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@halserach
Created March 26, 2024 12:34
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Exercises I did for Assignment 5.
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"provenance": []
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"id": "OVsjqIDVNX56"
},
"outputs": [],
"source": [
"# Import Libraries and packages\n",
"\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"source": [
"# Part 1: Initialize with Integers"
],
"metadata": {
"id": "4kLTC7HmO14l"
}
},
{
"cell_type": "code",
"source": [
"# Define list component manually\n",
"x = [0, 1, 2, 3, 4]\n",
"print(x)\n",
"y = np.array(x)\n",
"print(y)\n",
"\n",
"# Use list\n",
"x = list(range(0,5))\n",
"print(x)\n",
"y = np.array(x)\n",
"print(y)\n",
"\n",
"# Use unpacking\n",
"x = [*range(0,5)]\n",
"print(x)\n",
"y = np.array(x)\n",
"print(y)\n",
"\n",
"# Use list comprehension\n",
"x = [i for i in range(0,5)]\n",
"print(x)\n",
"y = np.array(x)\n",
"print(y)\n",
"\n",
"# Use other list\n",
"a = [0, 1, 2, 3, 4]\n",
"x = [i for i in a]\n",
"print(x)\n",
"y = np.array(x)\n",
"print(y)\n",
"\n",
"# Use numpy arange()\n",
"y = np.arange(0,5,1.0)\n",
"print(y)\n",
"\n",
"# Use numpy linspace()\n",
"y = np.linspace(0,4,5)\n",
"print(y)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "NF1irD_BO6Z5",
"outputId": "dc933814-079d-4dfc-f36f-0af30cdc2552"
},
"execution_count": 5,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"[0, 1, 2, 3, 4]\n",
"[0 1 2 3 4]\n",
"[0, 1, 2, 3, 4]\n",
"[0 1 2 3 4]\n",
"[0, 1, 2, 3, 4]\n",
"[0 1 2 3 4]\n",
"[0, 1, 2, 3, 4]\n",
"[0 1 2 3 4]\n",
"[0, 1, 2, 3, 4]\n",
"[0 1 2 3 4]\n",
"[0. 1. 2. 3. 4.]\n",
"[0. 1. 2. 3. 4.]\n"
]
}
]
},
{
"cell_type": "markdown",
"source": [
"# Part 2: Initialize with Float"
],
"metadata": {
"id": "92y6VGXOP0Rb"
}
},
{
"cell_type": "code",
"source": [
"# Use other list\n",
"i = [*range(0, 11)]\n",
"print(i, '\\n')\n",
"x = [j*0.5 for j in i]\n",
"print(x, '\\n')\n",
"y = np.array(x)\n",
"print(y)\n",
"\n",
"# Use numpy.arange()\n",
"y = np.arange(0,5.5,0.5)\n",
"print(y)\n",
"\n",
"# Use numpy.linspace()\n",
"y = np.linspace(0, 5, 11)\n",
"print(y)\n",
"\n",
"# Use numpy.linspace() with endpoint=False\n",
"y = np.linspace(0,5,10,endpoint=False)\n",
"print(y)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "I6jX5eY5P2B8",
"outputId": "98478a81-e163-40e0-808a-aee3df4ccfb7"
},
"execution_count": 6,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] \n",
"\n",
"[0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0] \n",
"\n",
"[0. 0.5 1. 1.5 2. 2.5 3. 3.5 4. 4.5 5. ]\n",
"[0. 0.5 1. 1.5 2. 2.5 3. 3.5 4. 4.5 5. ]\n",
"[0. 0.5 1. 1.5 2. 2.5 3. 3.5 4. 4.5 5. ]\n",
"[0. 0.5 1. 1.5 2. 2.5 3. 3.5 4. 4.5]\n"
]
}
]
},
{
"cell_type": "markdown",
"source": [
"# Part 3: Duration and Sampling Size"
],
"metadata": {
"id": "dVYbYVdQQcOd"
}
},
{
"cell_type": "code",
"source": [
"# sin(x), 0 <= x <= 2*pi, n=11, endpoint=True\n",
"x = np.linspace(0, 2*np.pi, 11)\n",
"print(np.round(x,2))\n",
"y = np.sin(x)\n",
"plt.plot(x, y, 'ob-')\n",
"plt.xlim(0,7)\n",
"plt.show()"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 447
},
"id": "hhDpSKptQhCP",
"outputId": "84bf2368-d1ee-4a65-f961-60681dea999d"
},
"execution_count": 8,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"[0. 0.63 1.26 1.88 2.51 3.14 3.77 4.4 5.03 5.65 6.28]\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"source": [
"# sin(x), 0 <= x <= 2*pi, n=11, endpoint=False\n",
"x = np.linspace(0, 2*np.pi, 11, False)\n",
"print(np.round(x,2))\n",
"y = np.sin(x)\n",
"plt.plot(x, y, 'ob-')\n",
"plt.xlim(0,7)\n",
"plt.show()"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 447
