn/oYVfG/vP6fNXDrtbc3dfohXR1Xn/5+zinMx9T8IeauzLWX74H++rfmZ78HvTH1+i3BQwYcMHj0XW2CIBRUVEKCgpSdXW11/7q6mo5nc42j3E6nR2OP/ff6upqxcXFeY359lvC3+ZwOORwOLq7jE4LCAhQQGhou8+njh6gyMvD5ao/o7bevw+Q5AwPUeroKySpV8YGBgZ0qY7Ab322I7DfWTX2++bvMTA0VIH/9A9Xb62vqzV3de6u8IceXsz6fNXDrtbc3dfohXR1Xn/5+zjnQv3r6hp7q+burq8z7P7vTE9+D/rjaxS9zxZvAQcHByslJUUlJSWefa2trSopKVF6enqbx6Snp3uNl6Ti4mLP+MTERDmdTq8xbrdb5eXl7c7pL4ICA1RwR5Kkb755vu3c44I7khQUGNBrY7taR1f4S829tb7erIP1+d9rtKvj6aG919fbc3eWv9Tcmz3ExbFFAJSkvLw8vfDCC9q2bZv27t2refPm6dSpU8rOzpYkzZw5U/n5+Z7x//Ef/6GioiL9/Oc/1759+7Rs2TL97//+r3JzcyV9c5ZtwYIFeuyxx/TOO+/oz3/+s2bOnKn4+HivC038VdY1cXrunuvkDA/x2u8MD9Fz91zndV+l3hrbnfG+Xl9vz+0Pa2R9/vca7c01Xuo9tOP6/GWN/lJzb/YQ3WeLq4DPeeaZZzw3gk5OTtaGDRuUlvbN1bITJ07U0KFDtXXrVs/4N954Q48++qjnRtBr1qxp80bQzz//vOrq6nTTTTfp2Wef1Xe+851O1eMPVxH5yx3buzL+dNNZJS19X5L0lxWZHX7A119qtuNvIejN9flDD/lNIN0f25X++UvNdvwe7M25e+t7sDdr9qffBOIPP799zVYB0N/wAuqerv7wgf+hh/ZG/+yPHl4cfn7b6C1gAAAA9AwCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACG8fsAWFtbqxkzZigsLEwRERGaM2eOGhoaOhx///33a+TIkRowYICuuuoqPfDAA6qvr/caFxAQcN722muv9fZyAAAAfK6frwu4kBkzZqiqqkrFxcVqbm5Wdna25s6dq1dffbXN8ceOHdOxY8e0bt06JSUl6W9/+5vuvfdeHTt2TG+++abX2C1btigrK8vzOCIiojeXAgAA4Bf8OgDu3btXRUVF+vTTTzV+/HhJ0saNG3X77bdr3bp1io+PP++Ya665Rv/1X//leTx8+HA9/vjjuueee3T27Fn16/d/S46IiJDT6ez9hQAAAPgRv34LuKysTBEREZ7wJ0kZGRkKDAxUeXl5p+epr69XWFiYV/iTpPnz5ysqKkqpqanavHmzLMvqcJ7Gxka53W6vDQAAwG78+gygy+VSTEyM175+/fopMjJSLperU3McP35cK1eu1Ny5c732r1ixQrfeeqtCQ0O1Y8cO3XfffWpoaNADDzzQ7lyrV6/W8uXLu74QAAAAP+KTM4CLFy9u8yKMb2/79u276K/jdrs1ZcoUJSUladmyZV7PLVmyRDfeeKOuvfZaLVq0SI888ojWrl3b4Xz5+fmqr6/3bEeOHLnoGgEAAPqaT84ALly4ULNnz+5wzLBhw+R0OlVTU+O1/+zZs6qtrb3gZ/dOnjyprKwsDRo0SG+//bb69+/f4fi0tDStXLlSjY2NcjgcbY5xOBztPgcAAGAXPgmA0dHRio6OvuC49PR01dXVqaKiQikpKZKkDz74QK2trUpLS2v3OLfbrczMTDkcDr3zzjsKCQm54NeqrKzU4MGDCXgAAOCS59efARw9erSysrKUk5OjwsJCNTc3Kzc3V9OnT/dcAXz06FFNmjRJL730klJTU+V2uzV58mSdPn1aL7/8stfFGtHR0QoKCtL27dtVXV2tCRMmKCQkRMXFxVq1apUeeughXy4XAACgT/h1AJSkV155Rbm5uZo0aZICAwM1bdo0bdiwwfN8c3Oz9u/fr9OnT0uSdu/e7blCeMSIEV5zHTx4UEOHDlX//v21adMmPfjgg7IsSyNGjND69euVk5PTdwsDAADwEb8PgJGRke3e9FmShg4d6nX7lokTJ17wdi5ZWVleN4AGAAAwiV/fBxAAAAA9jwAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGH8PgDW1tZqxowZCgsLU0REhObMmaOGhoYOj5k4caICAgK8tnvvvddrzOHDhzVlyhSFhoYqJiZGDz/8sM6ePdubSwEAAPAL/XxdwIXMmDFDVVVVKi4uVnNzs7KzszV37ly9+uqrHR6Xk5OjFStWeB6HhoZ6/tzS0qIpU6bI6XTq448/VlVVlWbOnKn+/ftr1apVvbYWAAAAf+DXAXDv3r0qKirSp59+qvHjx0uSNm7cqNtvv13r1q1TfHx8u8eGhobK6XS2+dyOHTv0l7/8Rb/73e8UGxur5ORkrVy5UosWLdKyZcsUHBzcK+sBAADwB379FnBZWZkiIiI84U+SMjIyFBgYqPLy8g6PfeWVVxQVFaVrrrlG+fn5On36tNe8Y8aMUWxsrGdfZmam3G63Pv/883bnbGxslNvt9toAAADsxq/PALpcLsXExHjt69evnyIjI+Vyudo97kc/+pGGDBmi+Ph4ffbZZ1q0aJH279+vt956yzPvt8OfJM/jjuZdvXq1li9f3t3lAAAA+AWfBMDFixfrySef7HDM3r17uz3/3LlzPX8eM2aM4uLiNGnSJH355ZcaPnx4t+fNz89XXl6e57Hb7VZCQkK35wMAAPAFnwTAhQsXavbs2R2OGTZsmJxOp2pqarz2nz17VrW1te1+vq8taWlpkqQDBw5o+PDhcjqd2rVrl9eY6upqSepwXofDIYfD0emvCwAA4I98EgCjo6MVHR19wXHp6emqq6tTRUWFUlJSJEkffPCBWltbPaGuMyorKyVJcXFxnnkff/xx1dTUeN5iLi4uVlhYmJKSkrq4GgAAAHvx64tARo8eraysLOXk5GjXrl36wx/+oNzcXE2fPt1zBfDRo0c1atQozxm9L7/8UitXrlRFRYUOHTqkd955RzNnztR3v/tdjR07VpI0efJkJSUl6cc//rH+9Kc/6f3339ejjz6q+fPnc4YPAABc8vw6AErfXM07atQoTZo0SbfffrtuuukmPf/8857nm5ubtX//fs9VvsHBwfrd736nyZMna9SoUVq4cKGmTZum7du3e44JCgrSu+++q6CgIKWnp+uee+7RzJkzve4bCAAAcKny66uAJSkyMrLDmz4PHTpUlmV5HickJGjnzp0XnHfIkCF67733eqRGAAAAO/H7M4AAAADoWQRAAAAAwxAAAQAADEMABAAAMAwBEAAAwDAEQAAAAMMQAAEAAAxDAAQAADAMARAAAMAwBEAAAADDEAABAAAMQwAEAAAwDAEQAADAMARAAAAAwxAAAQAADEMABAAAMAwBEAAAwDAEQAAAAMMQAAEAAAxDAAQAADAMARAAAMAwBEAAAADDEAABAAAMQwAEAAAwDAEQAADAMARAAAAAwxAAAQAADEMABAAAMAwBEAAAwDAEQAAAAMMQAAEAAAzj9wGwtrZWM2bMUFhYmCIiIjRnzhw1NDS0O/7QoUMKCAhoc3vjjTc849p6/rXXXuuLJQEAAPhUP18XcCEzZsxQVVWViouL1dzcrOzsbM2dO1evvvpqm+MTEhJUVVXlte/555/X2rVrddttt3nt37Jli7KysjyPIyIierx+AAAAf+PXAXDv3r0qKirSp59+qvHjx0uSNm7cqNtvv13r1q1TfHz8eccEBQXJ6XR67Xv77bf17//+77rsssu89kdERJw3FgAA4FLn128Bl5WVKSIiwhP+JCkjI0OBgYEqLy/v1BwVFRWqrKzUnDlzzntu/vz5ioqKUmpqqjZv3izLsjqcq7GxUW6322sDAACwG78+A+hyuRQTE+O1r1+/foqMjJTL5erUHC+++KJGjx6tG264wWv/ihUrdOuttyo0NFQ7duzQfffdp4aGBj3wwAPtzrV69WotX7686wsBAADwIz45A7h48eJ2L9Q4t+3bt++iv84//vEPvfrqq22e/VuyZIluvPFGXXvttVq0aJEeeeQRrV27tsP58vPzVV9f79mOHDly0TUCAAD0NZ+cAVy4cKFmz57d4Zhhw4bJ6XSqpqbGa//Zs2dVW1vbqc/uvfnmmzp9+rRmzpx5wbFpaWlauXKlGhsb5XA42hzjcDjafQ4AAMAufBIAo6OjFR0dfcFx6enpqqurU0VFhVJSUiRJH3zwgVpbW5WWlnbB41988UV9//vf79TXqqys1ODBgwl4AADgkufXnwEcPXq0srKylJOTo8LCQjU3Nys3N1fTp0/3XAF89OhRTZo0SS+99JJSU1M9xx44cEAfffSR3nvvvfPm3b59u6qrqzVhwgSFhISouLhYq1at0kMPPdRnawMAAPAVvw6AkvTKK68oNzdXkyZNUmBgoKZNm6YNGzZ4nm9ubtb+/ft1+vRpr+M2b96sK6+8UpMnTz5vzv79+2vTpk168MEHZVmWRowYofXr1ysnJ6fX1wMAAOBrfh8AIyMj273psyQNHTq0zdu3rFq1SqtWrWrzmKysLK8bQAMAAJjEr+8DCAAAgJ5HAAQAADAMARAAAMAwBEAAAADDEAABAAAMQwAEAAAwDAEQAADAMARAAAAAwxAAAQAADEMABAAAMAwBEAAAwDAEQAAAAMMQAAEAAAxDAAQAADAMARAAAMAwBEAAAADDEAABAAAMQwAEAAAwDAEQAADAMARAAAAAwxAAAQAADEMABAAAMAwBEAAAwDAEQAAAAMMQAAEAAAxDAAQAADAMARAAAMAwBEAAAADDEAABAAAMQwAEAAAwDAEQfa6l1fL8edfBWq/HsAd6aG/0z/7oIS6W3wfAxx9/XDfccINCQ0MVERHRqWMsy9LSpUsVFxenAQMGKCMjQ1988YXXmNraWs2YMUNhYWGKiIjQnDlz1NDQ0AsrwLcV7alSxvqdnsezt3yqm578QEV7qnxYFbqCHtob/bM/eoie4PcBsKmpSXfddZfmzZvX6WPWrFmjDRs2qLCwUOXl5Ro4cKAyMzN15swZz5gZM2bo888/V3Fxsd5991199NFHmjt3bm8sAf9f0Z4qzXt5t6rdjV77XfVnNO/l3fzjZQP00N7on/3RQ/SUAMuybHHeeOvWrVqwYIHq6uo6HGdZluLj47Vw4UI99NBDkqT6+nrFxsZq69atmj59uvbu3aukpCR9+umnGj9+vCSpqKhIt99+u7766ivFx8d3qia3263w8HDV19crLCzsotZ3qWtptXTTkx+oqv5Mm88HSHKGh+j3i25VUGBA3xaHTqGH9kb/7I8e9hx+ftvgDGBXHTx4UC6XSxkZGZ594eHhSktLU1lZmSSprKxMERERnvAnSRkZGQoMDFR5eXm7czc2Nsrtdntt6JxdB2vb/UdLkixJVfVntOtgbd8VhS6hh/ZG/+yPHqInXXIB0OVySZJiY2O99sfGxnqec7lciomJ8Xq+X79+ioyM9Ixpy+rVqxUeHu7ZEhISerj6S1fNyfb/0erOOPQ9emhv9M/+6CF6kk8C4OLFixUQENDhtm/fPl+U1qH8/HzV19d7tiNHjvi6JNuIGRTSo+PQ9+ihvdE/+6OH6En9fPFFFy5cqNmzZ3c4ZtiwYd2a2+l0SpKqq6sVFxfn2V9dXa3k5GTPmJqaGq/jzp49q9raWs/xbXE4HHI4HN2qy3SpiZGKCw+Rq/6M2vrQ6bnPrqQmRvZ1aegkemhv9M/+6CF6kk/OAEZHR2vUqFEdbsHBwd2aOzExUU6nUyUlJZ59brdb5eXlSk9PlySlp6errq5OFRUVnjEffPCBWltblZaWdnGLQ5uCAgNUcEeSpG/+kfq2c48L7kjig8t+jB7aG/2zP3qInuT3nwE8fPiwKisrdfjwYbW0tKiyslKVlZVe9+wbNWqU3n77bUlSQECAFixYoMcee0zvvPOO/vznP2vmzJmKj4/X1KlTJUmjR49WVlaWcnJytGvXLv3hD39Qbm6upk+f3ukrgNF1WdfE6bl7rpMz3PvtCWd4iJ675zplXRPXzpHwF/TQ3uif/dFD9BS/vw3M7NmztW3btvP2f/jhh5o4caKkb0Lfli1bPG8rW5algoICPf/886qrq9NNN92kZ599Vt/5znc8x9fW1io3N1fbt29XYGCgpk2bpg0bNuiyyy7rdG1cRt49La2Wdh2sVc3JM4oZ9M3bFfwfq73QQ3ujf/ZHDy8OP79tEAD9GS8gAADsh5/fNngLGAAAAD2LAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGKafrwuws3O/RMXtdvu4EgAA0Fnnfm6b/MvQCIAX4eTJk5KkhIQEH1cCAAC66uTJkwoPD/d1GT7B7wK+CK2trTp27JgGDRqkgICe/SXcbrdbCQkJOnLkyCX5ewpZn/1d6mtkffZ3qa+R9XWfZVk6efKk4uPjFRho5qfhOAN4EQIDA3XllVf26tcICwu7JL+xz2F99nepr5H12d+lvkbW1z2mnvk7x8zYCwAAYDACIAAAgGEIgH7K4XCooKBADofD16X0CtZnf5f6Glmf/V3qa2R9uBhcBAIAAGAYzgACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEA+pFDhw5pzpw5SkxM1IABAzR8+HAVFBSoqanJa9xnn32mm2++WSEhIUpISNCaNWt8VHH3PP7447rhhhsUGhqqiIiINscEBASct7322mt9W2g3dWZ9hw8f1pQpUxQaGqqYmBg9/PDDOnv2bN8W2oOGDh16Xr+eeOIJX5fVbZs2bdLQoUMVEhKitLQ07dq1y9cl9Zhly5ad16tRo0b5uqxu++ijj3THHXcoPj5eAQEB+s1vfuP1vGVZWrp0qeLi4jRgwABlZGToiy++8E2x3XShNc6ePfu8nmZlZfmm2G5YvXq1rr/+eg0aNEgxMTGaOnWq9u/f7zXmzJkzmj9/vi6//HJddtllmjZtmqqrq31U8aWBAOhH9u3bp9bWVv3yl7/U559/rqeeekqFhYX66U9/6hnjdrs1efJkDRkyRBUVFVq7dq2WLVum559/3oeVd01TU5PuuusuzZs3r8NxW7ZsUVVVlWebOnVq3xR4kS60vpaWFk2ZMkVNTU36+OOPtW3bNm3dulVLly7t40p71ooVK7z6df/99/u6pG55/fXXlZeXp4KCAu3evVvjxo1TZmamampqfF1aj/mXf/kXr179/ve/93VJ3Xbq1CmNGzdOmzZtavP5NWvWaMOGDSosLFR5ebkGDhyozMxMnTlzpo8r7b4LrVGSsrKyvHr6q1/9qg8rvDg7d+7U/Pnz9cknn6i4uFjNzc2aPHmyTp065Rnz4IMPavv27XrjjTe0c+dOHTt2TD/4wQ98WPUlwIJfW7NmjZWYmOh5/Oyzz1qDBw+2GhsbPfsWLVpkjRw50hflXZQtW7ZY4eHhbT4nyXr77bf7tJ6e1t763nvvPSswMNByuVyefc8995wVFhbm1Vc7GTJkiPXUU0/5uowekZqaas2fP9/zuKWlxYqPj7dWr17tw6p6TkFBgTVu3Dhfl9Er/vnfjdbWVsvpdFpr16717Kurq7McDof1q1/9ygcVXry2/m2cNWuWdeedd/qknt5QU1NjSbJ27txpWdY3Pevfv7/1xhtveMbs3bvXkmSVlZX5qkzb4wygn6uvr1dkZKTncVlZmb773e8qODjYsy8zM1P79+/X3//+d1+U2Gvmz5+vqKgopaamavPmzbIukVtWlpWVacyYMYqNjfXsy8zMlNvt1ueff+7Dyi7OE088ocsvv1zXXnut1q5da8u3tJuamlRRUaGMjAzPvsDAQGVkZKisrMyHlfWsL774QvHx8Ro2bJhmzJihw4cP+7qkXnHw4EG5XC6vfoaHhystLe2S6qcklZaWKiYmRiNHjtS8efN04sQJX5fUbfX19ZLk+dlXUVGh5uZmrz6OGjVKV1111SXXx77Uz9cFoH0HDhzQxo0btW7dOs8+l8ulxMREr3HngoTL5dLgwYP7tMbesmLFCt16660KDQ3Vjh07dN9996mhoUEPPPCAr0u7aC6Xyyv8Sd49tKMHHnhA1113nSIjI/Xxxx8rPz9fVVVVWr9+va9L65Ljx4+rpaWlzf7s27fPR1X1rLS0NG3dulUjR45UVVWVli9frptvvll79uzRoEGDfF1ejzr3/dRWP+36vdaWrKws/eAHP1BiYqK+/PJL/fSnP9Vtt92msrIyBQUF+bq8LmltbdWCBQt044036pprrpH0TR+Dg4PP+0z1pdbHvsYZwD6wePHiNi9q+Pb2zz9cjh49qqysLN11113KycnxUeWd1501dmTJkiW68cYbde2112rRokV65JFHtHbt2l5cQcd6en120JU15+XlaeLEiRo7dqzuvfde/fznP9fGjRvV2Njo41Xgn91222266667NHbsWGVmZuq9995TXV2dfv3rX/u6NHTT9OnT9f3vf19jxozR1KlT9e677+rTTz9VaWmpr0vrsvnz52vPnj22uejPzjgD2AcWLlyo2bNndzhm2LBhnj8fO3ZMt9xyi2644YbzLu5wOp3nXfl07rHT6eyZgruhq2vsqrS0NK1cuVKNjY0++b2QPbk+p9N53lWl/tDDf3Yxa05LS9PZs2d16NAhjRw5sheq6x1RUVEKCgpq83vMn3rTkyIiIvSd73xHBw4c8HUpPe5cz6qrqxUXF+fZX11dreTkZB9V1fuGDRumqKgoHThwQJMmTfJ1OZ2Wm5urd999Vx999JGuvPJKz36n06mmpibV1dV5nQW8lL8v+wIBsA9ER0crOjq6U2OPHj2qW265RSkpKdqyZYsCA71P0qanp+tnP/uZmpub1b9/f0lScXGxRo4c6dO3f7uyxu6orKzU4MGDffZLwXtyfenp6Xr88cdVU1OjmJgYSd/0MCwsTElJST3yNXrCxay5srJSgYGBnvXZRXBwsFJSUlRSUuK56ry1tVUlJSXKzc31bXG9pKGhQV9++aV+/OMf+7qUHpeYmCin06mSkhJP4HO73SovL7/gXQjs7KuvvtKJEye8Qq8/syxL999/v95++22Vlpae9zGnlJQU9e/fXyUlJZo2bZokaf/+/Tp8+LDS09N9UfIlgQDoR44ePaqJEydqyJAhWrdunb7++mvPc+f+L+dHP/qRli9frjlz5mjRokXas2ePfvGLX+ipp57yVdlddvjwYdXW1urw4cNqaWlRZWWlJGnEiBG67LLLtH37dlVXV2vChAkKCQlRcXGxVq1apYceesi3hXfShdY3efJkJSUl6cc//rHWrFkjl8ulRx99VPPnz/dZwL0YZWVlKi8v1y233KJBgwaprKxMDz74oO655x5bfiY1Ly9Ps2bN0vjx45Wamqqnn35ap06dUnZ2tq9L6xEPPfSQ7rjjDg0ZMkTHjh1TQUGBgoKC9MMf/tDXpXVLQ0OD19nLgwcPqrKyUpGRkbrqqqu0YMECPfbYY7r66quVmJioJUuWKD4+3ja3lZI6XmNkZKSWL1+uadOmyel06ssvv9QjjzyiESNGKDMz04dVd978+fP16quv6re//a0GDRrk+VxfeHi4BgwYoPDwcM2ZM0d5eXmKjIxUWFiY7r//fqWnp2vChAk+rt7GfH0ZMv7Pli1bLEltbt/2pz/9ybrpppssh8NhXXHFFdYTTzzho4q7Z9asWW2u8cMPP7Qsy7L+53/+x0pOTrYuu+wya+DAgda4ceOswsJCq6WlxbeFd9KF1mdZlnXo0CHrtttuswYMGGBFRUVZCxcutJqbm31X9EWoqKiw0tLSrPDwcCskJMQaPXq0tWrVKuvMmTO+Lq3bNm7caF111VVWcHCwlZqaan3yySe+LqnH3H333VZcXJwVHBxsXXHFFdbdd99tHThwwNdldduHH37Y5vfbrFmzLMv65lYwS5YssWJjYy2Hw2FNmjTJ2r9/v2+L7qKO1nj69Glr8uTJVnR0tNW/f39ryJAhVk5Ojtdtpvxdez/3tmzZ4hnzj3/8w7rvvvuswYMHW6Ghoda//uu/WlVVVb4r+hIQYFmXyL01AAAA0ClcBQwAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhvl//1g7jEWcFRMAAAAASUVORK5CYII=' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "x[1:] = np.diff(x)\n",
    "x[-1] = 1\n",
    "\n",
    "plt.figure()\n",
    "plt.stem(n, x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8624097-a6de-432b-9d85-6ee4c7404eed",
   "metadata": {},
   "source": [
    "Vamos agora calcular os coeficientes $c_w$ da série de Fourier deste sinal. Podemos ver que este sinalé $x[n] = x_q[n]-x_q[n-1]$, em que $x_q[n]$ é a onda quadrada do exemplo 3. Então podemos calcular a série de Fourier do sinal $x[n]$, usando a propriedade da primeira diferença:\n",
