Introducao.ipynb

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    "# Introdução\n",
    "\n",
    "Renato Naville Watanabe"
   ]
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   "source": [
    "## Preparação do ambiente"
   ]
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
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   "source": [
    "## Definição"
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   "source": [
    "O estudo da Engenharia se ocupa em boa parte do estudo de Sistemas. Se você está fazendo esse curso, você já deve ter feito diversos outros cursos sobre diferentes tipos de sistemas, como sistemas mecânicos, elétricos, biológicos, térmicos, fluídicos, econômicos, sociais, entre muitos outros."
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    "**Sistemas  nada mais são do que conjuntos de componentes que se interligam para realizar alguma coisa**."
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    "## Exemplos\n",
    "\n",
    "Vamos ver alguns exemplos de sistemas."
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    "---\n",
    "### Circuito RC\n",
    "\n",
    "<img src=https://upload.wikimedia.org/wikipedia/commons/thumb/e/e0/RC_Series_Filter_%28with_V%26I_Labels%29.svg/1920px-RC_Series_Filter_%28with_V%26I_Labels%29.svg.png width=\"400\">"
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    "Nele, a tensão de entrada $V_{in}$ vai modificar a tensão do capacitor $V_c$. Podemos representar o circuito RC com o diagrama de blocos abaixo. A tensão $V_{in}$, sendo a tensão do gerador, entra no bloco que representa o circuito RC. Saindo do bloco está a tensão no capacitor $V_c$."
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    "\n",
    "<img src=Imagens/RCsystem.png width=\"500\">"
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    "Alguém poderia perguntar qual a razão da tensão do gerador entrar no bloco e a tensão no capacitor sair. Isso vem do funcionamento do circuito. A tensão $V_{in}$ normalmente é algo que o operador controla e vai influenciar o funcionamento do circuito. A tensão $V_c$ é uma tensão que por algum motivo quem está analisando o circuito tem interesse. É claro que a tensão $V_R$ também  poderia ser o sinal de saída do sistema, dependendo do interesse da análise.\n",
    "\n",
    "---"
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    "---\n",
    "\n",
    "### Eletrocardiograma\n",
    "\n",
    "Outro exemplo é o eletrocardiograma, em que o potencial elétrico dos músculos cardíacos são captados por eletrodos e mostrados na tela ou papel em forma gráfica.\n",
    "\n",
    "\n",
    "<img src=https://upload.wikimedia.org/wikipedia/commons/thumb/5/53/Patient_lying_in_hospital_bed_in_intensive_care_unit_in_Germany_in_2015.jpg/800px-Patient_lying_in_hospital_bed_in_intensive_care_unit_in_Germany_in_2015.jpg width=\"300\">"
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    "Nós podemos  colocar o aparelho de ECG como um diagrama de blocos:\n",
    "\n",
    "<img src=Imagens/ECGsystem.png width=\"500\">\n",
    "\n",
    "\n",
    "---"
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    "---\n",
    "\n",
    "### Corpo humano\n",
    "\n",
    "Outro exemplo é o corpo humano, que é um sistema composto de diversos outros sistemas.\n",
    "\n",
    "<img src=https://static.sciencelearn.org.nz/images/images/000/002/307/full/The-body-s-systems20161104-16595-1aca5q9.jpg?167416796 width=\"300\">\n",
    "\n",
    "Cada subsistema do corpo humano realiza alguma ação em resposta a algum estímulo."
