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Jupyter notebooks and labs
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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"id": "9ca072d6-d840-4895-a991-38a960f43d4b", | |
"metadata": {}, | |
"source": [ | |
"# 5.\tDerivative of Gaussian source time function using finite difference\n", | |
"\n", | |
"Figure 26 show the code for generating gaussian source time function and its derivatives until order 4 that has been illustrated in fig. 27. In the figure, it shows that the behavior of changing form of curves along order is like the phase shifting, that actually every curves is shifting 90 degrees, so that the curve seem to move to the left side. For clarifying it, the order 2 show the main lobe has a reverse form than order 0 and back to the top at order 4. As the explanation, the order 0 seems to shift 180 degrees to the right then obtaining order 2 and shifting again 180 degrees (the total is 360 degrees from order 0) then obtaining order 4. The difference among them is the frequency which has been changed along the order by increasing the order is causing the increase of frequency.\n" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"id": "aea6cb4d-1d76-481d-b32f-8ba98494dd02", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"from finitediff import derivatives_at_point_by_finite_diff\n", | |
"import numpy as np\n", | |
"import matplotlib.pyplot as plt\n", | |
"\n", | |
"def fin_diff(x,y,h,m):\n", | |
" n_data = len(x)\n", | |
" yest = np.zeros((n_data,m+1))\n", | |
" for i, xf in enumerate(x):\n", | |
" lower_bound = max(0, i - h)\n", | |
" upper_bound = min(n_data - 1, i + h)\n", | |
" yi = derivatives_at_point_by_finite_diff(x[lower_bound:upper_bound],\n", | |
" y[lower_bound:upper_bound], xf, m)\n", | |
" yest[i,:] = yi[:]\n", | |
" return yest\n", | |
"\n", | |
"t = np.linspace(-3,3,100)\n", | |
"f = np.exp(-np.power(t,2))\n", | |
"m = 4\n", | |
"h = 5\n", | |
"fest = fin_diff(t,f,h,m)\n", | |
"\n", | |
"plt.figure()\n", | |
"plt.plot(t,f)\n", | |
"for i in range(m + 1):\n", | |
" plt.plot(t,fest[:,i], label='order = {}'.format(i))\n", | |
"plt.legend()\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"id": "6b5aed7f-753e-4086-9178-a30e503154c6", | |
"metadata": {}, | |
"source": [ | |
"Figure 26. The code for testing Gaussian function\n", | |
"\n", | |
"Figure 27. The result of Fig. 26" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"id": "da00cc4f-fb2c-4422-815c-8c24858a8773", | |
"metadata": {}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python 3", | |
"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": "3.8.8" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 5 | |
} |
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