TransfVarIndepDiscreto.ipynb

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      "source": [
        "# Transformações de sinais de tempo discreto na variável independente\n",
        "\n",
        "Renato Naville Watanabe"
      ]
    },
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      "source": [
        "## Preparação do ambiente"
      ]
    },
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      "source": [
        "# @title\n",
        "import sympy as sym\n",
        "from sympy.plotting import plot\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
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      "source": [
        "## Transformações\n",
        "\n",
        "O conceito de transformação de um sinal é extremamente importante na análise de sinais. Por exemplo, um equipamento que analisa o sinal de eletrocardiograma obtido de um paciente faz diversas transformações no sinal obtido para fornecer as informações necessárias. Outro exemplo a ser considerado é a transformação que o sistema nervoso e muscular faz ao receber os sinal neural e produzir força.\n",
        "\n",
        "Aqui veremos diversas transformações matemáticas que um sinal pode sofrer. Essas transformações serão muito importantes para caracterizar sistemas complexos mais para frente."
      ]
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        "### Deslocamento no tempo\n",
        "\n",
        "Uma transformação muito importante é o deslocamento no tempo. Essa transformação acontece quando temos dois sinais de tempo discreto $x$ e $y$ com:\n",
        "\n",
        "$$y[n] = x[n-N_d]$$\n",
        "\n",
        "\n",
        "\n",
        "Nesse caso, o sinais $x$ e $y$ têm a mesma forma, mas $y$ está deslocado no tempo em relação a $x$ (atrasado no caso de $N_d$ ser positivo e adiantado caso seja positivo).\n",
        "\n"
      ]
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      "source": [
        "---\n",
        "\n",
        "#### Exemplo 1\n",
        "\n",
        "O sinal $x_2[n] = \\cos\\left(\\pi \\frac{n-3}{N}\\right)$ é o sinal $x_1[n] = \\cos\\left(\\pi\\frac{n}{N}\\right)$ atrasado de 3 instantes."
      ]
    },
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        "colab": {
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          "height": 447
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      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7d7205f31d80>"
            ]
          },
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          "execution_count": 3
        },
        {
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          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# @title\n",
        "n = np.arange(0, 10)\n",
        "N = 5\n",
        "Nd = 3\n",
        "x1 = np.cos(np.pi*n/N)\n",
        "x2 = np.cos(np.pi*(n-Nd)/N)\n",
        "plt.stem(n, x1, linefmt='blue', label='x_1')\n",
        "plt.stem(n, x2, linefmt='red', label='x_2')\n",
        "plt.legend()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "606c2c22-f424-4d16-81a0-9e2b8d88fad5",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "606c2c22-f424-4d16-81a0-9e2b8d88fad5"
      },
      "source": [
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "55c54869-5f0b-42fa-b2fb-6fe540e8643b",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "55c54869-5f0b-42fa-b2fb-6fe540e8643b"
      },
      "source": [
        "### Reflexão no tempo\n",
        "\n",
        "A reflexão no tempo é a transformação em que um sinal aparece espelhado em relação à ordenada do gráfico.  Essa transformação irá aparecer numa operação muito importante entre sinais conhecida como convolução.  "
      ]
    },
    {
      "cell_type": "markdown",
      "id": "0f2f8f98-f834-4ee5-987a-6f46b1d48800",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "0f2f8f98-f834-4ee5-987a-6f46b1d48800"
      },
      "source": [
        "---\n",
        "\n",
        "#### Exemplo 2\n",
        "\n",
        "Abaixo um exemplo de reflexão no tempo para o caso discreto. Note que $x_1[n] = x_2[-n]$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "e5af77b9-79ed-4507-9fe2-79ca28cc12cd",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "e5af77b9-79ed-4507-9fe2-79ca28cc12cd",
        "outputId": "30cce806-f46c-43b1-ec8e-8a1cba4cfa2b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "cellView": "form"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7d71f103f0d0>"
            ]
          },
          "metadata": {},
          "execution_count": 4
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# @title\n",
        "n = np.arange(-5,6)\n",
        "x1 = (-0.5)**n - (0.7)**n\n",
        "x2 = (-0.5)**(-n) - (0.7)**(-n)\n",
        "plt.stem(n, x1, linefmt='blue', label='x_1')\n",
        "plt.stem(n, x2, linefmt='red', label='x_2')\n",
        "plt.legend()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "992a27b4-dd4b-4412-8132-127c07ef3e45",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "992a27b4-dd4b-4412-8132-127c07ef3e45"
      },
      "source": [
        "---\n",
        "\n",
        "### Mudança de escala\n",
        "\n",
        "Outra transformação importante é a mudança de escala de um sinal. Ao multiplicar o tempo por uma constante o sinal corre mais rápido (se a constante for maior do que 1) ou mais devagar (se a constante for menor do que 1).  Esse tipo de transformação é muito usado em aplicativos de mensagem, que possibilitam ouvir uma mensagem de áudio mais rapidamente.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "6b7587fe-3f54-4faf-bd6c-3e150b1e6f88",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "6b7587fe-3f54-4faf-bd6c-3e150b1e6f88"
      },
      "source": [
        "Abaixo estão exemplos de sinais de tempo discreto em diferentes escalas. Os três sinais têm o mesmo formato, embora devido à natureza discreta dos sinais, eles não tenham exatamente os mesmos valores.\n",
        "\n",
        "O sinal $x_2[n] = x_1[2n]$ é comprimido em relação ao $x_1[n]$. No caso de tempo discreto, essa mudança de escala com a escala maior do que 1 é chamada de subamostragem. Esse nome é usado porque o sinal perde alguns valores em relação ao sinal original. Note no gráfico que o sinal $x_2[n]$ não tem alguns valores que estão presentes no sinal $x_1[n]$.\n",
        "\n",
        "O sinal $x_3[n] = x_1[0.5n]$ é expandido em relação ao $x_1[n]$. No caso de tempo discreto, essa mudança de escala com a escala menor do que 1 é chamada de superamostragem. Esse nome é usado porque o sinal $x_3[n]$ tem valores que não estão presentes no sinal $x_1[n]$. No gráfico abaixo é possível observar esse fenômeno."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "5faa85ac-3c59-4ebb-89d0-ce288bb1227a",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "5faa85ac-3c59-4ebb-89d0-ce288bb1227a",
        "outputId": "e6812bba-5760-43a5-8fd2-2862561f629c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 450
        },
        "cellView": "form"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7d71f0f65d50>"
            ]
          },
          "metadata": {},
          "execution_count": 5
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# @title\n",
        "n = np.arange(0,30)\n",