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    "Abaixo está o diagrama de blocos de um subsistema específico do corpo humano, o pâncreas:\n",
    "\n",
    "\n",
    "<img src=Imagens/pancreassystem.png width=\"500\">\n",
    "\n",
    "O pâncreas libera insulina de acordo com o nível de glicose no sangue.\n",
    "\n",
    "---"
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    "---\n",
    "\n",
    "### Movimento do motorista dentro de um carro\n",
    "\n",
    "Um outro exemplo é o movimento que a cabeça do motorista faz quando o carro balança. Essa análise em um estudo de ergonomia do carro pode ser importante.\n",
    "\n",
    "\n",
    "<img src=Imagens/bancocarro.png width=\"500\">"
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    "O diagrama de blocos desse sistema é:\n",
    "\n",
    "<img src=Imagens/carro_system.png width=\"500\">\n",
    "\n",
    "---"
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    "---\n",
    "\n",
    "### Forno\n",
    "\n",
    "Um outro exemplo seria a temperatura dentro do forno após o fogo ser ligado. \n",
    "\n",
    "<img src=https://img.freepik.com/vetores-gratis/fogao-eletrico-com-forno-isolado-no-fundo-branco_1308-59051.jpg width=\"200\">"
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    "O diagrama de blocos do forno é:\n",
    "\n",
    "<img src=Imagens/forno_system.png width=\"500\">\n",
    "\n",
    "---"
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    "---\n",
    "\n",
    "### Inflação\n",
    "\n",
    "\n",
    "Um outro possível sistema seria considerar o sistema econômico do Brasil e medir a sua taxa de inflação a cada mês em resposta, por exemplo, à taxa de juros.\n",
    "\n",
    "\n",
    "<img src=Imagens/inflacao_system.png width=\"500\">\n",
    "\n",
    "\n",
    "---"
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   "source": [
    "Poderíamos dar muitos outros exemplos, mas vamos parar aqui. O objetivo desse curso é estudar como os sistemas de uma maneira geral se comportam em resposta a sinais que os influenciam. O estudo aqui não se preocupará em entender os mecanismos específicos de cada tipo de sistema, mas se ocupará das características comuns que esses sistemas têm. As técnicas vistas neste curso poderão ser aplicadas sempre que for possível conseguir uma descrição matemática do sistema sendo estudado."
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    "## O formalismo da teoria de sistemas\n",
    "\n",
    "Toda a teoria de sistemas é baseada no formalismo abaixo:\n",
    "\n",
    "\n",
    "<img src=Imagens/sistema.png width=\"500\">\n",
    "\n",
    "\n",
    "Como pôde ser visto nos exemplos acima, esse formalismo serve para muitos tipos de sistemas. Ele será usado até o final do curso. \n",
    "\n",
    "Sistemas podem ter um ou mais sinais de entrada de saída. Neste curso consideraremos apenas sistemas com uma entrada e uma saída.\n",
    "\n"
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    "## Sinais\n",
    "\n",
    "**Sinais são funções, na maioria das vezes do tempo, que vão servir de entrada e de saída para os sistemas.**\n",
    "\n",
    "Sinais podem representar diversos fenômenos, como velocidade de um carro, voz de uma pessoa, força exercida por um músculo, batimentos cardíacos, taxa de juros ao longo dos meses, entre infinitos outros exemplos.\n",
    "\n",
    "Matematicamente, sinais são representados como sendo gerados por funções de uma ou mais variáveis independentes. Aqui, consideraremos apenas uma **variável independente**, e na maioria das vezes, é o **tempo**.\n"
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    "### Sinais de tempo contínuo\n",
    "\n",
    "Para deixar claro que um sinal é de tempo contínuo, o tempo será sempre denotado por $t$ e estará entre parânteses. Por exempo,\n",
    "\n",
    "$$x(t) = \\cos(2\\pi t) $$\n",
    "\n",
    "Os sinais de tempo contínuo têm valores para todo $t$ pertencente ao conjunto dos números reais.\n",
    "\n",
    "Podemos representar um sinal contínuo através da forma gráfica."
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7fc9f152b700>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy as sym\n",
    "\n",
    "t = sym.symbols('t')\n",
    "sym.plot(sym.cos(2*sym.pi*t), (t,-3,3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1c59dd2-c201-42c5-8da2-262f11fa840a",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "source": [
    "Sinais de tempo contínuo podem ser usados para representar sinais que são definidos de forma contínua ao longo do tempo, como sinal da fala de uma pessoa, a temperatura de uma localidade ao longo do dia."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc56cf6b-9c4d-4529-b78e-e1c72c9b608b",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Sinais de tempo discreto\n",
    "\n",
    "Para deixar claro que um sinal é de tempo discreto, o tempo será representado por $n$ entre colchetes. Por exemplo:\n",
    "\n",
    "$$x[n] = \\cos\\left(\\frac{2\\pi n}{N}\\right) $$\n",
    "\n",