    "\n",
    "Os coeficientes de Fourier da onda quadrada do exemplo 3 é:\n",
    "\n",
    "$c_w = \\frac{1}{10}\\left(\\frac{\\mathrm{sen}(\\frac{w\\pi}{2})}{\\mathrm{sen}(\\frac{w\\pi}{10})}\\right)e^{j\\frac{-2w\\pi}{5}}$\n",
    "\n",
    "e\n",
    "\n",
    "$c_w = 0.5$, para $w=0, \\pm 10, \\pm 20, ...$\n",
    "\n",
    "\n",
    "Então  os coeficientes de $x[n]$: são:\n",
    "\n",
    "$a_w = (1-e^{-jw\\frac{2\\pi}{10}})c_w = (1-e^{-jw\\frac{\\pi}{5}})\\frac{1}{10}\\left(\\frac{\\mathrm{sen}(\\frac{w\\pi}{2})}{\\mathrm{sen}(\\frac{w\\pi}{10})}\\right)e^{j\\frac{-2w\\pi}{5}}=\\frac{1}{10}(e^{jw\\frac{\\pi}{10}}-e^{-jw\\frac{\\pi}{10}})\\left(\\frac{\\mathrm{sen}(\\frac{w\\pi}{2})}{\\mathrm{sen}(\\frac{w\\pi}{10})}\\right)e^{-j\\frac{2w\\pi}{5}}e^{-j\\frac{w\\pi}{10}}=\\frac{j}{5}(\\mathrm{sen}(w\\frac{\\pi}{10}))\\left(\\frac{\\mathrm{sen}(\\frac{w\\pi}{2})}{\\mathrm{sen}(\\frac{w\\pi}{10})}\\right)e^{-j\\frac{w\\pi}{2}}=0.2\\left(\\mathrm{sen}(\\frac{w\\pi}{2})\\right)e^{-j\\frac{\\pi}{2}(w-1)}$\n",
    "\n",
    "Para $w$ par, $\\mathrm{sen}(\\frac{w\\pi}{2})=0$. Então:\n",
    "\n",
    "$a_w = 0$, com $w$ par.\n",
    "\n",
    "Para $w$ ímpar:\n",
    "\n",
    "$a_w = 0.2$, com $w$ ímpar.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "763f5b12-84fe-4a97-a56f-2cfffcfdef40",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "12aff8acb37f4f93959f51e0517e5db1",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = np.arange(-10,11)\n",
    "c = np.zeros(len(n))\n",
    "c[1::2] = 0.2\n",
    "plt.figure()\n",
    "plt.subplot(2,1,1)\n",
    "plt.stem(n, np.abs(c))\n",
    "plt.xlabel('k')\n",
    "plt.title('|c|')\n",
    "plt.subplot(2,1,2)\n",
    "plt.stem(n, np.angle(c))\n",
    "plt.xlabel('k')\n",
    "plt.title(r'$\\angle c$')\n",
    "plt.subplots_adjust(wspace=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8001fc7-a47b-4fa4-93c7-95b0f47d02b6",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf792f4f-f804-4908-89a3-32049ec5d0b1",
   "metadata": {},
   "source": [
    "## Teorema de Parseval\n",
    "\n",
    "O teorema de Parseval diz que a potência do sinal é igual à soma dos quadrados dos módulos dos coeficientes da série de Fourier.\n",
    "\n",
    "$\\frac{1}{T_0}\\displaystyle\\sum_{n=n_0}^{n_0+T_0-1}|x[n]|^2 = \\sum_{k=n_0}^{n_0+T_0}|a_k|^2$\n",
    "\n",
    "A demonstração fica como exercício."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08baaab8-27a8-4a36-bdca-1fcbbac8a072",
   "metadata": {},
   "source": [
    "## Reconstrução do sinal\n",
    "\n",
    "Para reconstruir o sinal $x[n]$ a partir dos coeficientes de Fourier, basta usar a expressão de síntese do sinal $x[n]$.\n",
    "\n",
    "$x[n] = \\displaystyle\\sum_{k=n_0}^{n_0+T_0-1}a_ke^{jk\\omega_0 n}$\n",
    "\n",
    "Diferentemente do tempo contínuo, sinais em tempo discreto precisam de apenas um número finito de sinais. Então, no caso de sinais de tempo discreto, não ocorrem problemas de convergência. \n",
    "\n",
    "--- \n",
    "\n",
    "###  Exemplo 5\n",
    "\n",
    "Vamos reconstruir o sinal do exemplo 4. Os coeficientes da série de Fourier são dados pela seguinte expressão:\n",
    "\n",
    "$a_w = 0.2$, com $w$ ímpar.\n",
    "\n",
    "e \n",
    "\n",
    "$a_w = 0$ com $w$ par.\n",
    "\n",
    "Então a reconstrução do sinal $x[n]$ fica:\n",
    "\n",
    "$x[n] = \\displaystyle\\sum_{w=<T_0>}c_we^{jw\\frac{\\pi}{5} n}$\n",
    "\n",
