space-workshop/U02_3_Low_Pass.ipynb
Kai Vogelgesang 489ddd75b9
Init
2025-09-18 18:33:58 +02:00

319 lines
123 KiB
Plaintext
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

{
"cells": [
{
"cell_type": "markdown",
"id": "1a219eb5",
"metadata": {},
"source": [
"# Low-Pass Filter"
]
},
{
"cell_type": "markdown",
"id": "70bc7f0d",
"metadata": {},
"source": [
"```{figure} img/reference/shifted_waterfall.webp\n",
"---\n",
"name: fig:shifted_waterfall\n",
"---\n",
"Wasserfall-Diagramm nach dem Frequenz-Shift. Eine Kopie ist zur 0 gewandert, die andere auf -4.8kHz.\n",
"Außerdem ist die sogenannte *DC-Komponente*, die vorher auf der 0 war, jetzt bei -2.4kHz.\n",
"```\n",
"\n",
"Im nächsten Schritt filtern wir das Signal, so dass nur die Kopie des Basisbands übrig bleibt.\n",
"Weil darin 4160 Pixel pro Sekunde übertragen werden, reicht es im Spektrum von -2080 bis 2080 Hz (Das hängt mit dem Nyquist-Kriterium zusammen).\n",
"\n",
"Wir wollen also im Spektrum alles entfernen, was nicht in diesem Frequenz-Intervall liegt.\n",
"Das können wir als Multiplikation mit einer sogenannten Rechteck-Funktion ausdrücken:\n",
"```{math}\n",
"\\text{rect}(f) = \\left\\{\\begin{array}{rcl}\n",
" 1 && -\\frac{1}{2} < f < \\frac{1}{2} \\\\\n",
" 0 &:& \\text{sonst} \\\\\n",
"\\end{array}\\right.\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "3706c744",
"metadata": {
"tags": [
"remove-input"
]
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAjkAAAGwCAYAAABLvHTgAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAwwUlEQVR4nO3df1xUdb7H8feAMogKqCg/FMXS0vwBCsqimVasaF7Tu7WZeTPNKA1KpaxsS7bbFmTK2qZmWf7YbqXVlnXLdJMkyzASxbT8naaZoN7KIVRQOPeP1tmGH8YwAzMcX8/HYx678z3fc+YznI68Oed7vsdiGIYhAAAAk/HxdAEAAAD1gZADAABMiZADAABMiZADAABMiZADAABMiZADAABMiZADAABMqYmnC/CUiooKff/992rZsqUsFounywEAALVgGIaKi4sVEREhH58Ln6u5aEPO999/r8jISE+XAQAA6uDw4cPq0KHDBftctCGnZcuWkn75IQUGBnq4GgAAUBs2m02RkZH23+MXctGGnPOXqAIDAwk5AAA0MrUZasLAYwAAYEqEHAAAYEqEHAAAYEqEHAAAYEqEHAAAYEqEHAAAYEqEHAAAYEqEHAAAYEqEHAAAYEqEHAAAYEpeEXI2bNigkSNHKiIiQhaLRatWrfrNdXJyctS3b19ZrVZ16dJFy5Ytq/c6AQBA4+EVIaekpETR0dFasGBBrfofOHBAI0aM0NVXX62CggJNmzZNd9xxh9auXVvPlQIAgMbCKx7QOXz4cA0fPrzW/RctWqTOnTtr7ty5kqTu3bvr008/1V//+lclJSXVV5m4iPxcek4/nSrzdBnARS000F9Nfb3ib3E0Ul4RcpyVm5urxMREh7akpCRNmzatxnVKS0tVWlpqf2+z2eqrPDRyB06UaNi8DSo9V+HpUoCLWrewlvpg6qBaPW0aqE6jDDmFhYUKDQ11aAsNDZXNZtPp06fVrFmzKutkZGTosccea6gS0YjtLixW6bkKWSySH39FAg3OkFR2rkK7/nUs+jf19XRJaKQaZcipi5kzZyotLc3+3mazKTIy0oMVwdvFdmylN6cM8HQZwEXn59Jz6pnOGEu4rlGGnLCwMBUVFTm0FRUVKTAwsNqzOJJktVpltVobojwAAOAFGuW5+ISEBGVnZzu0ffjhh0pISPBQRQAAwNt4Rcj5+eefVVBQoIKCAkm/3CJeUFCgQ4cOSfrlUtP48ePt/SdPnqxvvvlGDzzwgHbt2qWFCxfq9ddf1/Tp0z1RPgAA8EJeEXI2b96sPn36qE+fPpKktLQ09enTR7NmzZIkHT161B54JKlz5856//339eGHHyo6Olpz587Viy++yO3jAADAzivG5AwZMkSGYdS4vLrZjIcMGaKtW7fWY1UAAKAx84ozOYB3qTlwAwAaD0IOAAAwJUIOUAMmWQU8g0MP7kLIAQAApkTIAQAApkTIAQAApkTIAQAApkTIAQAApkTIASq5wLyUABoYxyNcQcgBAACmRMgBamBhtg7AI5ijCu5CyAEAAKZEyAEAAKZEyAEAAKZEyAEAAKZEyAEAAKZEyAEqYVoOwHsYHJFwASEHAACYEiEHqAlzdQAewRxVcBdCDgAAMCVCDgAAMCVCDgAAMCVCDgAAMCVCDgAAMCVCDlCJwbQcgNfgeIQrCDkAAMCUCDlADZipA/AMCwcf3ISQAwAATImQAwAATImQAwAATImQAwAATImQAwDwWtxBDlcQcoBKDP5ZBQBTIOQAAABTIuQANWCuDgBo3Ag5AADAlAg5AADAlAg5AADAlAg5AADAlAg5AACvZRhM6YC6I+QAlfBvKgCYAyEHAACYEiEHqIFFTJQDeAJzVMFdCDkAAMCUCDkAAMCUCDkAAMCUCDkAAMCUCDkAAK/FjA5wBSEHqIR/VAHAHAg5AADAlAg5QA2YqwPwDOaogrsQcgAAgCkRcgAAgCkRcgAAgCkRcgAAgCkRcgAAXstgTge4gJADVGLwryoAmILXhJwFCxYoKipK/v7+io+PV15e3gX7z5s3T5dffrmaNWumyMhITZ8+XWfOnGmgagEAgLfzipCzcuVKpaWlKT09XVu2bFF0dLSSkpJ07Nixavu/+uqreuihh5Senq6dO3fqpZde0sqVK/Xwww83cOUwM+bJATyDYw/u4hUhJysrS8nJyZo4caKuuOIKLVq0SAEBAVqyZEm1/T/77DMNHDhQt9xyi6KiojR06FCNHTv2gmd/SktLZbPZHF4AAMC8PB5yysrKlJ+fr8TERHubj4+PEhMTlZubW+06AwYMUH5+vj3UfPPNN1q9erWuu+66Gj8nIyNDQUFB9ldkZKR7vwgAAPAqTTxdwIkTJ1ReXq7Q0FCH9tDQUO3atavadW655RadOHFCV155pQzD0Llz5zR58uQLXq6aOXOm0tLS7O9tNhtBBwAAE/P4mZy6yMnJ0ZNPPqmFCxdqy5Yteuutt/T+++/r8ccfr3Edq9WqwMBAhxcAADAvj5/JCQkJka+vr4qKihzai4qKFBYWVu06jz76qG699VbdcccdkqRevXqppKREd955p/70pz/Jx6dRZjcAQGXM6AAXeDwN+Pn5KTY2VtnZ2fa2iooKZWdnKyEhodp1Tp06VSXI+Pr6SmKOEwAA8AuPn8mRpLS0NN12222Ki4tT//79NW/ePJWUlGjixImSpPHjx6t9+/bKyMiQJI0cOVJZWVnq06eP4uPjtW/fPj366KMaOXKkPewAAICLm1eEnDFjxuj48eOaNWuWCgsLFRMTozVr1tgHIx86dMjhzM0jjzwii8WiRx55REeOHFHbtm01cuRIPfHEE576CjAhi5isA/AEjjy4i1eEHElKTU1VampqtctycnIc3jdp0kTp6elKT09vgMoAAEBj5PExOQAAAPWBkAMAAEyJkAMA8FoG95DDBYQcAABgSoQcoBKmWgIAcyDkAAAAUyLkADWwMFkH4BEWDj64CSEHAACYEiEHAACYEiEHAACYEiEHAOC1uNsRriDkAAAAUyLkAJUwwyoAmAMhBwAAmBIhBwDgVZglB+5CyAEAAKZEyAEAAKZEyAEAAKZEyAEAeC3udYQrCDkAAMCUCDlAJcywCgDmQMgBAACmRMgBamCxMFsH4AkcenAXQg4AADAlQg4AADAlQg4AADAlQg4AwGsZ3O4IFxByAACAKRFygEr4wxEAzIGQAwAATImQA9SAqToAz2COKrgLIQcAAJgSIQcAAJgSIQcA4LW4DwCuIOQAAABTIuQAAABTIuQAlXB6HADMgZADAABMiZAD1ICpOgCgcSPkAAAAUyLkAAAAUyLkAAC8Fg/MhSsIOQAAwJQIOQAAwJQIOUAlBufHAcAUCDkAAMCUCDlADZgmB/Ac5qmCOxByAACAKRFyAACAKRFyAABey+CRuXABIQcAAJgSIQcAAJgSIQeohJPjAGAOhBwAAGBKTVxZ+ezZsyosLNSpU6fUtm1btW7d2l11AR5nYaIOwGMs4qwqXOf0mZzi4mI999xzGjx4sAIDAxUVFaXu3burbdu26tSpk5KTk/XFF1/UR60AAAC15lTIycrKUlRUlJYuXarExEStWrVKBQUF2rNnj3Jzc5Wenq5z585p6NChGjZsmPbu3VvrbS9YsEBRUVHy9/dXfHy88vLyLtj/p59+UkpKisLDw2W1WnXZZZdp9erVznwdAABgYk5drvriiy+0YcMG9ejRo9rl/fv31+23365FixZp6dKl+uSTT9S1a9ff3O7KlSuVlpamRYsWKT4+XvPmzVNSUpJ2796tdu3aVelfVlam3//+92rXrp3efPNNtW/fXt9++62Cg4Od+ToAAG/HNSu4wKmQ89prr9Wqn9Vq1eTJk2u93aysLCUnJ2vixImSpEWLFun999/XkiVL9NBDD1Xpv2TJEv3www/67LPP1LRpU0lSVFTUBT+jtLRUpaWl9vc2m63W9QEAgMbH43dXlZWVKT8/X4mJifY2Hx8fJSYmKjc3t9p13