        "x1 = (0.7)**n - (0.5)**n\n",
        "x2 = (0.7)**(2*n) - (0.5)**(2*n)\n",
        "x3 = (0.7)**(0.5*n) - (0.5)**(0.5*n)\n",
        "plt.stem(n, x1, linefmt='blue', label='x_1')\n",
        "plt.stem(n, x2, linefmt='red', label='x_2')\n",
        "plt.stem(n, x3, linefmt='orange', label='x_3')\n",
        "plt.legend()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "6778bb68-31a1-4434-9631-16421ae2b6d6",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "6778bb68-31a1-4434-9631-16421ae2b6d6"
      },
      "source": [
        "## Simetria par e ímpar\n",
        "\n",
        "Uma propriedade útil para a análise de sinais é verificar se existe alguma simetria em relação ao tempo. Então são definidas duas simetrias:\n",
        "\n",
        "### Simetria par:\n",
        "\n",
        "Acontece se:\n",
        "\n",
        "$$x[n] = x[-n]$$\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "7e132098-b276-4a36-9d02-8c754a62cdf1",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "7e132098-b276-4a36-9d02-8c754a62cdf1",
        "outputId": "56efc902-588c-4795-a8e2-718b2f12c7a1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "cellView": "form"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# @title\n",
        "n = np.arange(-10,10)\n",
        "x = np.cos(0.2*np.pi*n)\n",
        "plt.stem(n, x, linefmt='blue', label='x')\n",
        "plt.legend()\n",
        "plt.grid()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "9a833251-b458-4d18-b628-2966f8dce17f",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "9a833251-b458-4d18-b628-2966f8dce17f"
      },
      "source": [
        "---\n",
        "\n",
        "### Simetria ímpar\n",
        "\n",
        "Acontece se:\n",
        "\n",
        "\n",
        "$$x[n] = -x[-n]$$\n",
        "\n",
        "\n",
        "Note que no caso do sinal ter simetria ímpar, $x[0] = 0$ (já que $x[0] = -x[0]$)."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "61a59d0b-c2d3-4aef-8b0e-4424fd71c15f",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "61a59d0b-c2d3-4aef-8b0e-4424fd71c15f"
      },
      "source": [
        "---\n",
        "\n",
        "#### Exempo 5\n",
        "\n",
        "O sinal seno, visto abaixo, tem simetria ímpar. Os instantes negativos têm os valores dos positivos com sinais trocados."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "d6e7d8db-91a8-4196-9675-7741708171ea",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "d6e7d8db-91a8-4196-9675-7741708171ea",
        "outputId": "bfad54ea-9c29-40b3-917f-a4aad14d9e58",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "cellView": "form"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# @title\n",
        "n = np.arange(-10,10)\n",
        "x = np.sin(0.2*np.pi*n)\n",
        "plt.stem(n, x, linefmt='blue', label='x')\n",
        "plt.legend()\n",
        "plt.grid()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "036eaa00-f349-4b4f-ad28-727f15ea39da",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "036eaa00-f349-4b4f-ad28-727f15ea39da"
      },
      "source": [
        "---\n",
        "\n",
        "### Decomposição em sinais pares e ímpares\n",
        "\n",
        "Qualquer sinal pode ser decomposto em uma parte par e uma parte ímpar. Abaixo as expressões decomposição para tempo contínuo\n",
        "\n",
        "$Par\\{x[n]\\} = \\frac{x[n]+x[-n]}{2}$\n",
        "\n",
        "e\n",
        "\n",
        "$Impar\\{x[n]\\} = \\frac{x[n]-x[-n]}{2}$"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "5c5b4835-76d4-46db-91ea-5185ee8377e2",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "5c5b4835-76d4-46db-91ea-5185ee8377e2"
      },
      "source": [
        "---\n",
        "\n",
        "\n",
        "#### Exemplo 6\n",
        "\n",
        "\n",
        "Por exemplo, no gráfico abaixo, são mostradas as partes par e ímpar do sinal $x[n] = 0.5^{n}-0.2^{n}$. As partes par e ímpar são encontradas usando as expressões acima.\n",
        "\n",
        "$$Par\\{x[n]\\} = \\frac{0.5^{n}-0.2^{n}+0.5^{-n}-0.2^{-n}}{2}$$\n",
        "\n",
        "$$Impar\\{x(t)\\} = \\frac{0.5^{n}-0.2^{n}-0.5^{-n}+0.2^{-n}}{2}$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "d87556a3-26d6-44a3-9aba-839573e8b850",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "d87556a3-26d6-44a3-9aba-839573e8b850",
        "outputId": "ec2696d6-6424-45ec-85bb-8424ef52e902",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "cellView": "form"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# @title\n",
        "\n",
        "n = np.arange(-5,6)\n",
        "x = 0.5**n - 0.2**n\n",
        "plt.stem(n, x, linefmt='blue', label='x')\n",
        "xpar = (0.5**n - 0.2**n+0.5**(-n) - 0.2**(-n))/2\n",
        "ximpar = (0.5**n - 0.2**n-0.5**(-n) + 0.2**(-n))/2\n",
        "plt.stem(n, ximpar, linefmt='green', label='x_{impar}')\n",
        "plt.stem(n, xpar, linefmt='red', label='x_{par}')\n",
        "\n",
        "plt.legend()\n",
        "plt.grid()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "b9bf6376-fbde-4956-a851-49965d1a98b6",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "b9bf6376-fbde-4956-a851-49965d1a98b6"
      },
      "source": [
        "---\n",
        "\n",
        "## Sinais periódicos\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "33fe8377-b951-40f2-b9cb-21aaa1469fbd",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "33fe8377-b951-40f2-b9cb-21aaa1469fbd"
      },
      "source": [
        "Um sinal de tempo discreto é periódico se existe uma constante inteira $N$ para a qual:\n",
        "\n",
        "$x[n] = x[n+kN]$\n",
        "\n",
        "para todo $n$ e $k$ inteiros."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "927a8e0b-f81c-4c11-8c0b-0d7b1d61bb8d",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "927a8e0b-f81c-4c11-8c0b-0d7b1d61bb8d"
      },
      "source": [
        "---\n",
        "\n",
        "#### Exemplo 8\n",
        "\n",
        "Abaixo está o gráfico do sinal\n",
        "\n",
        "$x[n] = \\mathrm{sen}\\left(\\frac{\\pi}{5}n + \\frac{\\pi}{4}\\right)$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "dfa01bb7-2af0-4c49-8e96-5fb280a8e4a7",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "dfa01bb7-2af0-4c49-8e96-5fb280a8e4a7",
        "outputId": "704c4627-1a18-4a6e-d7b8-85e259d2e963",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "cellView": "form"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<StemContainer object of 3 artists>"
            ]
          },
          "metadata": {},
          "execution_count": 19
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# @title\n",
        "n = np.arange(0, 30)\n",
        "Omega = np.pi/5\n",
        "theta = np.pi/4\n",
        "x = 10*np.sin(Omega*n+theta)\n",
        "plt.stem(n, x)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "51a53326-37fd-4396-b7b8-55e5b9d66e70",
      "metadata": {
        "id": "51a53326-37fd-4396-b7b8-55e5b9d66e70"
      },
      "source": [
        "O sinal acima tem período fundamental $N_0 = 10$.\n",
        "\n",
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "2dc4bc83-a6e7-48f6-b596-4c7e2cec1edb",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "2dc4bc83-a6e7-48f6-b596-4c7e2cec1edb"
      },