    "Para reconstruir o sinal, precisamos de apenas 10 amostras. Diferentemente da série de Fourier de tempo contínuo, não há problemas de convergências para o tempo discreto. O sinal sempre é reconstruído de forma exata.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "61adf43d-6c4e-41f2-948f-bf537a12ea29",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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       "model_id": "3d19340af9634e45af42d1a3e9f9583f",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = np.arange(-10,11)\n",
    "\n",
    "x = np.zeros(len(n))\n",
    "\n",
    "for k in range(0, 10):\n",
    "    if k%2==0:\n",
    "        c = 0\n",
    "    else:\n",
    "        c = 0.2\n",
    "    x = x + c*np.exp(1j*k*np.pi/5*n)\n",
    "\n",
    "plt.figure()\n",
    "plt.stem(n, x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76c8a0c2-9062-4979-899f-5e71b8bb65c7",
   "metadata": {},
   "source": [
    "Quanto maior o número de termos, melhor é a reconstrução."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ede3f0c4-fe23-4628-bb93-1d2140861eb8",
   "metadata": {},
   "source": [
    "## Séries de Fourier como entrada de um sistema linear e invariante no tempo\n",
    "\n",
    "Como já visto anteriormente se um sinal $x[n] = e^{j\\omega n}$ é usado como entrada de um sistema linear e invariante no tempo com resposta em frequência $H(e^{j\\omega})$, então sua saída será:\n",
    "\n",
    "$y[n] = H(e^{j\\omega})e^{j\\omega n}$\n",
    "\n",
    "Então ao expressar um sinal periódico como uma série de Fourier:\n",
    "\n",
    "$x[n] = \\displaystyle\\sum_{k=<T_0>} c_ke^{jk\\omega_0n}$\n",
    "\n",
    "a sua saída será:\n",
    "\n",
    "$y[n] = \\displaystyle\\sum_{k=<T_0>} c_kH(e^{j\\omega})e^{jk\\omega_0n}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31064d6a-7463-4f3b-873d-44a1ea7d5341",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### Exemplo 7\n",
    "\n",
    "Um sistema linear e invariante no tempo é um **filtro-ideal**, com a seguinte resposta em frequência:\n",
    "\n",
    "$H(e^{j\\omega}) = \\left\\{\\begin{array}{cc}1& ,|\\omega|< \\frac{8}{5}  \\\\0& \\text{, c.c.} \\end{array}\\right.$\n",
    "\n",
    "Um filtro-ideal é um sistema que tem ganho 1 até uma determinada frequência $\\omega_c$ e ganho 0 para frequências maiores do que $\\omega_c$.\n",
    "\n",
    "Um onda quadrada com período 10 e valor 1 entre 0 e 5 instantes e valor 0 entre 6 e 10 é usada como sinal de entrada. Esse sinal tem os seguintes coeficientes da série de Fourier (veja exemplo 3):\n",
    "\n",
    "$c_k = \\frac{1}{10}\\left(\\frac{\\mathrm{sen}(\\frac{k\\pi}{2})}{\\mathrm{sen}(\\frac{k\\pi}{10})}\\right)e^{j\\frac{-2k\\pi}{5}}$ para $k\\neq 0, \\pm 10, \\pm 20...$\n",
    "\n",
    "e $c_0=0,5$ para $k= 0, \\pm 10, \\pm 20...$.\n",
    "\n",
    "A frequência fundamental desse sinal é $\\omega_0 = \\frac{2\\pi}{10}=\\frac{\\pi}{5}$.\n",
    "\n",
    "Então, a saída desse sistema para a onda quadrada como entrada é:\n",
    "\n",
    "$y[n]=\\displaystyle\\sum_{k=-\\infty}^\\infty c_kH(e^{jk\\omega_0})e^{jk\\omega_0n}$\n",
    "\n",
    "Para $k = 3$, a frequência correspondente é $\\omega = 3\\omega_0 = 3\\frac{\\pi}{5}> \\frac{8}{5}$. Para frequências acima de $\\frac{8}{5}$, $H(e^{j\\omega}) = 0$. Então, a saída fica:\n",
    "\n",
    "$y[n] = \\displaystyle\\sum_{k=-2}^2 c_kH(e^{j\\omega})e^{jk\\omega_0n} = 0.5+\\displaystyle\\sum_{k=1}^2\\frac{1}{10}\\left(\\frac{\\mathrm{sen}(\\frac{-k\\pi}{2})}{\\mathrm{sen}(\\frac{-k\\pi}{10})}\\right)e^{j\\frac{2k\\pi}{5}}e^{-jk\\frac{\\pi}{5}n}+\\frac{1}{10}\\left(\\frac{\\mathrm{sen}(\\frac{k\\pi}{2})}{\\mathrm{sen}(\\frac{k\\pi}{10})}\\right)e^{j\\frac{-2k\\pi}{5}}e^{jk\\frac{\\pi}{5}n}$\n",