n33XSUkJCglJUWhoaHq2bOnnnzySZWXl9f4ORkZGQoKCrK/IiMj3f5dAACA96jT3VUnTpzQkiVLlJubq8LCQklSWFiYBgwYoAkTJqht27ZObau8vFyhoaEO7aGhodq1a1e163zzzTf66KOPNG7cOK1evVr79u3T3XffrbNnzyo9Pb3adWbOnKm0tDT7e5vNRtBB9Tg9DgCm4HTI+eKLL5SUlKSAgAAlJibqsssukyQVFRXpb3/7mzIzM7V27VrFxcW5vdjzKioq1K5dO73wwgvy9fVVbGysjhw5oqeffrrGkGO1WmW1WuutJgAA4F2cDjn33HOP/vjHP2rRokVV5hExDEOTJ0/WPffcU+OlpspCQkLk6+uroqIih/aioiKFhYVVu054eLiaNm0qX19fe1v37t1VWFiosrIy+fn5OfmtgKqYJQfwHIvFIhmcVoVrnB6Ts23bNk2fPr3aidIsFoumT5+ugoKCWm/Pz89PsbGxys7OtrdVVFQoOztbCQkJ1a4zcOBA7du3TxUVFfa2PXv2KDw8nIADAAAk1SHkhIWFXXAOm7y8vCrja35LWlqaFi9erOXLl2vnzp2aMmWKSkpK7HdbjR8/XjNnzrT3nzJlin744QdNnTpVe/bs0fvvv68nn3xSKSkpzn4dAABgUk5frrr//vt15513Kj8/X9dee6090BQVFSk7O1uLFy/WnDlznNrmmDFjdPz4cc2aNUuFhYWKiYnRmjVr7Ns+dOiQfHz+ncciIyO1du1aTZ8+Xb1791b79u01depUPfjgg85+HQCAF+OCFVzhdMhJSUlRSEiI/vrXv2rhwoX227bPDwBetmyZbrrpJqcLSU1NVWpqarXLcnJyqrQlJCRo06ZNTn8OAAC4ONTpFvIxY8ZozJgxOnv2rE6cOCHplwHE5yfmAwAA8DSXnkLetGlThYeHu6sWwCsYnCAHAFNweuDxli1bdODAAfv7l19+WQMHDlRkZKSuvPJKrVixwq0FAgAA1IXTIWfixInav3+/JOnFF1/UXXfdpbi4OP3pT39Sv379lJycrCVLlri9UKChVTNLAoAGwuEHd3D6ctXevXvtTxZfuHChnnnmGSUnJ9uX9+vXT0888YRuv/1291UJAADgJKfP5AQEBNgHGx85ckT9+/d3WB4fH+9wOQsAgLpi0mO4wumQM3z4cD333HOSpMGDB+vNN990WP7666+rS5cu7qkOAACgjpy+XPXUU09p4MCBGjx4sOLi4jR37lzl5OSoe/fu2r17tzZt2qS33367PmoFAACoNafP5ERERGjr1q1KSEjQmjVrZBiG8vLy9M9//lMdOnTQxo0bdd1119VHrQAAALVWp3lygoODlZmZqczMTHfXA3gcYwAAwBycPpPzWw4fPsydVQAAwOPcHnJ++OEHLV++3N2bBTyAmToAT2GeKriD05er3n333Qsu/+abb+pcDAAAgLs4HXJGjx4ti8Ui4wIDFyxEcACAG/AsObjC6ctV4eHheuutt1RRUVHta8uWLfVRJwAAgFOcDjmxsbHKz8+vcflvneUBAABoCE5frpoxY4ZKSkpqXN6lSxetX7/epaIAAABc5XTIGTRo0AWXN2/eXIMHD65zQYCncR4SAMzBbbeQc4kKAAB4E7eFHKvVqp07d7prc4DHcZMg4DkW5qmCGzh9uSotLa3a9vLycmVmZqpNmzaSpKysLNcqAwAAcIHTIWfevHmKjo5WcHCwQ7thGNq5c6eaN2/OPDkAALdgJARc4XTIefLJJ/XCCy9o7ty5uuaaa+ztTZs