    "Os sinais de tempo discreto só têm valores para $n$ inteiro. Eles não são definidos para $n$ entre os inteiros.\n",
    "\n",
    "Podemos representar um sinal de tempo discreto na forma gráfica. É comum usar o tipo de gráfico conhecido como *stem* para representar sinais de tempo discreto. Esse tipo de gráfico consiste em usar barras que vão do zero até o valor do sinal com uma pequena bolinha na sua ponta. É esse tipo de gráfico que usaremos no curso para sinais de tempo discreto. O gráfico do sinal acima é:\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "48cfbfcf-ac56-424f-b848-bce1aabf49b8",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<StemContainer object of 3 artists>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 10\n",
    "n = np.arange(-10,10)\n",
    "plt.stem(n, np.cos(2*np.pi*n/N))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bafe88d3-7c7b-4c8f-baa2-84edc2201f3c",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "source": [
    "Sinais de tempo discreto podem ser usados para representar sinais que só são definidos em alguns instantes, como a população de uma cidade a cada ano, o valor de uma ação a cada dia. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bdae83e6-f679-427e-8ed2-95bd46b51d6c",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Relação entre os sinais de tempo contínuo e discreto"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c24a2cb1-1b13-4a63-8f98-b17dc8885660",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "source": [
    "A maioria dos sinais presentes na natureza são de tempo contínuo. Isso pode fazer alguns pensarem que não é necessário para um engenheiro estudar sinais de tempo discreto. Talvez isso tenha sido verdade por um bom tempo, mas desde o advento dos computadores digitais, quase toda a análise e processamento dos sinais são feitos usando computadores. E computadores são inerentemente discretos.\n",
    "\n",
    "O que se costuma fazer é transformar um sinal de tempo contínuo para tempo discreto utilizando algum método de amostragem. Por exemplo, o sinal contínuo à esquerda é amostrado a cada 0,5 segundo e gera o sinal em tempo discreto à direita."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "616c8a9e-2e14-43f2-b78b-6956c66082d2",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<StemContainer object of 3 artists>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(1,2,1)\n",
    "tau = 1.5\n",
    "t = np.arange(0, 6, 0.01)\n",
    "x = np.exp(-tau*t)\n",
    "plt.plot(t, x)\n",
    "T = 0.5\n",
    "tamos = np.arange(0, 6, T)\n",
    "xamos = np.exp(-tau*tamos)\n",
    "plt.scatter(tamos, xamos, color='red')\n",
    "plt.subplot(1,2,2)\n",
    "n = np.arange(12)\n",
    "xdis = np.exp(-tau*n*T)\n",
    "plt.stem(n, xdis)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90b8d5b6-b63b-48ee-a434-b277f96305ad",
   "metadata": {},
   "source": [
    "Mais adiante, veremos mais as implicações de se fazer a amostragem de um sinal."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45bc8ad8-fbb3-4d0f-9dc0-ad1087211db4",
   "metadata": {},
   "source": [
    "## Importância dentro da Engenharia\n",
    "\n",
    "O conteúdo visto neste curso tem importância em várias áreas da Engenharia:\n",
    "\n",
    "- Processamento de Sinais\n",
    "\n",
    "- Instrumentação\n",
    "\n",
    "- Controle\n",
    "\n",
    "- Modelagem\n",
    "\n",
    "- Aprendizado de máquinas\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "330fda6f-b526-4771-88ec-b453ab2682c5",
   "metadata": {},
   "source": [
    "## Métodos vistos neste curso\n",
    "\n",
    "|**Tempo contínuo**                        | **Tempo discreto**                                                       |\n",
    "|-------------------------------------|------------------------------------------------------------------------|\n",
    "|Equações diferenciais                         |Equações de diferenças                                                                   |\n",
    "|Integral de convolução                        | Somatória de convolução                                                         |\n",
    "|Transformada de Laplace                              | Transformada Z                                                        |\n",
    "|Transformada de Fourier                           | Transformada de Fourier     de tempo discreto                                         |    \n",
    "|        -                     | Transformada discreta de Fourier                                                |\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20fad843-0a16-4c57-8014-7be29f19b5a5",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "source": [
    "## Execícios\n",
    "\n",
    "**1)** Escolha um sistema qualquer e identifique sua entrada e saída. Esse sistema tem entrada e saída de tempo discreto ou de tempo contínuo?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8067a88d-c054-43a4-b2f9-86f3f8dd91cb",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "source": [
    "**2)** Faça o gráfico dos sinais abaixo:\n",
    "\n",
    "a) $x_1(t) = e^{-3t}, t\\geq0$\n",
    "\n",