      "source": [
        "## Exercícios"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "01465bda-9c4c-47f8-9154-d48c6e522671",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "01465bda-9c4c-47f8-9154-d48c6e522671"
      },
      "source": [
        "**1)** Suponha que $x[n]$ seja um sinal com $x[n]=0$ para $n<-3$ e $n>2$. Para cada um dos sinais a seguir, determinar os valores de $n$ para os quais os sinais são zero.\n",
        "\n",
        "a) $y_1[n] = x[n-3]$\n",
        "\n",
        "b) $y_2[n] = x[n+4]$\n",
        "\n",
        "c) $y_3[n] = x[-n]$\n",
        "\n",
        "d) $y_4[n] = x[-n+2]$\n",
        "\n",
        "e) $y_5[n] = x[-n-2]$"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "c62f9c71-c5bd-4c3b-adb4-a629e4471a4e",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "c62f9c71-c5bd-4c3b-adb4-a629e4471a4e"
      },
      "source": [
        "**4)** O sinal de tempo discreto $x[n]$ é mostrado abaixo. Para os valores de $n$ não mostrados no gráfico, o valor de $x[n]=0$. Esboce os seguintes sinais:\n",
        "\n",
        "a) $y_1[n] = x[n-4]$\n",
        "\n",
        "b) $y_2[n] = x[2-n]$\n",
        "\n",
        "c) $y_3[n] = x[3n]$\n",
        "\n",
        "d) $y_4[n] = x[3n+1]$\n",
        "\n",
        "e) $y_5[n] = x[(n-1)^2]$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "1c92aafc-1c2c-4a3a-903f-ffaf95e9d7a1",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "1c92aafc-1c2c-4a3a-903f-ffaf95e9d7a1",
        "outputId": "50f3db75-ac25-452b-f885-060fadd463a9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "cellView": "form"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# @title\n",
        "k = np.arange(-5, 6)\n",
        "x = [0,-1, -0.5, 0.5, 1, 1, 1, 1, 0.5, 0,0]\n",
        "plt.stem(k,x)\n",
        "plt.xlabel('k')\n",
        "plt.title('x[n]')\n",
        "plt.ylabel('x[n]')\n",
        "plt.grid()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "064ae44d-efa4-4253-bc09-b7223d351b61",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "064ae44d-efa4-4253-bc09-b7223d351b61"
      },
      "source": [
        "**6)** Decomponha e rascunhe os seguintes sinais nas suas partes par e ímpar:\n",
        "\n",
        "\n",
        "a) $x_1[n] = \\left(\\frac{1}{2}\\right)^n$\n",
        "\n",
        "b) $x_2[n] = \\left(\\frac{1}{2}\\right)^n\\cos(n/10)$\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "82b63d11-2c24-4bdc-b6c8-9773c8161878",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "82b63d11-2c24-4bdc-b6c8-9773c8161878"
      },
      "source": [
        "## Referências\n",
        "\n",
        "- Oppenheim, M. Sistemas e Sinais, 2010\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"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "ee817172-1c18-4434-9e61-e7456cdb4ccc",
      "metadata": {
        "editable": true,
        "tags": [],
        "id": "ee817172-1c18-4434-9e61-e7456cdb4ccc"
      },
      "source": [
        "## Respostas dos exercícios"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "4b2ecb66",
      "metadata": {
        "id": "4b2ecb66"
      },
      "source": [
        "**1)** Resolvido por Jorge Vinicius Nascimento Lamar"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "8632148f",
      "metadata": {
        "id": "8632148f"
      },
      "source": [
        "**1)** a)  $y_1[n] = x[n-3]$\n",
        "\n",
        "Sabendo que $x[n] = 0$ para $n<-3$ e $n>2$\n",
        "\n",
        "É possivel determinar $y_1[n]=0$ fazendo:\n",
        "\n",
        "$$n-3 < -3$$\n",
        "e\n",
        "$$n-3 > 2$$\n",
        "\n",
        "portanto:\n",
        "$$n-3 < -3$$\n",
        "$$n-3+3 < -3+3$$\n",
        "$$n < 0$$\n",
        "\n",
        "e\n",
        "$$n-3 > 2$$\n",
        "$$n-3+3 > 2+3$$\n",
        "$$n > 5$$\n",
        "\n",
        "logo,  *$y_1[n]=0$* para *$n<0$* e *$n>5$*"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "3eb6e32a",
      "metadata": {
        "id": "3eb6e32a",
        "outputId": "35b8e02e-7e8f-46fe-d50a-e953e660802f"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f90f6a0a460>"
            ]
          },
          "execution_count": 18,
          "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": [
        "n = np.arange(-5,8)\n",
        "\n",
        "xn= [0, 0, 1, 1, 1,  1,  1,  1,  0,  0,  0,  0, 0]\n",
        "y1= [0, 0, 0, 0, 0,  1,  1,  1,  1,  1,  1,  0, 0]\n",
        "\n",
        "plt.subplot(2, 1, 1)\n",
        "plt.stem(n, xn, linefmt='blue', label='x[n]')\n",
        "plt.legend()\n",
        "plt.subplot(2, 1, 2)\n",
        "plt.stem(n, y1, linefmt='red', label='y_1[n]')\n",
        "plt.legend()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "c647d996",
      "metadata": {
        "id": "c647d996"
      },
      "source": [
        "**1)** b) $y_2[n] = x[n+4]$\n",
        "\n",
        "Sabendo que $x[n] = 0$ para $n<-3$ e $n>2$\n",
        "\n",
        "É possivel determinar $y_1[n]=0$ fazendo:\n",
        "\n",
        "$$n+4 < -3$$\n",
        "e\n",
        "$$n+4 > 2$$\n",
        "\n",
        "portanto:\n",
        "$$n+4 < -3$$\n",
        "$$n+4-4 < -3-4$$\n",
        "$$n < -7$$\n",
        "\n",
        "e\n",
        "$$n+4 > 2$$\n",
        "$$n+4-4 > 2-4$$\n",
        "$$n > -2$$\n",
        "\n",
        "logo,  *$y_2[n]=0$* para *$n<-7$* e *$n>-2$*"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "8f6ee0d3",
      "metadata": {
        "id": "8f6ee0d3",
        "outputId": "8d21b00c-62c2-4fe5-919a-4a682ed22154"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f90f68bc2e0>"
            ]
          },
          "execution_count": 19,
          "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": [
        "n = np.arange(-10,10)\n",
        "\n",
        "xn= np.zeros(len(n))\n",
        "xn[7:13]=1\n",
        "y1= np.zeros(len(n))\n",
        "y1[3:9]=1\n",
        "\n",
        "plt.subplot(2, 1, 1)\n",
        "plt.stem(n, xn, linefmt='blue', label='x[n]')\n",
        "plt.legend()\n",
        "plt.subplot(2, 1, 2)\n",
        "plt.stem(n, y1, linefmt='red', label='y_1[n]')\n",
        "plt.legend()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "61430255",
      "metadata": {
        "id": "61430255"
      },
      "source": [
        "**1)** c) $y_3[n] = x[-n]$\n",
        "\n",
        "Sabendo que $x[n] = 0$ para $n<-3$ e $n>2$\n",
        "\n",
        "É possivel determinar $y_1[n]=0$ fazendo:\n",
        "\n",
        "$$-n < -3$$\n",
        "e\n",
        "$$-n > 2$$\n",
        "\n",
        "portanto:\n",
        "$$-n < -3$$\n",
        "$$n > 3$$\n",
        "\n",
        "e\n",
        "$$-n > 2$$\n",
        "$$n < -2$$\n",
        "\n",
        "\n",
        "logo,  *$y_2[n]=0$* para *$n<-2$* e *$n>3$*"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "ca0be78b",
      "metadata": {
        "id": "ca0be78b",
        "outputId": "4da721e0-15f0-4680-e841-88f3a7a8f9e0"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f90f68036a0>"
            ]
          },
          "execution_count": 20,
          "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": [
        "n = np.arange(-10,10)\n",
        "\n",
        "xn= np.zeros(len(n))\n",
        "xn[7:13]=1\n",
        "y1= np.zeros(len(n))\n",