    "\n",
    "$y[n] = \\frac{1}{10}\\left(\\frac{\\mathrm{sen}(-\\pi)}{\\mathrm{sen}(-\\frac{\\pi}{5})}\\right)e^{j\\frac{4\\pi}{5}}e^{-j2\\frac{\\pi}{5}n} + \\frac{1}{10}\\left(\\frac{\\mathrm{sen}(-\\frac{\\pi}{2})}{\\mathrm{sen}(-\\frac{\\pi}{10})}\\right)e^{j\\frac{2\\pi}{5}}e^{-j\\frac{\\pi}{5}n} + \\frac{1}{10}0.5 + \\frac{1}{10}\\left(\\frac{\\mathrm{sen}(\\frac{\\pi}{2})}{\\mathrm{sen}(\\frac{\\pi}{10})}\\right)e^{j\\frac{-2\\pi}{5}}e^{j\\frac{\\pi}{5}n} + \\frac{1}{10}\\left(\\frac{\\mathrm{sen}(\\pi)}{\\mathrm{sen}(\\frac{\\pi}{5})}\\right)e^{j\\frac{-4\\pi}{5}}e^{j2\\frac{\\pi}{5}n}$\n",
    "\n",
    "$y[n] = \\frac{1}{10}\\left(\\frac{0}{\\mathrm{sen}(-\\frac{\\pi}{5})}\\right)e^{j\\frac{4\\pi}{5}}e^{-j2\\frac{\\pi}{5}n} + \\frac{1}{10}\\left(\\frac{-1}{\\mathrm{sen}(-\\frac{\\pi}{10})}\\right)e^{j\\frac{2\\pi}{5}}e^{-j\\frac{\\pi}{5}n} + \\frac{1}{20} + \\frac{1}{10}\\left(\\frac{1}{\\mathrm{sen}(\\frac{\\pi}{10})}\\right)e^{j\\frac{-2\\pi}{5}}e^{j\\frac{\\pi}{5}n} + \\frac{1}{10}\\left(\\frac{0}{\\mathrm{sen}(\\frac{\\pi}{5})}\\right)e^{j\\frac{-4\\pi}{5}}e^{j2\\frac{\\pi}{5}n}$\n",
    "\n",
    "$y[n] = \\frac{1}{10}\\left(\\frac{1}{0.31}\\right)e^{j\\frac{2\\pi}{5}}e^{-j\\frac{\\pi}{5}n} + \\frac{1}{20} + \\frac{1}{10}\\left(\\frac{1}{0.31}\\right)e^{j\\frac{-2\\pi}{5}}e^{j\\frac{\\pi}{5}n} = \\frac{1}{20}+\\cos\\left(\\frac{\\pi}{5}n-\\frac{2\\pi}{5}\\right)$\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62843e49-f0b3-47dc-bb04-77e0979675da",
   "metadata": {},
   "source": [
    "## Exercícios\n",
    "\n",
    "**1)** Demonstre o teorema de Parseval para série de Fourier de tempo discreto.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71248493-24f5-420d-9bda-a4b49efa8676",
   "metadata": {},
   "source": [
    "**2)** Calcule os coeficientes da série de Fourier dos sinais abaixo:\n",
    "\n",
    "a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "8f875bf2-e8aa-43dd-b219-c1c1ae8b39b1",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "40190868a2af43d69186b77281aa5ad7",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
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       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = np.arange(-10,11)\n",
    "x = [1,-5, 3,1,1, -5, 3,1,1,-5,3,1,1,-5,3,1,1, -5,3,1,1]\n",
    "plt.figure()\n",
    "plt.stem(n, x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5fa4bd5-ac5e-4c0d-b779-fbbc4913eaba",
   "metadata": {
    "tags": []
   },
   "source": [
    "b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "7c38bff1-81bb-4d2f-a270-1f374e7f267c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "aae4bb040aaa4c1faa9997f0e909bc52",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = np.arange(-10,11)\n",
    "x = [2,2, -1,-1,-1,2,2,-1,-1,-1,2,2,-1,-1,-1,2,2,-1,-1,-1,2]\n",
    "plt.figure()\n",
    "plt.stem(n, x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a62d0ea8-06c5-4e29-bcf5-38505724bba5",
   "metadata": {
    "tags": []
   },
   "source": [
    "c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "cd8c4bdc-3d45-420d-b34d-b6c860238d97",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "93ca20e6d2df42b4b268f1f9389d00b6",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = np.arange(-10,11)\n",
    "x = [1,2, 3,4,1,2, 3,4,1,2, 3,4,1,2, 3,4,1,2, 3,4,1]\n",
    "plt.figure()\n",
    "plt.stem(n, x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d28f447d-9d40-4d85-8cfd-ffda881f90c8",
   "metadata": {},
   "source": [
