Lugovtsov/project/data-processing/gen-data.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 398,
   "id": "50f27832-a7b1-4fac-b9b8-988606608b84",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 481,
   "id": "80a10edc-520c-4b05-af86-29dbb440717e",
   "metadata": {},
   "outputs": [],
   "source": [
    "l = int(7e5)\n",
    "t = np.linspace(0, 1e-1, l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 482,
   "id": "70c787d1-fa7a-4d43-95ec-73f9929f357b",
   "metadata": {},
   "outputs": [],
   "source": [
    "nu = 1.6e3\n",
    "phi1 = 0\n",
    "a1 = 10\n",
    "phi2 = np.pi / 2\n",
    "a2 = 1350e-3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 483,
   "id": "8730fd74-6b30-4b92-87af-7205d5732ac9",
   "metadata": {},
   "outputs": [],
   "source": [
    "V1 = a1*np.sin(nu*t/(2*np.pi) + phi1)\n",
    "V2 = a2*np.sin(nu*t/(2*np.pi) + phi2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 484,
   "id": "b0aaf4c1-aee0-4ecf-99ad-560f93770840",
   "metadata": {},
   "outputs": [],
   "source": [
    "f = V1\n",
    "g = np.random.normal(loc=V2, scale=0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 485,
   "id": "b66882de-6ed3-4931-8049-33c27da52528",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, f)\n",
    "plt.plot(t, g)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 486,
   "id": "e56a0992-4cdc-4839-9aea-91a2497c2696",
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(r'sig1.csv', 'w') as file:\n",
    "    string = 'voltage[V],time[ns]\\n'\n",
    "    for i in range(l):\n",
    "        string += f'{f[i]:.10f},{t[i]*1e9:.4f}\\n'\n",
    "    file.write(string)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 487,
   "id": "29fee1dc-eb0e-4e10-958a-640203b7e4ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(r'sig2.csv', 'w') as file:\n",
    "    string = 'voltage[V],time[ns]\\n'\n",
    "    for i in range(l):\n",
    "        string += f'{g[i]:.10f},{t[i]*1e9:.4f}\\n'\n",
    "    file.write(string)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 488,
   "id": "c11ded9c-8375-4740-bcf1-3b07bfc07b19",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "Ff = np.fft.fft(f)\n",
    "Fg = np.fft.fft(g)\n",
    "lamb = Fg / Ff\n",
    "freq = np.fft.fftfreq(l, d=t[1])\n",
    "\n",
    "lamb = np.append(lamb[(l // 2):], lamb[:(l // 2)])\n",
    "freq = np.append(freq[(l // 2):], freq[:(l // 2)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 498,
   "id": "571b64d7-be74-4733-96a7-aa363d78808a",
   "metadata": {},
   "outputs": [],
   "source": [
    "lim = 20\n",
    "mid = l // 2\n",
    "ll = mid - lim\n",
    "rl = mid + lim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 499,
   "id": "125739fb-685a-462e-a78e-ecb846a4a5be",
   "metadata": {},
   "outputs": [],
   "source": [
    "cur_freq = freq[ll:rl]\n",
    "cur_lamb = lamb[ll:rl]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 500,