        "y1[8:14]=1\n",
        "\n",
        "plt.subplot(2, 1, 1)\n",
        "plt.stem(n, xn, linefmt='blue', label='x[n]')\n",
        "plt.legend()\n",
        "plt.subplot(2, 1, 2)\n",
        "plt.stem(n, y1, linefmt='red', label='y_1[n]')\n",
        "plt.legend()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "2b058106",
      "metadata": {
        "id": "2b058106"
      },
      "source": [
        "**1)** d) $y_4[n] = x[-n+2]$\n",
        "\n",
        "Sabendo que $x[n] = 0$ para $n<-3$ e $n>2$\n",
        "\n",
        "É possivel determinar $y_1[n]=0$ fazendo:\n",
        "\n",
        "$$-n+2 < -3$$\n",
        "e\n",
        "$$-n+2 > 2$$\n",
        "\n",
        "portanto:\n",
        "$$-n+2 < -3$$\n",
        "$$-n+2-2 < -3-2$$\n",
        "$$-n < -5$$\n",
        "$$n > 5$$\n",
        "e\n",
        "$$-n+2 > 2$$\n",
        "$$-n+2-2 > 2-2$$\n",
        "$$-n > 0$$\n",
        "$$n < 0$$\n",
        "\n",
        "logo,  *$y_2[n]=0$* para *$n<0$* e *$n>5$*"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "afe16312",
      "metadata": {
        "id": "afe16312"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "6bc2f3d2",
      "metadata": {
        "id": "6bc2f3d2",
        "outputId": "3bccaa0d-866c-4ba5-ceb6-53b5673e9030"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f90f67b5f10>"
            ]
          },
          "execution_count": 21,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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LeHo2/XzlCuDhoYzYSo+v5NyJuqq2fn7zu2mIiIhIVixGiIiISFYsRoiIiEhWLEaIiIhIVixGiIiISFYsRoiIiEhWLEaIiIhIVixGiIiISFYsRoiIiEhWLEaIiIhIVixGiIiISFYsRoiIiEhWLEaIiIhIVixGiIiISFYsRoiIiEhWLEaIiIhIVixGiIiISFYsRoiIiEhWLEaIiIhIVixGiIiISFZ2FSOpqakICQmBm5sbwsLCcOjQoTaNO3LkCFxcXHDffffZs1kiIiLqhiQXI5mZmUhMTMTy5ctRUFCAqKgoREdHo7i4uNVxRqMRsbGxmDBhgt3JEhERUfcjuRhZt24d4uPjMWvWLAwdOhTr169HUFAQ0tLSWh03Z84cPPvss4iIiLA7WSIiIup+JBUjdXV1yM/Ph16vt2jX6/XIy8uzOS4jIwM///wzkpOT27Qdk8mE6upqiwcRERF1T5KKkcrKSjQ0NECn01m063Q6lJeXWx1z7tw5LF26FFu3boWLi0ubtpOSkgKtVmt+BAUFSUmTiIiIFMSuC1hVKpXFcyFEizYAaGhowLPPPouVK1di8ODBbY6/bNkyGI1G86OkpMSeNImIiEgB2nao4n/5+vrC2dm5xVGQioqKFkdLAKCmpgbff/89CgoKMH/+fABAY2MjhBBwcXHBvn37MH78+BbjNBoNNBqNlNSIiIhIoSQdGVGr1QgLC0N2drZFe3Z2NiIjI1v09/LywsmTJ3HixAnzIyEhAUOGDMGJEycwevTo9mVPREREiifpyAgAJCUl4YUXXkB4eDgiIiKwceNGFBcXIyEhAUDTKZbS0lJs3rwZTk5OCA0NtRjv5+cHNze3Fu1ERETUM0kuRmJiYlBVVYVVq1bBYDAgNDQUWVlZCA4OBgAYDIbbrjlCRERE1EwlhBByJ3E71dXV0Gq1MBqN8PLykjsdIoeqrQU8PZt+vnIF8PBQRmylx1dy7kRdVVs/v/ndNERERCQrFiNEREQkKxYjREREJCsWI0RERCQrFiNEREQkKxYjREREJCsWI0RERCQrFiNEREQkKxYjREREJCsWI0RERCQrFiNEREQkKxYjREREJCsWI0RERCQrFiNEREQkKxYjREREJCsWI0RERCQrFiNEREQkKxYjREREJCsWI0RERCQru4qR1NRUhISEwM3NDWFhYTh06JDNvjt27MDEiRPRt29feHl5ISIiAnv37rU7YSIiIupeJBcjmZmZSExMxPLly1FQUICoqChER0ejuLjYav+DBw9i4sSJyMrKQn5+PsaNG4dp06ahoKCg3ckTERGR8qmEEELKgNGjR2PkyJFIS0sztw0dOhTTp09HSkpKm2IMGzYMMTExeOONN9rUv7q6GlqtFkajEV5eXlLSJVKc2lrA07Pp5ytXAA8PZcRWenwl507UVbX181vSkZG6ujrk5+dDr9dbtOv1euTl5bUpRmNjI2pqauDt7W2zj8lkQnV1tcWDiIiIuidJxUhlZSUaGhqg0+ks2nU6HcrLy9sU47333kNtbS1mzJhhs09KSgq0Wq35ERQUJCVNIiIiUhC7LmBVqVQWz4UQLdqs2bZtG1asWIHMzEz4+fnZ7Lds2TIYjUbzo6SkxJ40iYiISAFcpHT29fWFs7Nzi6MgFRUVLY6W3CozMxPx8fH47LPP8Mgjj7TaV6PRQKPRSEmNiIiIFErSkRG1Wo2wsDBkZ2dbtGdnZyMyMtLmuG3btmHmzJn4+9//jilTptiXKREREXVLko6MAEBSUhJeeOEFhIeHIyIiAhs3bkRxcTESEhIANJ1iKS0txebNmwE0FSKxsbH44IMPMGbMGPNRFXd3d2i12g7cFSIiIlIiycVITEwMqqqqsGrVKhgMBoSGhiIrKwvBwcEAAIPBYLHmyIYNG1BfX4958+Zh3rx55va4uDh8+umn7d8DIiIiUjTJ64zIgeuMUE/CtTTkia/k3Im6KoesM0JERETU0ViMEBERkaxYjBAREZGsWIwQERGRrFiMEBERkaxYjBAREZGsWIwQERGRrFiMEBERkaxYjBAREZGsWIwQERGRrFiMEBERkaxYjBAREZGsWIwQERGRrFiMEBERkaxYjBAREZGsWIwQERGRrFiMEBERkaxYjBAREZGsWIwQERGRrFzkTkAuDY0C3xVdRkXNdfj1dsOoEG84O6kYvxPiKzn3zohPZA8lv++VnLvS43eVv2d2FSOpqal45513YDAYMGzYMKxfvx5RUVE2++fm5iIpKQmnT59GYGAgXn31VSQkJNiddHvtOWXAyt2FMBivm9sCtG5InnYPHg0NYHwHxldy7p0Rn8geSn7fKzl3pcfvSn/PJJ+myczMRGJiIpYvX46CggJERUUhOjoaxcXFVvsXFRVh8uTJiIqKQkFBAV5//XUsXLgQX3zxRbuTt8eeUwa8tOW4xS8fAMqN1/HSluPYc8rA+A6Kr+TcOyM+kT2U/L5Xcu5Kj9/V/p6phBBCyoDRo0dj5MiRSEtLM7cNHToU06dPR0pKSov+r732Gnbt2oUzZ86Y2xISEvDDDz/g6NGjbdpmdXU1tFotjEYjvLy8pKRroaFR4IE1Xzf98oWApqHO4nUVAJ2XG/YnPWTXYaqGRoFH1uWivPq61dd7cnwl594Z8W9WexXQ+TX9/EsF4NGrXeE6LbbS4ysxdyW/75Wcu9Lj24ptclYDKhVUAPy1bjj82vh2/z1r6+e3pGKkrq4OvXr1wmeffYYnnnjC3P7yyy/jxIkTyM3NbTHmwQcfxIgRI/DBBx+Y23bu3IkZM2bg6tWrcHV1bTHGZDLBZDJZ7ExQUFC7i5GjP1fhmb99AwDQ1Jvw5VfL7Y5FRETUnUyf+iZMLhrz822zxyBioE+7Yra1GJF0mqayshINDQ3Q6XQW7TqdDuXl5VbHlJeXW+1fX1+PyspKq2NSUlKg1WrNj6CgIClp2lRRY73CJCIiIkud+Zlp1wWsKpXlYRshRIu22/W31t5s2bJlSEpKMj9vPjLSXn693cw/m5zVmD71Tav9Pv3zKIwO8ZYc/9uiy5iZ8d1t+/XE+ErOvTPiE9lDye97Jeeu9Pi2Ypuc1RbPb/7MdDRJxYivry+cnZ1bHAWpqKhocfSjmb+/v9X+Li4u8PGxfvhHo9FAo9FYfa09RoV4I0DrhnLjdQiVyuJwFADzebJRQ++Ekx3nyUYNdYe3j7YpvpXXe3J8JefeGfGJ7KHk972Sc1d6/DbH7sR/WEk6TaNWqxEWFobs7GyL9uzsbERGRlodExER0aL/vn37EB4ebvV6EUdydlIhedo9AJp+2Tdrfp487R67L9hhfHlid4f4RPZQ8vteybkrPX5X/Hsm+dbepKQkfPLJJ9i0aRPOnDmDRYsWobi42LxuyLJlyxAbG2vun5CQgIsXLyIpKQlnzpzBpk2bkJ6ejiVLlnTcXkjwaGgA0p4fCX+t5eEnf60b0p4f2e57qxlfntjdIT6RPZT8vldy7kqP39X+nkm+tRdoWvRs7dq1MBgMCA0Nxfvvv48HH3wQADBz5kxcuHABOTk55v65ublYtGiRedGz1157TdKiZx11a+/NlLxintLjKzn3zohPZA8lv++VnLvS4zs6d4fc2isXRxQjRERE5Fht/fxWxHfTNNdL1dXVMmdCREREbdX8uX274x6KKEZqamoAoMPWGyEiIqLOU1NTA61Wa/N1RZymaWxsRFlZGXr37t3qeiZSNa9fUlJS0iNO//Sk/eW+dl89aX+5r91XT9lfIQRqamoQGBgIJyfb98wo4siIk5MT+vXr57D4Xl5e3frNcKuetL/c1+6rJ+0v97X76gn729oRkWaSb+0lIiIi6kgsRoiIiEhWPboY0Wg0SE5OdsjS811RT9pf7mv31ZP2l/vaffW0/b0dRVzASkRERN1Xjz4yQkRERPJjMUJERESyYjFCREREsmIxQkRERLLq9sXIm2++icjISPTq1Qt9+vSx2qe4uBjTpk2Dh4cHfH19sXDhQtTV1bUa12QyYcGCBfD19YWHhwcee+wxXLp0yQF7YJ+cnByoVCqrj2PHjtkcN3PmzBb9x4wZ04mZ22/AgAEtcl+6dGmrY4QQWLFiBQIDA+Hu7o6HH34Yp0+f7qSM7XPhwgXEx8cjJCQE7u7uGDhwIJKTk2/7nlXS3KampiIkJARubm4ICwvDoUOHWu2fm5uLsLAwuLm54Q9/+AM+/vjjTsrUfikpKbj//vvRu3dv+Pn5Yfr06Th79myrY2z9f/3jjz92Utb2WbFiRYuc/f39Wx2jxDltZu1vkUqlwrx586z2V+q8diRFrMDaHnV1dXjqqacQERGB9PT0Fq83NDRgypQp6Nu3Lw4fPoyqqirExcVBCIEPP/zQZtzExETs3r0b27dvh4+PDxYvXoypU6ciPz8fzs7OjtylNomMjITBYLBo+9d//Vfs378f4eHhrY599NFHkZGRYX6uVqsdkqMjrFq1CrNnzzY/9/T0bLX/2rVrsW7dOnz66acYPHgwVq9ejYkTJ+Ls2bPo3bu3o9O1y48//ojGxkZs2LABgwYNwqlTpzB79mzU1tbi3XffbXWsEuY2MzMTiYmJSE1NxdixY7FhwwZER0ejsLAQ/fv3b9G/qKgIkydPxuzZs7FlyxYcOXIEc+fORd++ffHkk0/KsAdtk5ubi3nz5uH+++9HfX09li9fDr1ej8LCQnh4eLQ69uzZsxardvbt29fR6bbbsGHDsH//fvPz1v5OKnVOmx07dgwNDQ3m56dOncLEiRPx1FNPtTpOifPaYUQPkZGRIbRabYv2rKws4eTkJEpLS81t27ZtExqNRhiNRquxfv/9d+Hq6iq2b99ubistLRVOTk5iz549HZ57R6irqxN+fn5i1apVrfaLi4sTjz/+eOck1cGCg4PF+++/3+b+jY2Nwt/fX7z99tvmtuvXrwutVis+/vhjB2ToOGvXrhUhISGt9lHK3I4aNUokJCRYtN19991i6dKlVvu/+uqr4u6777ZomzNnjhgzZozDcnSEiooKAUDk5uba7HPgwAEBQPz222+dl1gHSE5OFsOHD29z/+4yp81efvllMXDgQNHY2Gj1daXOa0fq9qdpbufo0aMIDQ1FYGCguW3SpEkwmUzIz8+3OiY/Px83btyAXq83twUGBiI0NBR5eXkOz9keu3btQmVlJWbOnHnbvjk5OfDz88PgwYMxe/ZsVFRUOD7BDrJmzRr4+Pjgvvvuw5tvvtnqqYuioiKUl5dbzKNGo8FDDz3UZefRFqPRCG9v79v26+pzW1dXh/z8fIs5AQC9Xm9zTo4ePdqi/6RJk/D999/jxo0bDsu1oxmNRgBo0zyOGDECAQEBmDBhAg4cOODo1DrEuXPnEBgYiJCQEDz99NM4f/68zb7dZU6Bpvf0li1b8OKLL972i16VOK8dpccXI+Xl5dDpdBZtd9xxB9RqNcrLy22OUavVuOOOOyzadTqdzTFyS09Px6RJkxAUFNRqv+joaGzduhVff/013nvvPRw7dgzjx4+HyWTqpEzt9/LLL2P79u04cOAA5s+fj/Xr12Pu3Lk2+zfP1a3z35Xn0Zqff/4ZH374IRISElrtp4S5raysRENDg6Q5sfb/sE6nQ319PSorKx2Wa0cSQiApKQkPPPAAQkNDbfYLCAjAxo0b8cUXX2DHjh0YMmQIJkyYgIMHD3ZittKNHj0amzdvxt69e/G3v/0N5eXliIyMRFVVldX+3WFOm3355Zf4/fffW/2HoFLntUPJfWjGHsnJyQJAq49jx45ZjLF1mmb