    "d) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "d061b517-d54e-4338-aaab-8752aa86c59c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "035b4ba0be92430989f6781cca87c939",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = np.arange(-10,11)\n",
    "x = [1,1, 1,1,1,0, 0,0,0,0, 1,1,1,1,1,0,0,0, 0,0,1]\n",
    "plt.figure()\n",
    "plt.stem(n, x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9a31550-4cd6-43d8-9a64-2c1c5633a388",
   "metadata": {},
   "source": [
    "**3)** Considere um sistema com a seguinte resposta em frequência:\n",
    "\n",
    "$H(e^{j\\omega}) = \\left\\{\\begin{array}{cc}1 &, |\\omega|< \\frac{\\pi}{6} \\\\ 0 &,\\frac{\\pi}{6} \\leq |\\omega|< \\pi \\\\ H(e^{j(\\omega-2\\pi)})&, \\forall \\omega\\end{array}\\right.$\n",
    "\n",
    "\n",
    "Qual a saída do sistema para a seguinte entrada:\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "afe074e4-f43f-40a3-95e3-443e4b8a0cc9",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0d6aa81466c54bc8a6564870cf4f3002",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = np.arange(-10,11)\n",
    "x = [1,2, 3,1,2,3, 1,2,3,1, 2,3,1,2,3,1,2,3, 1,2,3]\n",
    "plt.figure()\n",
    "plt.stem(n, x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb2fcee7-9ace-476e-b7e0-0669e1d44116",
   "metadata": {},
   "source": [
    "**4)** Um sistema de tempo discreto tem a seguinte resposta ao impulso:\n",
    "\n",
    "$h[n] = a\\delta[n] + b\\delta[n-1] + c\\delta[n-2]$\n",
    "\n",
    "O sinal $x[n]$, mostrado no gráfico abaixo, é colocado na entrada do sistema."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "ff864f57-06bf-4446-8ccd-38018e9b8cec",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a2a7b06532e6453ea49dc8bd00ecf19b",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = np.arange(-10,11)\n",
    "x = [1,0,4,2, 1,0,4,2, 1,0,4,2, 1,0,4,2, 1,0,4,2, 1]\n",
    "plt.figure()\n",
    "plt.stem(n, x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b0af8f7-fbce-4450-8340-21cbc2ad7222",
   "metadata": {},
   "source": [
    "É obtido o seguinte sinal de saída:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "23cb95bc-7413-4ecf-9380-b3014e51bcca",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "16924a59ff4e48998372c532d2006e9c",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = np.arange(-10,11)\n",
    "x = [10,4,10,4, 10,4,10,4, 10,4,10,4, 10,4,10,4, 10,4,10,4, 10]\n",
    "plt.figure()\n",
    "plt.stem(n, x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d36bc4e-8383-41e9-8957-b1d13e89900f",
   "metadata": {},
   "source": [
    "Quais os valores de $a$, $b$ e $c$?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34cdca2a-52de-4009-9730-8ab388050770",
   "metadata": {},
   "source": [
    "**5)** Encontre e faça o gráfico dos coeficientes da série de Fourier dos seguintes sinais.\n",
    "\n",
    "a) $x_1[n] = \\mathrm{sen}(3.2\\pi n)+\\cos(2.4\\pi n)$\n",
    "\n",
    "b) $x_2[n] = \\cos(2.2\\pi n)+\\cos(3.3\\pi n)$\n",
    "\n",
    "c) $x_3[n] = \\cos\\left(\\frac{2\\pi}{4}n\\right) + \\cos\\left(\\frac{2\\pi}{7}n\\right) $\n",
    "\n",
    "d) $x_4[n] = \\cos\\left(\\frac{2\\pi}{5}n\\right) + \\cos\\left(\\frac{2\\pi}{9}n\\right) $"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d35a77e-7419-405e-8d9d-05f9a372b42d",
   "metadata": {},
   "source": [
    "**6)** Encontre e faça o gráfico dos coeficientes da série de Fourier dos seguintes sinais.\n",
    "\n",
    "a) $x_1[n] = \\left\\{\\begin{array}{cc}\\delta[n]&, 0<n<N_0 \\\\ x_1[n-N_0]&, \\forall n \\end{array}\\right.$\n",
    "\n",