},
"id": "BcwqsPFTRNSW",
"outputId": "9d2dd1bd-f21d-4754-8c59-dc223c8d5ef3"
},
"execution_count": 9,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"[0. 0.57 1.14 1.71 2.28 2.86 3.43 4. 4.57 5.14 5.71]\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"## Number of points, sampling rate, duration"
],
"metadata": {
"id": "eeK4KO6dRbik"
}
},
{
"cell_type": "code",
"source": [
"# 10 points in 2s => SR = 5 Hz\n",
"N = 10\n",
"D = 2\n",
"SR = N/D; print('SR =', SR)\n",
"\n",
"t = np.linspace(0, D, N, endpoint=False) ; T = 1\n",
"\n",
"x = np.sin(2*np.pi/T*t)\n",
"\n",
"plt.plot(t, x, 'ob-')\n",
"plt.xticks(np.linspace(0, D, 11)) ; plt.xlabel('t(s)') ; plt.ylabel('x')\n",
"plt.xlim(0, D)\n",
"plt.grid()\n",
"plt.show()"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 466
},
"id": "sIW4M6XcRYRP",
"outputId": "469ad179-408b-46b3-d91c-4a4a81438b7e"
},
"execution_count": 10,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"SR = 5.0\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"source": [
"# 20 points in 2s => SR = 5 Hz\n",
"N = 20\n",
"D = 2\n",
"SR = N/D; print('SR =', SR)\n",
"\n",
"t = np.linspace(0, D, N, endpoint=False) ; T = 1\n",
"\n",
"x = np.sin(2*np.pi/T*t)\n",
"\n",
"plt.plot(t, x, 'ob-')\n",
"plt.xticks(np.linspace(0, D, 11)) ; plt.xlabel('t(s)') ; plt.ylabel('x')\n",
"plt.xlim(0, D)\n",
"plt.grid()\n",
"plt.show()"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 466
},
"id": "tkuYj4GASCG2",
"outputId": "b4b0d0bb-ad78-4ff8-a037-48a948c20a27"
},
"execution_count": 11,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"SR = 10.0\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"source": [
"# 50 points in 2s => SR = 5 Hz\n",
"N = 50\n",
"D = 2\n",
"SR = N/D; print('SR =', SR)\n",
"\n",
"t = np.linspace(0, D, N, endpoint=False) ; T = 1\n",
"\n",
"x = np.sin(2*np.pi/T*t)\n",
"\n",
"plt.plot(t, x, 'ob-')\n",
"plt.xticks(np.linspace(0, D, 11)) ; plt.xlabel('t(s)') ; plt.ylabel('x')\n",
"plt.xlim(0, D)\n",
"plt.grid()\n",
"plt.show()"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 466
},
"id": "yEP4Xoz6SFE6",
"outputId": "2a6f48b1-3fc1-41aa-9659-517588e19753"
},
"execution_count": 12,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"SR = 25.0\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"source": [
"# 200 points in 2s => SR = 5 Hz\n",
"N = 200\n",
"D = 2\n",
"SR = N/D; print('SR =', SR)\n",
"\n",
"t = np.linspace(0, D, N, endpoint=False) ; T = 1\n",
"\n",
"x = np.sin(2*np.pi/T*t)\n",
"\n",
"plt.plot(t, x, 'ob-')\n",
"plt.xticks(np.linspace(0, D, 11)) ; plt.xlabel('t(s)') ; plt.ylabel('x')\n",
"plt.xlim(0, D)\n",
"plt.grid()\n",
"plt.show()"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 466
},
"id": "qGH-2ET7SHYQ",
"outputId": "53e31f5c-0b55-4d92-bf8d-842ba664b295"
},
"execution_count": 13,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"SR = 100.0\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"source": [
"# 2000 points in 2s => SR = 5 Hz\n",
"N = 2000\n",
"D = 2\n",
"SR = N/D; print('SR =', SR)\n",
"\n",
"t = np.linspace(0, D, N, endpoint=False) ; T = 1\n",
"\n",
"x = np.sin(2*np.pi/T*t)\n",
"\n",
"plt.plot(t, x, 'ob-')\n",
"plt.xticks(np.linspace(0, D, 11)) ; plt.xlabel('t(s)') ; plt.ylabel('x')\n",
"plt.xlim(0, D)\n",
"plt.grid()\n",
"plt.show()"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 466
},
"id": "Mk9E0Z6HSOKW",
"outputId": "8df1a3d4-7809-4181-ae34-979ae4b6ba0d"
},
"execution_count": 14,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"SR = 1000.0\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
}
]
}
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