27NlCr9e3aHd1dRXbtm2zuv2tW7cKtVrdov2RRx4Rc+bMsW+n2siefS8pKRFOTk7i888/l7y9srIy4erqKr744ouO2gVJ7NnfZp9//rkAICorK62+fuTIEQFAlJWVWbTPmjVLTJo0qcP35Xbs2dfS0lIxaNAgER8fL3l7cs+tNaWlpQKAyMvLs2hfvXq1GDJkiNUxd911l3jrrbcs2g4fPiwACIPB4LBcO9LcuXNFcHCwKCkpkTx26tSpYtq0aQ7IynGuXLkidDqdeO+996y+3h3mtJlerxdTp06VPE6J89oeiryAdf78+Xj66adb7TNgwIA2xfL398e3335r0fbbb7/hxo0bLSrzm8fU1dXht99+szg6UlFRgcjIyDZt11727HtGRgZ8fHzw2GOPSd5eQEAAgoODce7cOcljO0J75rr5TpF//vOf8PHxafF689X85eXlCAgIMLdXVFTYnHtHkrqvZWVlGDduHCIiIrBx40bJ25N7bq3x9fWFs7Nzi6Mgrc2Jv7+/1f4uLi5W572rWbBgAXbt2oWDBw+iX79+ksePGTMGW7ZscUBmjuPh4YE//vGPNt97Sp/TZhcvXsT+/fuxY8cOyWOVOK/tochixNfXF76+vh0SKyIiAm+++SYMBoP5A2nfvn3QaDQICwuzOiYsLAyurq7Izs7GjBkzAAAGgwGnTp3C2rVrOyQvW6TuuxACGRkZiI2Nhaurq+TtVVVVoaSkxOLDujO1Z64LCgoAwGbuISEh8Pf3R3Z2NkaMGAGg6fxubm4u1qxZY1/C7SBlX0tLSzFu3DiEhYUhIyMDTk7Sz7jKPbfWqNVqhIWFITs7G0888YS5PTs7G48//rjVMREREdi9e7dF2759+xAeHm7Xe76zCCGwYMEC7Ny5Ezk5OQgJCbErTkFBQZeaw7YwmUw4c+YMoqKirL6u1Dm9VUZGBvz8/DBlyhTJY5U4r+0i96EZR7t48aIoKCgQK1euFJ6enqKgoEAUFBSImpoaIYQQ9fX1IjQ0VEyYMEEcP35c7N+/X/Tr10/Mnz/fHOPSpUtiyJAh4ttvvzW3JSQkiH79+on9+/eL48ePi/Hjx4vhw4eL+vr6Tt/H1uzfv18AEIWFhVZfHzJkiNixY4cQQoiamhqxePFikZeXJ4qKisSBAwdERESEuPPOO0V1dXVnpi1ZXl6eWLdunSgoKBDnz58XmZmZIjAwUDz22GMW/W7eXyGEePvtt4VWqxU7duwQJ0+eFM8884wICAjo0vvbfGpm/Pjx4tKlS8JgMJgfN1Pq3G7fvl24urqK9PR0UVhYKBITE4WHh4e4cOGCEEKIpUuXihdeeMHc//z586JXr15i0aJForCwUKSnpwtXV1e7Tkt2ppdeeklotVqRk5NjMYdXr14197l1X99//32xc+dO8dNPP4lTp06JpUuXCgBd6lSbNYsXLxY5OTni/Pnz4ptvvhFTp04VvXv37nZzerOGhgbRv39/8dprr7V4rbvMa0fq9sVIXFyc1XPvBw4cMPe5ePGimDJlinB3dxfe3t5i/vz54vr16+bXi4qKWoy5du2amD9/vvD29hbu7u5i6tSpori4uBP3rG2eeeYZERkZafN1ACIjI0MIIcTVq1eFXq8Xffv2Fa6urqJ///4iLi6uS+7XrfLz88Xo0aOFVqsVbm5uYsiQISI5OVnU1tZa9Lt5f4Vour03OTlZ+Pv7C41GIx588EFx8uTJTs5emoyMDJvXlNxMyXP717/+VQQHBwu1Wi1GjhxpcbtrXFyceOihhyz65+TkiBEjRgi1Wi0GDBgg0tLSOjlj6WzN4c3vz1v3dc2aNWLgwIHCzc1N3HHHHeKBBx4Q//jHPzo/eYliYmJEQECAcHV1FYGBgeJPf/qTOH36tPn17jKnN9u7d68AIM6ePdvite4yrx1JJYQQnXYYhoiIiOgWPf7WXiIiIpIXixEiIiKSFYsRIiIikhWLESIiIpIVixEiIiKSFYsRIiIikhWLESIiIpIVixEiIiKSFYsRIiIikhWLESIiIpKVIr61t7GxEWVlZejduzdUKpXc6RAREVEbCCFQU1ODwMDAVr9dXBHFSFlZGYKCguROg4iIiOxQUlKCfv362XxdEcVI7969ATTtjJeXl8zZEBERUVtUV1cjKCjI/DluiyKKkeZTM15eXixGiIiIFOZ2l1goohghIgKAhkaB74ouo6LmOvx6u2FUiDecnTrmOjJHxmZ8+WKTMkguRg4ePIh33nkH+fn5MBgM2LlzJ6ZPn97qmNzcXCQlJeH06dMIDAzEq6++ioSEBHtzJqIeaM8pA1buLoTBeN3cFqB1Q/K0e/BoaECXjc348sUm5ZB8a29tbS2GDx+Ojz76qE39i4qKMHnyZERFRaGgoACvv/46Fi5ciC+++EJyskTUM+05ZcBLW45bfGABQLnxOl7achx7Thm6ZGzGly82KYtKCCHsHqxS3fbIyGuvvYZdu3bhzJkz5raEhAT88MMPOHr0aJu2U11dDa1WC6PRyGtGiHqYhkaBB9Z83eIDq5kKgL/WDYdfGy/50L4jYzO+fLEBoKGhATdu3JA8jqRxdXWFs7Ozzdfb+vnt8GtGjh49Cr1eb9E2adIkpKen48aNG3B1dW0xxmQywWQymZ9XV1c7Ok0i6qK+K7ps8wMLAAQAg/E6viu6jIiBPl0mNuPLE1sIgfLycvz++++S8iH79enTB/7+/u1aB8zhxUh5eTl0Op1Fm06nQ319PSorKxEQ0PKcYEpKClauXOno1IhIASpqbH9g2dOvs2IzvjyxmwsRPz8/9OrViwtlOpAQAlevXkVFRQUAWP08b6tOuZvm1jdD85khW2+SZcuWISkpyfy8+T5lIup5/Hq7dWi/zorN+J0fu6GhwVyI+PhIPxJE0rm7uwMAKioq4Ofn1+opm9Y4/Ltp/P39UV5ebtFWUVEBFxcXm28WjUZjXlOEa4sQ9WyjQrwRoHWDrX/fqtB098WoEO8uFZvxOz928zUivXr1kpwP2a/5992ea3QcXoxEREQgOzvbom3fvn0IDw+3er0IEdHNnJ1USJ52DwC0+OBqfp487R67LnJ0ZGzGly82T810ro74fUsuRq5cuYITJ07gxIkTAJpu3T1x4gSKi4sBNJ1iiY2NNfdPSEjAxYsXkZSUhDNnzmDTpk1IT0/HkiVL2p08EfUMj4YGIO35kfDvrbFo99e6Ie35ke1aj8KRsRlfvtjt0dAocPTnKvzXiVIc/bkKDY1233RKbSUkOnDggEDThc4Wj7i4OCGEEHFxceKhhx6yGJOTkyNGjBgh1Gq1GDBggEhLS5O0TaPRKAAIo9EoNV0i6kbqq2tEXtAfxZdDHxR5p0pEfUOjImIzfufEvnbtmigsLBTXrl2zO5f/Plkmxry1XwS/9pX5Meat/eK/T5bZHVNucXFx5s/qnTt3tnnczZ/3jz/+uM1+rf3e2/r53a51RjoL1xkhIgBAbS3g6dn085UrgIeHMmIzfqfEvn79OoqKihASEgI3N+kX1TYvwnbrh2LzSQg5j9bYYjAYsHjxYuTn5+PcuXNYuHAh1q9fb9Fn5syZ+OWXX5CRkYE77rgDGo3GerBb1NXV4fLly3j55ZdhMpnw5ZdfWu3X2u+9rZ/fDr9mhIiIqKtraBRYubuwRSECwNy2cndhlztlYzKZ0LdvXyxfvhzDhw+32U+j0cDf37/NhQgAqNVq+Pv7m++YcSQWI0RE1ONJWYSto23evBk+Pj4Wi30CwJNPPmlxDaY1AwYMwAcffIDY2Fhotdo2b/PChQtQqVTYsWMHxo0bh169emH48OFtXhm9o7EYISKiHs/RC8i15qmnnkJDQwN27dplbqusrMRXX32FP//5zx2+vZstX74cS5YswYkTJzB48GA888wzqK+vd+g2rWExQkREPZ6jF5Brjbu7O5599llkZGSY27Zu3Yp+/frh4Ycf7vDt3WzJkiWYMmUKBg8ejJUrV+LixYv45z//6dBtWsNihIiIejxHLyB3O7Nnz8a+fftQWloKAMjIyMDMmTMdvmbKvffea/65eTn35uXdOxOLESIi6vEcvYDc7YwYMQLDhw/H5s2bcfz4cZw8eRIzZ850yLZudvPio82FT2Njo8O3eysWI0RERJB/EbZZs2YhIyMDmzZtwiOPPNKjvpOtU74oj4iISA5CCIhr19rcX/8HLSbMHo5j909Ahac3/P5jE+4frIOzkwqNV6+2OY7K3V3yKZbnnnsOS5Yswd/+9jds3ry5zeOaV0S/cuUKfv31V5w4cQJqtRr33HOPpO3LicUIERF1W+LaNZwdGSZ53B3uwB0NvwDPToE9l3MOOZ4PlcQv7PPy8sKTTz6Jf/zjH5g+fXqbx40YMcL8c35+Pv7+978jODgYFy5ckLR9ObEYISIi6iIMBgOee+45SYuT2bOQ+oABA1qM69Onj12xOgKLESIi6rZU7u4Ycjxflu1KcfnyZezbtw9ff/01Pvroow7P56uvvoKnpye2b9+OqVOntmnMoUOHEB0dDZPJhClTpnR4TjdjMUJERN2WSqWSfLpEDiNHjsRvv/2GNWvWYMiQIeb2YcOG4eLFi1bHbNiwAc8999xtY69duxb/7//9PwD/d/tuW4SHh5uvR/Fs/u4gB2ExQkREJDNb13dkZWXhxo0bVl/T6XRtiu3n5wc/Pz/JObm7u2PQoEGSx9mDxQgREVEXFRwcLHcKnYLrjBAREZGsWIwQEVG3IscKoj1ZR/y+eZqGiIi6BbVaDScnJ5SVlaFv375Qq9UO/26XnkwIgbq6Ovz6669wcnKCWq22OxaLESIi6hacnJwQEhICg8GAsrIyudPpMXr16oX+/fvDycn+ky0sRoiIqNtQq9Xo378/6uvr0dDQIHc63Z6zszNcXFzafQTKrmIkNTUV77zzDgwGA4YNG4b169cjKirKZv+tW7di7dq1OHfuHLRaLR599FG8++678PHxsTtxIiIia1QqFVxdXS2+kZa6NsnHVDIzM5GYmIjly5ejoKAAUVFRiI6ORnFxsdX+hw8fRmxsLOLj43H69Gl89tlnOHbsGGbNmtXu5ImIiEj5JBcj69atQ3x8PGbNmoWhQ4di/fr1CAoKQlpamtX+33zzDQYMGICFCxciJCQEDzzwAObMmYPvv/++3ckTERGR8kkqRurq6pCfnw+9Xm/RrtfrkZeXZ3VMZGQkLl26hKysLAgh8Msvv+Dzzz9vdZ17k8mE6upqiwcRERF1T5KKkcrKSjQ0NLRYglan06G8vNzqmMjISGzduhUxMTFQq9Xw9/dHnz598OGHH9rcTkpKCrRarfkRFBQkJU0iIiJSELvuw7n1qlkhhM0raQsLC7Fw4UK88cYbyM/Px549e1BUVISEhASb8ZctWwaj0Wh+lJSU2JMmERERKYCku2l8fX3h7Ozc4ihIRUWFzS/sSUlJwdixY/HKK68AAO699154eHggKioKq1evtvoNghqNBhqNRkpqREREpFCSjoyo1WqEhYUhOzvboj07OxuRkZFWx1y9erXFQijOzs4Amo6oEBERUc8m+TRNUlISPvnkE2zatAlnzpzBokWLUFxcbD7tsmzZMsTGxpr7T5s2DTt27EBaWhrOnz+PI0eOYOHChRg1ahQCAwM7bk+IiIhIkSQvehYTE4OqqiqsWrUKBoMBoaGhyMrKMn/NscFgsFhzZObMmaipqcFHH32ExYsXo0+fPhg/fjzWrFnTcXtBREREiqUSCjhXUl1dDa1WC6PRCC8vL7nTISK51NYCnp5NP1+5Anh4KCM248sXm2TV1s9v+7/VhoiIiKgDsBghIiIiWbEYISIiIlmxGCEiIiJZsRghIiIiWbEYISIiIlmxGCEiIiJZsRghIiIiWbEYISIiIlmxGCEiIiJZsRghIiIiWbEYISIiIlmxGCEiIiJZsRghIiIiWbEYISIiIlmxGCEiIiJZsRghIiIiWbEYISIiIlmxGCEiIiJZsRghIiIiWdlVjKSmpiIkJARubm4ICwvDoUOHWu1vMpmwfPlyBAcHQ6PRYODAgdi0aZNdCRMREVH34iJ1QGZmJhITE5GamoqxY8diw4YNiI6ORmFhIfr37291zIwZM/DLL78gPT0dgwYNQkVFBerr69udPBERESmf5GJk3bp1iI+Px6xZswAA69evx969e5GWloaUlJQW/ffs2YPc3FycP38e3t7eAIABAwa0L2siIiLqNiSdpqmrq0N+fj70er1Fu16vR15entUxu3btQnh4ONauXYs777wTgwcPxpIlS3Dt2jWb2zGZTKiurrZ4EBERUfck6chIZWUlGhoaoNPpLNp1Oh3Ky8utjjl//jwOHz4MNzc37Ny5E5WVlZg7dy4uX75s87qRlJQUrFy5UkpqREREpFB2XcCqUqksngshWrQ1a2xshEqlwtatWzFq1ChMnjwZ69atw6effmrz6MiyZctgNBrNj5KSEnvSJCIiIgWQdGTE19cXzs7OLY6CVFRUtDha0iwgIAB33nkntFqtuW3o0KEQQuDSpUu46667WozRaDTQaDRSUiMiIiKFknRkRK1WIywsDNnZ2Rbt2dnZiIyMtDpm7NixKCsrw5UrV8xtP/30E5ycnNCvXz87UiYiIqLuRPJpmqSkJHzyySfYtGkTzpw5g0WLFqG4uBgJCQkAmk6xxMbGmvs/++yz8PHxwZ///GcUFhbi4MGDeOWVV/Diiy/C3d294/aEiIiIFEnyrb0xMTGoqqrCqlWrYDAYEBoaiqysLAQHBwMADAYDiouLzf09PT2RnZ2NBQsWIDw8HD4+PpgxYwZWr17dcXtBREREiqUSQgi5k7id6upqaLVaGI1GeHl5yZ0OEcmlthbw9Gz6+coVwMNDGbEZX77YJKu2fn7zu2mIiIhIVixGiIiISFYsRoiIiEhWLEaIiIhIVixGiIiISFYsRoiIiEhWLEaIiIhIVixGiIiISFYsRoiIiEhWLEaIiIhIVixGiIiISFYsRoiIiEhWLEaIiIhIVixGiIiISFYsRoiIiEhWLEaIiIhIVixGiIiISFYsRoiIiEhWLEaIiIhIVnYVI6mpqQgJCYGbmxvCwsJw6NChNo07cuQIXFxccN9999mzWSIiIuqGJBcjmZmZSExMxPLly1FQUICoqChER0ejuLi41XFGoxGxsbGYMGGC3ckSERFR9yO5GFm3bh3i4+Mxa9YsDB06FOvXr0dQUBDS0tJaHTdnzhw8++yziIiIsDtZIiIi6n4kFSN1dXXIz8+HXq+3aNfr9cjLy7M5LiMjAz///DOSk5Pty5KIiIi6LRcpnSsrK9HQ0ACdTmfRrtPpUF5ebnXMuXPnsHTpUhw6dAguLm3bnMlkgslkMj+vrq6WkiYREREpiF0XsKpUKovnQogWbQDQ0NCAZ599FitXrsTgwYPbHD8lJQVardb8CAoKsidNIiIiUgBJxYivry+cnZ1bHAWpqKhocbQEAGpqavD9999j/vz5cHFxgYuLC1atWoUffvgBLi4u+Prrr61uZ9myZTAajeZHSUmJlDSJiIhIQSSdplGr1QgLC0N2djaeeOIJc3t2djYef/zxFv29vLxw8uRJi7bU1FR8/fXX+PzzzxESEmJ1OxqNBhqNRkpqREREpFCSihEASEpKwgsvvIDw8HBERERg48aNKC4uRkJCAoCmoxqlpaXYvHkznJycEBoaajHez88Pbm5uLdqJiIioZ5JcjMTExKCqqgqrVq2CwWBAaGgosrKyEBwcDAAwGAy3XXOEiIiIqJlKCCHkTuJ2qqurodVqYTQa4eXlJXc6RCSX2lrA07Pp5ytXAA8PZcRmfPlik6za+vnN76YhIiIiWbEYISIiIlmxGCEiIiJZsRghIiIiWbEYISIiIlmxGCEiIiJZsRghIiIiWbEYISIiIlmxGCEiIiJZsRghIiIiWbEYISIiIlmxGCEiIiJZsRghIiIiWbEYISIiIlmxGCEiIiJZsRghIiIiWbEYISIiIlmxGCEiIiJZsRghIiIiWbEYISIiIlnZVYykpqYiJCQEbm5uCAsLw6FDh2z23bFjByZOnIi+ffvCy8sLERER2Lt3r90JExERUfciuRjJzMxEYmIili9fjoKCAkRFRSE6OhrFxcVW+x88eBATJ05EVlYW8vPzMW7cOEybNg0FBQXtTp6IiIiUTyWEEFIGjB49GiNHjkRaWpq5bejQoZg+fTpSUlLaFGPYsGGIiYnBG2+80ab+1dXV0Gq1MBqN8PLykpIuEXUntbWAp2fTz1euAB4eyojN+PLFJlm19fNb0pGRuro65OfnQ6/XW7Tr9Xrk5eW1KUZjYyNqamrg7e1ts4/JZEJ1dbXFg4iIiLonScVIZWUlGhoaoNPpLNp1Oh3Ky8vbFOO9995DbW0tZsyYYbNPSkoKtFqt+REUFCQlTSIiIlIQuy5gValUFs+FEC3arNm2bRtWrFiBzMxM+Pn52ey3bNkyGI1G86OkpMSeNImIiEgBXKR09vX1hbOzc4ujIBUVFS2OltwqMzMT8fHx+Oyzz/DII4+02lej0UCj0UhJjYiIiBRK0pERtVqNsLAwZGdnW7RnZ2cjMjLS5rht27Zh5syZ+Pvf/44pU6bYlykRERF1S5KOjABAUlISXnjhBYSHhyMiIgIbN25EcXExEhISADSdYiktLcXmzZsBNBUisbGx+OCDDzBmzBjzURV3d3dotdoO3BUiIiJSIsnFSExMDKqqqrBq1SoYDAaEhoYiKysLwcHBAACDwWCx5siGDRtQX1+PefPmYd68eeb2uLg4fPrpp+3fAyIiIlI0yeuMyIHrjBARAGWvdcH48sQmWTlknREiIiKijsZihIiIiGTFYoSIiIhkxWKEiIiIZMVihIiIiGTFYoSIiIhkxWKEiIiIZMVihIiIiGTFYoSIiIhkxWKEiIiIZMVihIiIiGTFYoSIiIhkxWKEiIiIZMVihIiIiGTFYoSIiIhkxWKEiIiIZMVihIiIiGTFYoSIiIhkxWKEiIiIZGVXMZKamoqQkBC4ubkhLCwMhw4darV/bm4uwsLC4Obmhj/84Q/4+OOP7Uq2IzU0Chz9uQr/daIUR3+uQkOjYPxOiq/k3JUeX8m5E9lL6e97Jf9NaCsXqQMyMzORmJiI1NRUjB07Fhs2bEB0dDQKCwvRv3//Fv2LioowefJkzJ49G1u2bMGRI0cwd+5c9O3bF08++WSH7IRUe04ZsHJ3IQzG6+a2AK0bkqfdg0dDAxjfgfGVnLvS4ys5dyJ7Kf19r+S/CVKohBCSyqDRo0dj5MiRSEtLM7cNHToU06dPR0pKSov+r732Gnbt2oUzZ86Y2xISEvDDDz/g6NGjbdpmdXU1tFotjEYjvLy8pKTbwp5TBry05Thu3WnV//437fmR7ZoExpcnNuPLF7sz4pvV1gKenk0/X7kCeHi0P2ZnxGZ8WWIr/X2v5L8Jzdr6+S3pyEhdXR3y8/OxdOlSi3a9Xo+8vDyrY44ePQq9Xm/RNmnSJKSnp+PGjRtwdXWVkkK7NDQKrNxd2PTLFwKahjqL11UAUnYUYMIALzg7qayFuG38lB0FUNebrL7ek+MrOXelx1dy7i1cuwaoVC1/7giOjM34nR5b6e97Of4mmJzVECoVVABW7i7ExHv82///bBtJOjJSVlaGO++8E0eOHEFkZKS5/a233sK///u/4+zZsy3GDB48GDNnzsTrr79ubsvLy8PYsWNRVlaGgICWlZfJZILJ9H+/pOrqagQFBbX7yMjRn6vwzN++AQBo6k348qvldsciIiLqTqZPfRMmF435+bbZYxAx0KddMdt6ZMSuC1hVt1StQogWbbfrb629WUpKCrRarfkRFBRkT5otVNRcv30nIiIi6tTPTEmnaXx9feHs7Izy8nKL9oqKCuh0Oqtj/P39rfZ3cXGBj4/1imvZsmVISkoyP28+MtJefr3dzD+bnNWYPvVNq/0+/fMojA7xlhz/26LLmJnx3W379cT4Ss5d6fGVnDuRvZT+vpfjb4LJWW3x/ObPTEeTVIyo1WqEhYUhOzsbTzzxhLk9Ozsbjz/+uNUxERER2L17t0Xbvn37EB4ebvN6EY1GA41GY/W19hgV4o0ArRvKjdchVCqLw1FA0zk4f60bRg29E052nCcbNdQd3j7apvhWXu/J8ZWcu9LjKzl3Insp/X3fJf4mdOI/HiSfpklKSsInn3yCTZs24cyZM1i0aBGKi4uRkJAAoOmoRmxsrLl/QkICLl68iKSkJJw5cwabNm1Ceno6lixZ0nF70UbOTiokT7sHwP9dMdys+XnytHvsvmCH8eWJzfjyxe6M+ET2UPr7Xsl/E+whuRiJiYnB+vXrsWrVKtx33304ePAgsrKyEBwcDAAwGAwoLi429w8JCUFWVhZycnJw33334d/+7d/wl7/8RbY1Rh4NDUDa8yPhr7U8/OSvdeuQW5kYX57YjC9f7M6IT2QPpb/vlfw3QSrJ64zIoSPXGWnW0CjwXdFlVNRch1/vpsNRHVkFMr48sRlfvtidEZ/IHkp/3yv5b0JbP78VUYwYjUb06dMHJSUlHVaMEBERkWM134Dy+++/Q6vV2uwneTl4OdTU1ABAh93iS0RERJ2npqam1WJEEUdGGhsbUVZWht69e7e6nolUzRVbTzni0pP2l/vaffWk/eW+dl89ZX+FEKipqUFgYCCcnGxfpqqIIyNOTk7o16+fw+J7eXl16zfDrXrS/nJfu6+etL/c1+6rJ+xva0dEmtm1AisRERFRR2ExQkRERLLq0cWIRqNBcnKyQ1Z77Yp60v5yX7uvnrS/3Nfuq6ft7+0o4gJWIiIi6r569JERIiIikh+LESIiIpIVixEiIiKSFYsRIiIiklW3L0befPNNREZGolevXujTp4/VPsXFxZg2bRo8PDzg6+uLhQsXoq6urtW4JpMJCxYsgK+vLzw8PPDYY4/h0qVLDtgD++Tk5EClUll9HDt2zOa4mTNntug/ZsyYTszcfgMGDGiR+9KlS1sdI4TAihUrEBgYCHd3dzz88MM4ffp0J2VsnwsXLiA+Ph4hISFwd3fHwIEDkZycfNv3rJLmNjU1FSEhIXBzc0NYWBgOHTrUav/c3FyEhYXBzc0Nf/jDH/Dxxx93Uqb2S0lJwf3334/evXvDz88P06dPx9mzZ1sdY+v/6x9//LGTsrbPihUrWuTs7+/f6hglzmkza3+LVCoV5s2bZ7W/Uue1IyliBdb2qKurw1NPPYWIiAikp6e3eL2hoQFTpkxB3759cfjwYVRVVSEuLg5CCHz44Yc24yYmJmL37t3Yvn07fHx8sHjxYkydOhX5+flwdnZ25C61SWRkJAwGg0Xbv/7rv2L//v0IDw9vdeyjjz6KjIwM83O1Wu2QHB1h1apVmD17tvm5p6dnq/3Xrl2LdevW4dNPP8XgwYOxevVqTJw4EWfPnkXv3r0dna5dfvzxRzQ2NmLDhg0YNGgQTp06hdmzZ6O2thbvvvtuq2OVMLeZmZlITExEamoqxo4diw0bNiA6OhqFhYXo379/i/5FRUWYPHkyZs+ejS1btuDIkSOYO3cu+vbtiyeffFKGPWib3NxczJs3D/fffz/q6+uxfPly6PV6FBYWwsPDo9WxZ8+etVi1s2/fvo5Ot92GDRuG/fv3m5+39ndSqXPa7NixY2hoaDA/P3XqFCZOnIinnnqq1XFKnNcOI3qIjIwModVqW7RnZWUJJycnUVpaam7btm2b0Gg0wmg0Wo31+++/C1dXV7F9+3ZzW2lpqXBychJ79uzp8Nw7Ql1dnfDz8xOrVq1qtV9cXJx4/PHHOyepDhYcHCzef//9NvdvbGwU/v7+4u233za3Xb9+XWi1WvHxxx87IEPHWbt2rQgJCWm1j1LmdtSoUSIhIcGi7e677xZLly612v/VV18Vd999t0XbnDlzxJgxYxyWoyNUVFQIACI3N9dmnwMHDggA4rfffuu8xDpAcnKyGD58eJv7d5c5bfbyyy+LgQMHisbGRquvK3VeO1K3P01zO0ePHkVoaCgCAwPNbZMmTYLJZEJ+fr7VMfn5+bhx4wb0er25LTAwEKGhocjLy3N4zvbYtWsXKisrMXPmzNv2zcnJgZ+fHwYPHozZs2ejoqLC8Ql2kDVr1sDHxwf33Xcf3nzzzVZPXRQVFaG8vNxiHjUaDR566KEuO4+2GI1GeHt737ZfV5/buro65OfnW8wJAOj1eptzcvTo0Rb9J02ahO+//x43btxwWK4dzWg0AkCb5nHEiBEICAjAhAkTcODAAUen1iHOnTuHwMBAhISE4Omnn8b58+dt9u0ucwo0vae3bNmCF1988bZf9KrEee0oPb4YKS8vh06ns2i74447oFarUV5ebnOMWq3GHXfcYdGu0+lsjpFbeno6Jk2ahKCgoFb7RUdHY+vWrfj666/x3nvv4dixYxg/fjxMJlMnZWq/l19+Gdu3b8eBAwcwf/58rF+/HnPnzrXZv3mubp3/rjyP1vz888/48MMPkZCQ0Go/JcxtZWUlGhoaJM2Jtf+HdTod6uvrUVlZ6bBcO5IQAklJSXjggQcQGhpqs19AQAA2btyIL774Ajt27MCQIUMwYcIEHDx4sBOzlW706NHYvHkz9u7di7/97W8oLy9HZGQkqqqqrPbvDnPa7Msvv8Tvv//e6j8ElTqvHUruQzP2SE5OFgBafRw7dsxijK3TNLNnzxZ6vb5Fu6urq9i2bZvV7W/dulWo1eoW7Y888oiYM2eOfTvVRvbse0lJiXBychKff/655O2VlZUJV1dX8cUXX3TULkhiz/42+/zzzwUAUVlZafX1I0eOCACirKzMon3WrFli0qRJHb4vt2PPvpaWlopBgwaJ+Ph4yduTe26tKS0tFQBEXl6eRfvq1avFkCFDrI656667xFtvvWXRdvjwYQFAGAwGh+XakebOnSuCg4NFSUmJ5LFTp04V06ZNc0BWjnPlyhWh0+nEe++9Z/X17jCnzfR6vZg6darkcUqc1/ZQ5AWs8+fPx9NPP91qnwEDBrQplr+/P7799luLtt9++w03btxoUZnfPKaurg6//fabxdGRiooKREZGtmm79rJn3zMyMuDj44PHHntM8vYCAgIQHByMc+fOSR7bEdoz1813ivzzn/+Ej49Pi9ebr+YvLy9HQECAub2iosLm3DuS1H0tKyvDuHHjEBERgY0bN0rentxza42vry+cnZ1bHAVpbU78/f2t9ndxcbE6713NggULsGvXLhw8eBD9+vWTPH7MmDHYsmWLAzJzHA8PD/zxj3+0+d5T+pw2u3jxIvbv348dO3ZIHqvEeW0PRRYjvr6+8PX17ZBYERERePPNN2EwGMwfSPv27YNGo0FYWJjVMWFhYXB1dUV2djZmzJgBADAYDDh16hTWrl3bIXnZInXfhRDIyMhAbGwsXF1dJW+vqqoKJSUlFh/Wnak9c11QUAAANnMPCQmBv78/srOzMWLECABN53dzc3OxZs0a+xJuByn7WlpainHjxiEsLAwZGRlwcpJ+xlXuubVGrVYjLCwM2dnZeOKJJ8zt2dnZePzxx62OiYiIwO7duy3a9u3bh/DwcLve851FCIEFCxZg586dyMnJQUhIiF1xCgoKutQctoXJZMKZM2cQFRVl9XWlzumtMjIy4OfnhylTpkgeq8R5bRe5D8042sWLF0VBQYFYuXKl8PT0FAUFBaKgoEDU1NQIIYSor68XoaGhYsKECeL48eNi//79ol+/fmL+/PnmGJcuXRJDhgwR3377rbktISFB9OvXT+zfv18cP35cjB8/XgwfPlzU19d3+j62Zv/+/QKAKCwstPr6kCFDxI4dO4QQQtTU1IjFixeLvLw8UVRUJA4cOCAiIiLEnXfeKaqrqzszbcny8vLEunXrREFBgTh//rzIzMwUgYGB4rHHHrPod/P+CiHE22+/LbRardixY4c4efKkeOaZZ0RAQECX3t/mUzPjx48Xly5dEgaDwfy4mVLndvv27cLV1VWkp6eLwsJCkZiYKDw8PMSFCxeEEEIsXbpUvPDCC+b+58+fF7169RKLFi0ShYWFIj09Xbi6utp1WrIzvfTSS0Kr1YqcnByLObx69aq5z637+v7774udO3eKn376SZw6dUosXbpUAOhSp9qsWbx4scjJyRHnz58X33zzjZg6daro3bt3t5vTmzU0NIj+/fuL1157rcVr3WVeO1K3L0bi4uKsnns/cOCAuc/FixfFlClThLu7u/D29hbz588X169fN79eVFTUYsy1a9fE/Pnzhbe3t3B3dxdTp04VxcXFnbhnbfPMM8+IyMhIm68DEBkZGUIIIa5evSr0er3o27evcHV1Ff379xdxcXFdcr9ulZ+fL0aPHi20Wq1wc3MTQ4YMEcnJyaK2ttai3837K0TT7b3JycnC399faDQa8eCDD4qTJ092cvbSZGRk2Lym5GZKntu//vWvIjg4WKjVajFy5EiL213j4uLEQw89ZNE/JydHjBgxQqjVajFgwACRlpbWyRlLZ2sOb35/3rqva9asEQMHDhRubm7ijjvuEA888ID4xz/+0fnJSxQTEyMCAgKEq6urCAwMFH/605/E6dOnza93lzm92d69ewUAcfbs2RavdZd57UgqIYTotMMwRERERLfo8bf2EhERkbxYjBAREZGsWIwQERGRrFiMEBERkaxYjBAREZGsWIwQERGRrFiMEBERkaxYjBAREZGsWIwQERGRrFiMEBERkaxYjBAREZGsWIwQERGRrP4/DNVOUzVCcTwAAAAASUVORK5CYII=",