21bJly3TFFVe4tUAAAIC6cHpMzkMPPaSVK1dqypQpuv/++3X27Nn6qAsAAMAldRp43K9fP+Xn5+v48eOKi4vTjh07uEQFAAC8itOXq85r0aKFli9frhUrVigxMVHl5eXurAvwGMYAAIA51DnknHfzzTfryiuvVH5+vjp16uSOmgAAAFzm9OWqWbNmVXl2VYcOHTRq1Cg1b97cbYUBnsYFWMCDOADhBk6HnO+++07Dhw9Xhw4dNGXKFH3wwQcqKyurj9oAAADqzOmQs2TJEhUWFuq1115Ty5YtNW3aNIWEhOiGG27Q3//+d/3www/1UScA4CLEEDm4wqmQ88ADD+jMmTPy8fHRoEGDNHv2bO3evVuff/654uPj9fzzzysiIkJXXXWV5syZoyNHjtRX3QAAABfkVMiZN2+eTp48KUmaMGGCTp06JUnq3r27HnjgAW3cuFGHDx/Wbbfdpk8++USvvfaa+ysGAACoBadCTkREhAoKCiRJL7/8sn7++ecqfdq2batJkybpnXfe0f333++WIgEAAJzlVMi57777NHLkSA0aNEiS9MorrygvL0+nT5+ul+IATzAYBQAApuBUyLnnnnu0efNmDRs2TIZhaMGCBRowYIACAwPVvXt33XzzzcrMzNQHH3xQX/UCAADUitOTAfbu3Vu9e/fWsmXLlJubq+bNm+vLL79UQUGBCgoK9M477+iJJ55QcXFxfdQLNBieVAJ4Docf3KHOMx7v3bvX/v/j4+MVHx9vf28wLz4AAPAwpy5XHTp0qFb9zj+sk1vIAQCu4I9muMKpkNOvXz/ddddd+uKLL2rsc/LkSS1evFg9e/bUP/7xD5cLBAAAqAunLld9/fXXeuKJJ/T73/9e/v7+io2NVUREhPz9/fXjjz/q66+/1ldffaW+fftq9uzZuu666+qrbgAAgAty6kxOmzZtlJWVpaNHj2r+/Pnq2rWrTpw4YR+fM27cOOXn5ys3N5eAAwAAPKpOA4+bNWumG2+8UTfeeKO76wE8jiEAAGAOTj+g87wBAwbIZrO5sxYAAAC3qXPI2bRpk86cOVOl3Waz6cEHH3SpKMAbWJipA/AY5qmCOzgdcm688UZlZmbKYrHo2LFjVZaXlJRozpw5bikOAHBx4/IxXOH0mJyOHTvqvffek2EYio6OVps2bRQdHa3o6GjFxMRo9+7dCg8Pr49aAQAAas3pkJOVlSVJ8vPz08aNG/X9999r69atKigo0Ntvv62KigrNnj3b7YUCAAA4o86PdcjOzlazZs00atQojRo1yp01AQAAuKzOA4/vvfdeff7551Xa9+/fz8M5AQCAx9U55OzevVtDhgyp0r5u3TqNHTvWlZoAj2KcIwCYQ51DTmBgoH788ccq7YMGDdKmTZtcKgoAAMBVdQ45w4YNq/ZWcR8fH5WVlblUFOANmKcD8BzmqYI71DnkPP744/r44491ww03aPv27ZKkM2fO6KmnnlLv3r3dViAAAEBd1PnuqsjISG3atElTpkxRdHS0rFarzp07p6CgIP3v//6vO2sEAABwWp1DjiR16tRJq1ev1rfffqtt27apadOmio+PV+vWrd1VHwAAQJ24FHLO69Spkzp16uSOTQEAALhFncfknDx5Unfeeae6dOmi7t276+jRoy4Xs2DBAkVFRcnf31/x8fHKy8ur1XorVqyQxWLR6NGjXa4BAACYQ51DTkpKirZv367Zs2fr22+/1enTpyVJ06dP1/z5853e3sqVK5WWlqb09HRt2bJF0dHRSkpKqvYhoL928OBB3X///