    "b) $x_2(t) = \\cos(2t)$\n",
    "\n",
    "c) $x_3[n] = \\frac{1}{3^n}, n\\geq 0$\n",
    "\n",
    "d) $x_4[n] = \\cos\\left(\\frac{\\pi}{2}n\\right)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5cb4df22-6fa7-4755-b1db-bd34b3be5b88",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Referências\n",
    "\n",
    "- Oppenheim, M.   e Willsky, S., Sistemas e Sinais, 2010\n",
    "- Ulaby, FT e Yagle, AE, Signals & Systems: Theory and Applications, 2018, [ss2.eecs.umich.edu](ss2.eecs.umich.edu)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1469b52d-85b2-445e-aa8f-201257215e27",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "## Solução dos exercícios"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4608dd10-af8f-4f46-8dd7-3902b5fd3c23",
   "metadata": {},
   "source": [
    "**1)** Resolvido por Juliana Soares da Silva de Oliveira\n",
    "\n",
    "\n",
    "O corpo humano é um sistema complexo composto por vários subsistemas interligados. Um exemplo disso é o coração, que desempenha um papel vital no funcionamento do corpo humano. \n",
    "\n",
    "Ao considerarmos o coração como um subsistema específico, podemos identificar sua entrada e saída. A entrada do coração consiste no sangue que chega às suas câmaras cardíacas, mais precisamente nas aurículas. Esse sangue contém oxigênio, nutrientes e resíduos metabólicos, sendo transportado pelos vasos sanguíneos em todo o corpo. Por sua vez, a saída do coração é representada pelo sangue bombeado pelas câmaras cardíacas, ou seja, pelos ventrículos. Essa função é comparada a uma bomba que impulsiona o sangue para os vasos sanguíneos, permitindo sua distribuição para os tecidos e órgãos de todo o organismo.\n",
    "\n",
    "Em relação ao tempo, a entrada e a saída do coração são contínuas. O sangue flui de maneira ininterrupta para dentro e para fora do coração, sem pausas ou intervalos discretos. Esse fluxo contínuo é essencial para o funcionamento adequado do sistema circulatório e para suprir as necessidades do corpo humano."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b36dff6-22b4-45c6-9d93-75753c4a73e9",
   "metadata": {},
   "source": [
    "**2)** Resolvido por Juliana Soares da Silva de Oliveira\n",
    "\n",
    "a) $x_1(t) = e^{-3t}, t\\geq0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2e9614bb-8f82-4dc3-a2a3-d3bca0a555d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "t = np.linspace(0, 5, 100)\n",
    "\n",
    "y = np.exp(-3 * t)\n",
    "\n",
    "plt.plot(t, y)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('x1(t)')\n",
    "plt.title('Gráfico do sinal x1(t)')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "defc3344-4b5c-4478-b801-ee28b8bb941b",
   "metadata": {},
   "source": [
    "b) $x_2(t) = \\cos(2t)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ef869412-a23a-443a-90b7-e4a6e7a6de08",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "t = np.linspace(0, 4*np.pi, 100)\n",
    "x2 = np.cos(2*t)\n",
    "\n",
    "plt.plot(t, x2)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('x2(t)')\n",
    "plt.title('Gráfico do sinal x2(t)')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75a82374-1ccd-4013-a156-ab4e0b898cc7",
   "metadata": {},
   "source": [
    "c) $x_3[n] = \\frac{1}{3^n}, n\\geq 0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c39da7bc-3cfb-4278-9df7-ce28b62a583e",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_375997/3631554767.py:8: MatplotlibDeprecationWarning: The 'use_line_collection' parameter of stem() was deprecated in Matplotlib 3.6 and will be removed two minor releases later. If any parameter follows 'use_line_collection', they should be passed as keyword, not positionally.\n",
      "  plt.stem(n, x3, use_line_collection=True)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "n = np.arange(0, 10)\n",
    "\n",
    "x3 = 1 / (3 ** n)\n",
    "\n",
    "plt.stem(n, x3, use_line_collection=True)\n",
    "plt.xlabel('n')\n",
    "plt.ylabel('x3[n]')\n",
    "plt.title('Gráfico do sinal x3[n]')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38c4c397-fa34-45c7-98de-e3d3195c24be",
   "metadata": {},
   "source": [
    "d) $x_4[n] = \\cos\\left(\\frac{\\pi}{2}n\\right)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4e5667a4-bce0-4f1e-a522-f7c773ea1ff3",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_375997/2864134416.py:8: MatplotlibDeprecationWarning: The 'use_line_collection' parameter of stem() was deprecated in Matplotlib 3.6 and will be removed two minor releases later. If any parameter follows 'use_line_collection', they should be passed as keyword, not positionally.\n",
      "  plt.stem(n, x4, use_line_collection=True)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "n = np.arange(-10, 11)\n",
    "\n",
    "x4 = np.cos(n * np.pi / 2)\n",
    "\n",
    "plt.stem(n, x4, use_line_collection=True)\n",
    "plt.xlabel('n')\n",
    "plt.ylabel('x4[n]')\n",
    "plt.title('Gráfico do sinal x4[n]')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fe0cd8ea-7251-46c3-951f-546bcaf20fd8",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}