    "b) $x_2[n] = \\left\\{\\begin{array}{cc}\\delta[n]-\\delta[n-2]&, 0<n<4 \\\\ x_2[n-4]&, \\forall n \\end{array}\\right.$\n",
    "\n",
    "c) $x_3[n] = \\left\\{\\begin{array}{cc}\\delta[n]-\\delta[n-2] +\\delta[n-4]-\\delta[n-6] &, 0<n<8 \\\\ x_3[n-8]&, \\forall n \\end{array}\\right.$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53b8fcfd-94cd-4138-bbc1-10c25ddf7341",
   "metadata": {},
   "source": [
    "**7)** Encontre a saída dos sistemas abaixo para a seguinte entrada:\n",
    "\n",
    "$x[n] = \\left\\{\\begin{array}{cc}1-\\delta[n] - \\delta[n-6]&, 0<n<12 \\\\ x[n-12]&, \\forall n \\end{array}\\right.$\n",
    "\n",
    "a) $H(z) =  \\frac{10z-8}{z^2}$\n",
    "\n",
    "b) $y[n] = 0.5y[n-1] + 2x[n]$\n",
    "\n",
    "c) $H(z) = \\frac{1}{1+0.9z^{-1}}$\n",
    "\n",
    "d) $y[n] = -0.4y[n-1] + x[n-1]$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36518ccd-3f65-4b3e-a302-b3b3b582ffd3",
   "metadata": {},
   "source": [
    "## Referências\n",
    "\n",
    "\n",
    "- Ulaby, FT e Yagle, AE, Signals & Systems: Theory and Applications, 2018, [ss2.eecs.umich.edu](ss2.eecs.umich.edu)\n",
    "- Lathi, BP, Sinais e Sistemas Lineares, 2007\n",
    "- Oppenheim, M.  e Willsky, S., Sistemas e Sinais, 2010"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c640804-cc3b-4938-8c8e-1ca8bc1829c6",
   "metadata": {},
   "source": [
    "## Solução dos exercícios"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4cd024bc-3db0-40d6-ab66-9fbeceba38a4",
   "metadata": {},
   "source": [
    "**1)** Resolvido por Catherine\n",
    "\n",
    "$$\n",
    "\\frac{1}{N} \\sum_{k=0}^{N-1} |a_k|^2 + |b_k|^2 = \\sum_{n=-\\infty}^\\infty |x[n]|^2\n",
    "$$\n",
    "\n",
    "**Demonstração:**\n",
    "A Série de Fourier de \\(x[n]\\) é dada por:\n",
    "\n",
    "$$\n",
    "x[n] = \\sum_{k=-\\infty}^\\infty c_k e^{j2\\pi nk/N}\n",
    "$$\n",
    "\n",
    "onde $c_k = a_k - jb_k$ são os coeficientes complexos da Série de Fourier.\n",
    "\n",
    "A energia do sinal no domínio do tempo é definida como:\n",
    "\n",
    "$$\n",
    "E_x = \\sum_{n=-\\infty}^\\infty |x[n]|^2\n",
    "$$\n",
    "\n",
    "Substituindo a expressão da Série de Fourier:\n",
    "\n",
    "$$\n",
    "E_x = \\sum_{n=-\\infty}^\\infty \\left|\\sum_{k=-\\infty}^\\infty c_k e^{j2\\pi nk/N}\\right|^2\n",
    "$$\n",
    "\n",
    "$$\n",
    "E_x = \\sum_{n=-\\infty}^\\infty \\left(\\sum_{k=-\\infty}^\\infty c_k e^{j2\\pi nk/N}\\right) \\left(\\sum_{m=-\\infty}^\\infty c_m^* e^{-j2\\pi nm/N}\\right)\n",
    "$$\n",
    "\n",
    "$$\n",
    "E_x = \\sum_{n=-\\infty}^\\infty \\sum_{k=-\\infty}^\\infty \\sum_{m=-\\infty}^\\infty c_k c_m^* e^{j2\\pi n(k-m)/N}\n",
    "$$\n",
    "\n",
    "$$\n",
    "E_x = \\sum_{k=-\\infty}^\\infty \\sum_{m=-\\infty}^\\infty c_k c_m^* \\sum_{n=-\\infty}^\\infty e^{j2\\pi n(k-m)/N}\n",
    "$$\n",
    "\n",
    "A soma interna envolvendo \\(n\\) é uma série de impulsos periódicos \\(N\\), o que significa que:\n",
    "\n",
    "$$\n",
    "\\sum_{n=-\\infty}^\\infty e^{j2\\pi n(k-m)/N} = N \\cdot \\delta[k-m]\n",
    "$$\n",
    "\n",
    "\n",
    "$$\n",
    "E_x = N \\sum_{k=-\\infty}^\\infty c_k c_k^* = N \\sum_{k=-\\infty}^\\infty |c_k|^2\n",
    "$$\n",
    "\n",
    "$$\n",
    "E_x = N \\sum_{k=-\\infty}^\\infty (a_k^2 + b_k^2)\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\frac{1}{N} \\sum_{k=-\\infty}^\\infty (a_k^2 + b_k^2) = \\sum_{n=-\\infty}^\\infty |x[n]|^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0141c318-13e8-4772-a37c-829727878b4d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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