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@astropenguin
Last active June 10, 2021 07:23
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "b3ea633f-8159-445c-8cf5-40498b117375",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "5fcc585c-9479-4a7f-b90b-151466030244",
"metadata": {},
"outputs": [],
"source": [
"f_sample = 1.0 # Hz\n",
"t_signal = np.arange(-5, 5+1/1000, 1/1000)\n",
"t_sample = np.arange(-5, 5+1/f_sample, 1/f_sample)\n",
"\n",
"\n",
"def signal(t: np.ndarray, f_signal: float) -> np.ndarray:\n",
" return np.sin(2 * np.pi * f_signal * t)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "95d36bbe-9b3f-44eb-9266-f02fb81060c6",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1200x400 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(12, 4), dpi=100)\n",
"\n",
"f_signal = 0.9 * f_sample # Hz\n",
"f_alias = f_sample - f_signal # Hz\n",
"f_alias = (f_signal + 0.5*f_sample) % f_sample - 0.5*f_sample\n",
"\n",
"ax.plot(t_signal, signal(t_signal, f_signal), color=\"gray\", label=f\"Signal ({f_signal:.2f} Hz)\")\n",
"ax.plot(t_sample, signal(t_sample, f_signal), \"o\", color=\"gray\", label=f\"Sample ({f_sample:.2f} Hz)\")\n",
"ax.plot(t_signal, signal(t_signal, f_alias), alpha=0.5, label=f\"Alias ({f_alias:.2f} Hz)\")\n",
"\n",
"ax.set_xlabel(\"Time (s)\")\n",
"ax.set_ylabel(\"Amplitude (arb. unit)\")\n",
"ax.set_ylim(-1.49, 1.49)\n",
"ax.legend(ncol=3, loc=\"upper left\")\n",
"ax.grid()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "4bd39501-6d4e-4539-a139-470072727553",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1200x400 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(12, 4), dpi=100)\n",
"\n",
"f_signal = np.arange(0, 3*f_sample, 0.001*f_sample)\n",
"f_alias = (f_signal + 0.5*f_sample) % f_sample - 0.5*f_sample\n",
"\n",
"ax.plot(f_signal, f_alias)\n",
"ax.set_xlabel(\"Signal frequency (Hz)\")\n",
"ax.set_ylabel(\"Alias frequency (Hz)\")\n",
"ax.set_ylim(-0.59, 0.59)\n",
"ax.grid()"
]
}
],
"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": "3.8.10"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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