   "id": "8bc8887d-bc88-4e3b-99c9-309f2e9ee0eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7eff6c678730>]"
      ]
     },
     "execution_count": 500,
     "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": [
    "plt.plot(cur_freq, np.absolute(cur_lamb))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 501,
   "id": "22214b98-571f-45e4-9fdd-44551aab288a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7eff6c772590>]"
      ]
     },
     "execution_count": 501,
     "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": [
    "plt.plot(cur_freq, np.angle(cur_lamb))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 497,
   "id": "61d8e664-bf3c-4991-bcc7-d7f937d66abd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7eff6c4ee5c0>]"
      ]
     },
     "execution_count": 497,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAioAAAGvCAYAAAB1pf5FAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjYuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8o6BhiAAAACXBIWXMAAA9hAAAPYQGoP6dpAABQwklEQVR4nO3dd3hTZfsH8G/Sveku0EFbKEN2WWUoozJEFEVcKFMU3uLCn0oFRUXBgTh4ERS1gIIgrwKijCJbKJsCBVooq6WlLasT6Ep+fxTSpkmapM3JOUm+n+vKRXLOyckdmnHnGfcjUyqVShARERFJkFzsAIiIiIh0YaJCREREksVEhYiIiCSLiQoRERFJFhMVIiIikiwmKkRERCRZTFSIiIhIspioEBERkWTZix1AQykUCmRnZ8PDwwMymUzscIiIiMgASqUSRUVFaNKkCeRy3e0mFp+oZGdnIyQkROwwiIiIqB4yMzMRHBysc7/FJyoeHh4Aqp6op6enyNEQERGRIQoLCxESEqL6HtfF4hOVe909np6eTFSIiIgsjL5hGxxMS0RERJLFRIWIiIgki4kKERERSRYTFSIiIpIsJipEREQkWUxUiIiISLKYqBAREZFkMVEhIiIiyWKiQkRERJLFRIWIiIgki4kKERERSRYTFSIiIpIsJiomlJJVgKm/JeNKwW2xQyEiIlJz6XoJpv6WjLO5RWKHYhQmKib08Px/8ceRLLz6a7LYoWh1peA2Hvnvv/j98GWxQyEisjo/J13E8AV7cLOkTOxQtBqbcBB/HMnC4wv3ih2KUZioCCD9arHYIWj10V+ncfxyAd5YfUzsUIiIrM67604iOTMf87elix2KVheulQAAiu5UiByJcZioWKnySgX+PXsNt8qqX5DFpZb14iQiskS3yytV14tLK7An/RoqFUoRI7JsTFQEklNwB4O/2oUV+zNEefy5iWl47sf9mPzLEVEen4iIgFGL92HUD/uxePd5UR7/h93nMfSb3ci/Jc3uKEMwURHInI2nkZpThHfWnBDl8X9JugQA2HnmqsH3qahUCBUOEZHVMOaz8tjlAgDA/0QaG/jR36dxMrsQC3ecE+XxTYGJikBulVVqbFMqlZLNav+77SxavbsJKVkFYodCRCRZ+89fR8t3N2HJngtih6KVru+Y0grL/SHKRMWMZqxNQccPt2B7ap7YoWiYm3gGFQolPlx/SuxQiIgk6/VVyahUKPG+BD8r/zyWjY4fbsGnm1LFDsWkmKiY0fK741XmJqaJHAkREQlHnIGz7/95EgAsuptHGyYqFuzwpZuYt+UMyiy4SY+IyFbdKqvA3M1p7HLXg4lKA1y8VoK8ojuCP87e9Gt47Ns9OH2lUG37iIV78c3Ws1i696Lec2w8ccXggbVZ+bfxz6lcKJWcTkdEVKlQYvPJHOQWGvZ5/+uBTGxLzdV73Nf/nMV/t6fj4fn/qm0/mnETj327B0czbtYrXmNcKbiNzBu3BH+chmCiUk/XikvRd+4OdPt4q8a+GyauSvjsD/txNCMfE5Yc1Lr//DX9BeYmLzd8mnKvT7bhhWWHsPlkjsH3ISKyVqsOZuKlnw+j39wdBt9n/JJDeo85VevH5z0jFu7F0Yx8jBC4gmylQomYOdvQ57PtajW3pIaJSj2dza1ODkorKrFgu/CVCG+YecbQvvM3zPp4RERStD2tagKEttmcQrhXG07IGnGLdp7DnRqF6a4WlQr3YA1kL3YAlqLgdjk8ne0hk8k09v2w+wI+36x7gGxyZj46hjQSMDoiIiJ1Seeu69z3ycZUuDjYad2nUChRXFYBT2cHoUIzCltUDHDo4g10+CARr61K1rpf20ComsM7nv4+SaDIxKFUKk3evUVEJCZr/Ex7ZvG+Ovef0bGK8oSlB9H+/USk5mjvmjI3JioGuDfVa11yttb9+tZwuFOuPivH0DGqtVfgvFOuwAtLD2Hfed1Zsjl89PdpdJ61BeuSs0SNg4jIFH7edwmdZ23B1/+c1XuskFMMdqTl4cVl6mNblEqlYKsx6/ru2p5WNfFCrCVgamOiYgKJp/SP7jbWqoMZ6DRrC77654za9n9O5+Lp7+vOkg1RcLscTy5Kws/7Lhl93x//rarIOGdDw4sKfb/rHDacuNLg8xCR7fnjyGWDZj3q8+7aFADAl7U+bw3x/a5zeHbxPrXxHvU1NuGgxvfJrL9Oo9OsLYJ8Tq48mGnycwqBiUo9aRmqYrSM67cwYclBHLyoOWh12h9VawR9pSPDL7pT3qDHXrTzHA5cvKF6g4rh+OV8zN6Qiv8YMSOJiOieqb8dw8w/TyI7/7ZoMczekIq9565jVQO/9HUlOj/dLdU/e8NpjX27z17FC0sPqaZNm+BrSZI4mNZM9p67prp+r7EtbsURnMgqwNbUPFz8ZKhR51u8u+Y6E8a/PG+VVk9FKy4VZ1ratWLpjjInIssh1mdYzXEtDW1R+f2I8YsWPv/jAQBV3UM/ju2qtu/wJeuZtclERQelUokpK47Cudao6L3p19CzuZ/R53t28X6NbVkN+BVQYsI35rdmmFpNRGQNao4x1NbKUV+1xzIaI0dLIboRC+s3iWNHWvVadEol8NLPh+Dp7IDPR3aod3wNJXjXT1ZWFp577jn4+vrCxcUF7dq1w6FD1YOFlEol3nvvPTRu3BguLi6IjY3F2bP6BzQJLbvgDv4+cQW/H7msNnf+2R/240qBeM2MQrhebH2j3YmIhGZopVpLoFQCqTmFGJtQXVj04vUSbD6Zi9WHL+udNCIkQROVmzdvolevXnBwcMDGjRtx6tQpfPHFF/D29lYd89lnn+Gbb77BokWLsH//fri5uWHQoEG4c0fcF4Cijj9Kdr70XpwVlQrMXJeC3yxkcBQRkS1auvciZm84LeoXvy5nctWrnFdUVsco5vgXQbt+Pv30U4SEhCAhIUG1LTw8XHVdqVTiq6++wowZM/Doo48CAJYtW4bAwECsXbsWTz/9tJDhNYj+P5p5X4TNp29UXR/eqane40/naJ8/bwxdA4orKhX4YP0p9Iz0xZB2jRv8OEREDbHm6GWkZBVixtDWWot2msKFayV6j7lVVoGZd1c4Xns0Cy2DPASJxdoI2qLy559/okuXLhg5ciQCAgLQqVMnLF68WLX/woULyMnJQWxsrGqbl5cXunfvjqQk7f1rpaWlKCwsVLuIQVehnHvqqpUi9GJ/tQdllVdq9n0euCDcQKvfj1zGz/suGbW+EBGRUF5fdQw//nsBO9IMW5i1tpof2UodP0K1TfWtvX7O4l3VkyDyJFay/sJ1zURLoJzOaIImKufPn8fChQvRokULbN68GZMnT8Yrr7yCpUuXAgBycqoWvQsMDFS7X2BgoGpfbXPmzIGXl5fqEhISIuRT0OnddSfr3L81NU/nvpu3yrDlVC4qtCQQ9zQkl8m/pT51ub5z5ev7Is0rlNYbkIgIqPrsNadFO8+r3b5eIsxnY3mlAoknc1BYR9mKJXrqzYxL0L7orRQI2vWjUCjQpUsXzJ49GwDQqVMnpKSkYNGiRRgzZky9zhkfH4+pU6eqbhcWFoqWrNRXbmEpJi7Tv7JmfR3JuImSMstYbIqIyFLp+0F5pcbMzvS8Yng6C/OVeya3GC/+fFiQc0uBoC0qjRs3Rps2bdS2tW7dGhkZVWV5g4KCAAC5ueqV+HJzc1X7anNycoKnp6faxdbVbvnYIkClXCIiapgjGflih2CRBE1UevXqhbQ09VWFz5w5g7CwMABVA2uDgoKwdetW1f7CwkLs378fMTExQoZm8e6VsReTRLoviYgs3qy/TokdgmQJmqi8/vrr2LdvH2bPno309HSsWLEC33//PeLi4gAAMpkMr732Gj766CP8+eefOHHiBEaPHo0mTZpg+PDhQoam1+FLN3Xu+6Ue6+MIKfWKNFa4JCIiw6XnFes/yIxWH1Ifz1iza0vbYFtzETRR6dq1K9asWYNff/0Vbdu2xaxZs/DVV19h1KhRqmPeeustvPzyy3jxxRfRtWtXFBcXY9OmTXB2dhYyNL3uTSEDgKJS9QFKa46aftXghowjEas5Uah
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(freq, lamb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "95f5907e-94b0-4102-8e01-f313d3fb3aca",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "c6c2f53c-98a6-4b27-a8b3-03028c24126c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.arange(1024)\n",
    "sp = np.fft.fft(np.sin(t))\n",
    "freq = np.fft.fftfreq(t.shape[-1])\n",
    "plt.plot(freq, abs(sp))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "71804e1a-1895-4bbe-9b3a-c46c7a25948a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.000155473701438"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "omega = freq[abs(sp).argmax()]\n",
    "omega * 2*np.pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e723f8f7-bb64-4cd1-9d83-38be08e5baeb",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read"
   ]
  }
 ],
 "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": "3.10.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}