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "n = np.arange(-10,10)\n",
        "\n",
        "xn= np.zeros(len(n))\n",
        "xn[7:13]=1\n",
        "y1= np.zeros(len(n))\n",
        "y1[10:16]=1\n",
        "\n",
        "plt.subplot(2, 1, 1)\n",
        "plt.stem(n, xn, linefmt='blue', label='x[n]')\n",
        "plt.legend()\n",
        "plt.subplot(2, 1, 2)\n",
        "plt.stem(n, y1, linefmt='red', label='y_1[n]')\n",
        "plt.legend()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "ff3eaf30",
      "metadata": {
        "id": "ff3eaf30"
      },
      "source": [
        "**1)** e) $y_5[n] = x[-n-2]$\n",
        "Sabendo que $x[n] = 0$ para $n<-3$ e $n>2$\n",
        "\n",
        "É possivel determinar $y_1[n]=0$ fazendo:\n",
        "\n",
        "$$-n-2 < -3$$\n",
        "e\n",
        "$$-n-2 > 2$$\n",
        "\n",
        "portanto:\n",
        "$$-n-2 < -3$$\n",
        "$$-n-2+2 < -3+2$$\n",
        "$$-n < -1$$\n",
        "$$n > 1$$\n",
        "e\n",
        "$$-n-2 > 2$$\n",
        "$$-n-2+2 > 2+2$$\n",
        "$$-n > 4$$\n",
        "$$n < -4$$\n",
        "\n",
        "logo,  *$y_2[n]=0$* para *$n<-4$* e *$n>1$*"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "e708dba4",
      "metadata": {
        "scrolled": true,
        "id": "e708dba4",
        "outputId": "6d87cfbe-1cbe-441b-b44c-120c86ecedbd"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f90f6978c40>"
            ]
          },
          "execution_count": 22,
          "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": [
        "n = np.arange(-10,10)\n",
        "\n",
        "xn= np.zeros(len(n))\n",
        "xn[7:13]=1\n",
        "y1= np.zeros(len(n))\n",
        "y1[6:12]=1\n",
        "\n",
        "plt.subplot(2, 1, 1)\n",
        "plt.stem(n, xn, linefmt='blue', label='x[n]')\n",
        "plt.legend()\n",
        "plt.subplot(2, 1, 2)\n",
        "plt.stem(n, y1, linefmt='red', label='y_1[n]')\n",
        "plt.legend()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "047797d5-359c-4529-94fd-ad0f3ae0a471",
      "metadata": {
        "id": "047797d5-359c-4529-94fd-ad0f3ae0a471"
      },
      "source": [
        "**2)** Resolvido por Frederico Ercolin Guazzelli\n",
        "**2)** a) $y_1(t) = x(1-t)$\n",
        "\n",
        "Substituindo $x(t)$ em $y_1(t)$\n",
        "\n",
        "\n",
        "$y_1(t) = x(1-t) = 0$ para t > 5\n",
        "\n",
        "Neste caso, $y_1(t)$ será igual a zero quando $1 - t > 5$.\n",
        "\n",
        "Resolvendo para t:\n",
        "$$1 - t > 5$$\n",
        "$$ -t > 5-1$$\n",
        "$$-t > 4$$\n",
        "portanto,\n",
        "$$t < -4$$\n",
        "\n",
        "logo,  *$y_1(t)$* será igual a zero quando *$t < -4$*.\n",
        "\n",
        "**2)** b) $y_2(t) = x(-t)$\n",
        "\n",
        "Substituindo $x(t)$ em $y_2(t)$\n",
        "\n",
        "\n",
        "$y_2(t) = x(-t) = 0$ para t > 5\n",
        "\n",
        "Neste caso, $y_2(t)$ será igual a zero quando $ - t > 5$.\n",
        "\n",
        "Resolvendo para t:\n",
        "$$ - t > 5$$\n",
        "$$ t < -5$$\n",
        "\n",
        "portanto,\n",
        "$$t < -5$$\n",
        "\n",
        "logo,  *$y_2(t)$* será igual a zero quando *$t < -5$*.\n",
        "\n",
        "\n",
        "**2)** c) $y_3(t) = x\\left(\\frac{t}{2}\\right)$\n",
        "\n",
        "Substituindo $x(t)$ em $y_3(t)$\n",
        "\n",
        "\n",
        "$y_3(t) = x\\left(\\frac{t}{2}\\right) = 0$ para t > 5\n",
        "\n",
        "Neste caso, $y_3(t)$ será igual a zero quando $ \\frac{t}{2} > 5$.\n",
        "\n",
        "Resolvendo para t:\n",
        "$$ \\frac{t}{2} > 5$$\n",
        "$$ t > 5*2$$\n",
        "\n",
        "portanto,\n",
        "$$t < 10$$\n",
        "\n",
        "logo,  *$y_3(t)$* será igual a zero quando *$t > 10$*.\n",
        "\n",
        "**2)** d) $y_4(t) = x(6t)$\n",
        "\n",
        "Substituindo $x(t)$ em $y_4(t)$\n",
        "\n",
        "\n",
        "$y_4(t) = x(6t) = 0$ para t > 5\n",
        "\n",
        "Neste caso, $y_4(t)$ será igual a zero quando $ 6t > 5$.\n",
        "\n",
        "Resolvendo para t:\n",
        "$$ 6t > 5$$\n",
        "\n",
        "portanto,\n",
        "$$t > \\frac{5}{6}$$\n",
        "\n",
        "logo,  *$y_4(t)$* será igual a zero quando *$t > \\frac{5}{6} $*."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "b9375fdb-5e5d-4614-8ffd-bb3b92ca5803",
      "metadata": {
        "id": "b9375fdb-5e5d-4614-8ffd-bb3b92ca5803"
      },
      "source": [
        "**3)** Resolvido por Rafaela Farto de Camargo Fernandes\n",
        "\n",
        "a) $y_1(t) = x(t-3)$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "f1f9e82d-bc17-47a7-a252-0723f7b2d916",
      "metadata": {
        "tags": [],
        "id": "f1f9e82d-bc17-47a7-a252-0723f7b2d916",
        "outputId": "4c4457d4-cbe5-48a0-dbd5-83a799b28336"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Definindo o intervalo de tempo para o gráfico\n",
        "t = np.linspace(-3, 6, 1000)  # Intervalo de -3 a 6\n",
        "\n",
        "# Defina o sinal original y(t).\n",
        "def y(t):\n",
        "    if -2 <= t < -1:\n",
        "        return 1\n",
        "    elif -1 <= t < 0:\n",
        "        return -t\n",
        "    elif 0 <= t < 1:\n",
        "        return -2 * t\n",
        "    elif 1 <= t < 2:\n",
        "        return 2 * t - 4\n",
        "    else:\n",
        "        return 0\n",
        "\n",
        "# Defina o sinal transformado y1(t) = x(t - 3)\n",
        "def y1(t):\n",
        "    return y(t - 3)\n",
        "\n",
        "# Calcule os valores de y1(t) para o intervalo de tempo especificado\n",
        "y1_values = [y1(ti) for ti in t]\n",
        "\n",
        "# Crie o gráfico\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.plot(t, y1_values, label='y1(t)')\n",
        "plt.title('Sinal Transformado y1(t) = x(t - 3)')\n",
        "plt.xlabel('t')\n",
        "plt.ylabel('y1(t)')\n",
        "plt.grid(True)\n",
        "plt.axhline(0, color='black', linewidth=0.7, linestyle='--')\n",
        "plt.axvline(0, color='black', linewidth=0.7, linestyle='--')\n",
        "plt.xlim(-3, 6)\n",
        "plt.ylim(-2, 2)\n",
        "plt.legend()\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "cf260b44-89d9-4cd1-80a2-9ab23836712c",
      "metadata": {
        "id": "cf260b44-89d9-4cd1-80a2-9ab23836712c"
      },
      "source": [
        "b) $y_2(t) = x(1-t)$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "9562bb6a-6d6b-4afe-9934-e56529a9cc33",
      "metadata": {
        "tags": [],
        "id": "9562bb6a-6d6b-4afe-9934-e56529a9cc33",
        "outputId": "0dc87131-6ce1-47dc-8387-21cce2aedcd9"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Definindo o intervalo de tempo para o gráfico\n",
        "t = np.linspace(-3, 6, 1000)  # Intervalo de -3 a 6\n",
        "\n",
        "# Defina o sinal original y(t).\n",
        "def y(t):\n",
        "    if -2 <= t < -1:\n",
        "        return 1\n",
        "    elif -1 <= t < 0:\n",
        "        return -t\n",
        "    elif 0 <= t < 1:\n",
        "        return -2 * t\n",
        "    elif 1 <= t < 2:\n",
        "        return 2 * t - 4\n",
        "    else:\n",
        "        return 0\n",
        "\n",
        "# Defina o sinal transformado y2(t) = x(1 - t)\n",
        "def y2(t):\n",
        "    return y(1 - t)\n",
        "\n",
        "# Calcule os valores de y2(t) para o intervalo de tempo especificado\n",
        "y2_values = [y2(ti) for ti in t]\n",
        "\n",
        "# Crie o gráfico\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.plot(t, y2_values, label='y2(t)')\n",
        "plt.title('Sinal Transformado y2(t) = x(1 - t)')\n",
        "plt.xlabel('t')\n",
        "plt.ylabel('y2(t)')\n",
        "plt.grid(True)\n",
        "plt.axhline(0, color='black', linewidth=0.7, linestyle='--')\n",
        "plt.axvline(0, color='black', linewidth=0.7, linestyle='--')\n",
        "plt.xlim(-3, 6)\n",
        "plt.ylim(-2, 2)\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "b069e4ad-3b58-4d4f-832b-867160b86c1d",
      "metadata": {
        "id": "b069e4ad-3b58-4d4f-832b-867160b86c1d"
      },
      "source": [
        "c) $y_3(t) = x(2-\\frac{t}{3})$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "a4cdae9b-5f32-4a7b-83f4-a0e07ba08faf",
      "metadata": {
        "tags": [],
        "id": "a4cdae9b-5f32-4a7b-83f4-a0e07ba08faf",
        "outputId": "77b1ef03-25d8-4137-8036-8c37f35a415c"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Definindo o intervalo de tempo para o gráfico\n",
        "t = np.linspace(-3, 6, 1000)  # Intervalo de -3 a 6\n",
        "\n",
        "# Defina o sinal original y(t).\n",
        "def y(t):\n",
        "    if -2 <= t < -1:\n",
        "        return 1\n",
        "    elif -1 <= t < 0:\n",
        "        return -t\n",
        "    elif 0 <= t < 1:\n",
        "        return -2 * t\n",
        "    elif 1 <= t < 2:\n",
        "        return 2 * t - 4\n",
        "    else:\n",
        "        return 0\n",
        "\n",
        "# Defina o sinal transformado y3(t) = x(2-t/3)\n",
        "def y3(t):\n",
        "    return y(2-t/3)\n",
        "\n",
        "# Calcule os valores de y2(t) para o intervalo de tempo especificado\n",
        "y3_values = [y3(ti) for ti in t]\n",
        "\n",
        "# Crie o gráfico\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.plot(t, y2_values, label='y3(t)')\n",
        "plt.title('Sinal Transformado y3(t) = x(2-t/3)')\n",
        "plt.xlabel('t')\n",
        "plt.ylabel('y3(t)')\n",
        "plt.grid(True)\n",
        "plt.axhline(0, color='black', linewidth=0.7, linestyle='--')\n",
        "plt.axvline(0, color='black', linewidth=0.7, linestyle='--')\n",
        "plt.xlim(-3, 6)\n",
        "plt.ylim(-2, 2)\n",
        "plt.legend()\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "021049c7-cee9-46fa-9709-439d6f249218",
      "metadata": {
        "id": "021049c7-cee9-46fa-9709-439d6f249218"
      },
      "source": [
        "**5)** Resolvido por Juliana Soares da Silva de Oliveira\n",
        "\n",
        "a)\n",
        "$x_1(-t) = \\mathrm{sen}(2(-t))\\cos(2(-t)) = -\\mathrm{sen}(2t)\\cos(2t) = -x_1(t) ≠ x_1(t)$\n",
        "\n",
        "Como $x_1(-t) = -x_1(t)$, podemos concluir que o sinal $x_1(t)$ é ímpar.\n",
        "\n",
        "b)\n",
        "$x_2(-t) = \\mathrm{sen}((-t)^2) = \\mathrm{sen}(t^2) = x_2(t)$\n",
        "\n",
        "Como $x_2(-t) = x_2(t)$, podemos concluir que o sinal $x_2(t)$ é par."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "9f56de37-c635-4368-81f6-b7e9521dd00e",
      "metadata": {
        "id": "9f56de37-c635-4368-81f6-b7e9521dd00e"
      },
      "source": [
        "**6)** Resolvido por Frederico Ercolin Guazzelli\n",
        "\n",
        "Parte par definida como:\n",
        "\n",
        "$ x_p(t) = \\frac{1}{2}[x(t)+x(-t)] $ e $ x_p[n] = \\frac{1}{2}(x[t]+x[-t]) $\n",
        "\n",
        "Parte ímpar definida como:\n",
        "\n",
        "$ x_i(t) = \\frac{1}{2}[x(t)-x(-t)] $ e $ x_i[n] = \\frac{1}{2}(x[t]-x[-t]) $\n",
        "\n",
        " a) $x_1(t) = \\mathrm{sen}(\\omega_0t)$\n",
        "\n",
        "Parte par:\n",
        "$$ x_{1p}(t) = \\frac{1}{2}[\\mathrm{sen}(\\omega_0t) + \\mathrm{sen}(-\\omega_0t)] = \\frac{1}{2}[\\mathrm{sen}(\\omega_0t) - \\mathrm{sen}(\\omega_0t)] = 0$$\n",
        "\n",
        "Parte ímpar:\n",
        "$$ x_{1i}(t) = \\frac{1}{2}[\\mathrm{sen}(\\omega_0t) - \\mathrm{sen}(-\\omega_0t)] = \\frac{1}{2}[\\mathrm{sen}(\\omega_0t) + \\mathrm{sen}(\\omega_0t)] = \\mathrm{sen}(\\omega_0t) $$\n",
        "\n",
        "b) $x_2(t) = \\cos(\\omega_0t)$\n",
        "\n",
        "Parte par:\n",
        "$$ x_{2p}(t) = \\frac{1}{2}[\\cos(\\omega_0t) + \\cos(-\\omega_0t)] = \\frac{1}{2}[\\cos(\\omega_0t) + \\cos(\\omega_0t)] = \\cos(\\omega_0t)$$\n",
        "\n",
        "Parte ímpar:\n",
        "$$ x_{2i}(t) = \\frac{1}{2}[\\cos(\\omega_0t) - \\cos(-\\omega_0t)] = \\frac{1}{2}[\\cos(\\omega_0t) - \\cos(\\omega_0t)] = 0 $$\n",
        "\n",
        "c) $x_3(t) = \\cos(\\omega_0t+\\theta)$\n",
        "\n",
        "Parte par:\n",
        "$$ x_{3p}(t) = \\frac{1}{2}[\\cos(\\omega_0t+\\theta) + \\cos(-\\omega_0t-\\theta)] = \\frac{1}{2}[\\cos(\\omega_0t+\\theta) + \\cos(\\omega_0t+\\theta)] = \\cos(\\omega_0t+\\theta)$$\n",
        "\n",
        "Parte ímpar:\n",
        "$$ x_{3i}(t) \\frac{1}{2}[\\cos(\\omega_0t+\\theta) - \\cos(-\\omega_0t-\\theta)] = \\frac{1}{2}[\\cos(\\omega_0t+\\theta) - \\cos(\\omega_0t+\\theta)] = 0 $$\n",
        "\n",
        "d) $x_4[n] = \\left(\\frac{1}{2}\\right)^n$\n",
        "\n",
        "Parte par:\n",
        "$$ x_{4p}[n] = \\frac{1}{2}[\\left(\\frac{1}{2}\\right)^n + \\left(\\frac{1}{2}\\right)^{-n}] = \\frac{1}{2}(2^{n-n})= \\frac{1}{2}$$\n",
        "\n",
        "Parte ímpar:\n",
        "$$ x_{4i}[n] = \\frac{1}{2}[\\left(\\frac{1}{2}\\right)^n - \\left(\\frac{1}{2}\\right)^{-n}] = \\frac{1}{2}(2^{n-n}-2^{-n+n})= \\frac{1}{2}(1 - 2^{-2n})$$\n",
        "\n",
        "e) $x_5[n] = \\left(\\frac{1}{2}\\right)^n\\cos(n/10)$\n",
        "\n",
        "Parte par:\n",
        "$$ x_{5p}[n] = \\frac{1}{2}[\\left(\\frac{1}{2}\\right)^n\\cos(n/10) + \\left(\\frac{1}{2}\\right)^{-n}\\cos(-n/10)] = \\frac{1}{2}(2^{n-n}\\cos(n/10)+ 2^{-n+n}\\cos(-n/10))= \\frac{1}{2}(\\cos(n/10)+\\cos(n/10)) = \\cos(n/10)$$\n",
        "\n",
        "Parte ímpar:\n",
        "$$ x_{5i}[n] = \\frac{1}{2}[\\left(\\frac{1}{2}\\right)^n\\cos(n/10) - \\left(\\frac{1}{2}\\right)^{-n}\\cos(-n/10)] = \\frac{1}{2}(2^{n-n}\\cos(n/10)- 2^{-n+n}\\cos(-n/10))= \\frac{1}{2}(\\cos(n/10)-\\cos(n/10)) = 0$$"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "19f13039-3461-4de7-b738-e1301b0bec28",
      "metadata": {
        "id": "19f13039-3461-4de7-b738-e1301b0bec28"
      },
      "source": [
        "**8)** Resolvido por Juliana Soares da Silva de Oliveira\n",
        "\n",
        "\n",
        "$\\mathrm{sen}(at) = \\frac{2π}{a}$\n",
        "\n",
        "$\\mathrm{sen}(2t) = \\frac{2π}{2} = π$\n",
        "\n",
        "Portanto, o período fundamental do sinal $x(t) = sen(2t)$ é $π$. Isso significa que a função se repete a cada $π$ unidades de tempo."
      ]
    },
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