Ro0aFCdvgdQBU8EBABTqHPI+eCDD7Rw4UL94Q9/kK+vr709KSlJy5cvd3p7WVlZSk5O1sSJE3XFFVdo0aJFCggI0JIlS2pcp7y8XOPGjdNjjz2mSy65pE7fAwAAmFOdQ45hGGrZsmWV9q5du2rv3r1ObausrEz5+flKTEz8d2E+PkpMTFRubm6N6/33f/+32rVrp0mTJv3mZ5SWlspmszm8gAthnhzAczj+4A51DjnDhw/XK6+8UqW9pKREFif/6zxx4oTKy8sVGhrq0B4aGqrCwsJq1/n000/10ksvafHixbX6jIyMDAUFBdlfkZGRTtUIAGh4XD2GK+p8d1VmZqZiY2Ml/XJWx2Kx6MyZM3r88cfVt29ftxVYneLiYt16661avHixQkJCarXOzJkzlZaWZn9vs9kIOgAAmFidQk55ebny8/O1bt06zZgxQ6dOnVL//v1VXFyswMBArV692qnthYSEyNfXV0VFRQ7tRUVFCgsLq9J///79OnjwoEaOHGlvq6iokCQ1adJEu3fv1qWXXuqwjtVqldVqdaouAADQeNUp5Pj6+mrs2LH66quvtHbtWh06dMhhMsBWrVo5tT0/Pz/FxsYqOzvbfht4RUWFsrOzlZqaWqV/t27d7I+SOO+RRx5RcXGxnnnmGc7QAACAul+u6tevnw4cOKBLLrlEHTt2VMeOHV0qJC0tTbfddpvi4uLUv39/zZs3TyUlJZo4caIkafz48Wrfvr0yMjLk7++vnj17OqwfHBwsSVXaAQDAxanOIeeee+7Rww8/rDfffNMtZ07GjBmj48ePa9asWSosLFRMTIzWrFljH4x86NAh+fjUeZw0UGuMcwQAc6hzyBkzZowkqUePHrr++us1ZMgQ9enTR7169ZKfn1+dtpmamlrt5SlJysnJueC6y5Ytq9NnAgAAc6pzyDlw4IC2bdumgoICbdu2TRkZGTp48KCaNGmiyy+/XF9++aU76wQanEVM1AF4Ckcf3KHOIef8Qzmvv/56e1txcbEKCgoIOAAAtzC4gAwXuOUp5Oe1bNlSgwYN4jlSAADA4xjJCwAATImQAwAATImQAwAATImQA1TCAwEBwBwIOQAAwJQIOUBNmKgD8BiLhQMQriPkAAC8FpeP4QpCDgAAMCVCDgAAMCVCDgAAMCVCDgAAMCVCDlCJwUhHADAFQg4AADAlQg5QA2bpADzn/PHHeVW4gpADAABMiZADAABMiZADAABMiZADAABMiZADAABMiZADVMLdHABgDoQcAABgSoQcoAYWCzPlAB7zr8OPGcjhCkIOAAAwJUIOAAAwJUIOAAAwJUIOAAAwJUIOAAAwJUIOUAk3cwCAORByAACAKRFygBowSw7gOeePP06swhWEHAAAYEqEHAAAYEqEHAAAYEqEHAAAYEqEHAAAYEqEHKAS7uYAAHMg5AAAAFMi5AA1sDBRDuAxln8dgMxADlcQcgAAgCkRcgAAgCkRcgAAgCkRcgAAgCkRcgAAgCkRcoBKDG7nAABTIOQAALwYf3Sg7gg5QA2YJgfwHOapgjsQcgAAgCkRcgAAgCkRcgAAgCkRcgAAgCkRcgAAgCkRcgAAgCkRcgAAXou5OeEKrwo5CxYsUFRUlPz9/RUfH6+8vLwa+y5evFiDBg1Sq1at1KpVKyUmJl6wP+AsCxN1AB7D0Qd38JqQs3LlSqWlpSk9PV1btmxRdHS0kpKSdOzYsWr75+TkaOzYsVq/fr1yc3MVGRmpoUOH6siRIw1cOQAA8EZeE3KysrKUnJysiRMn6oorrtCiRYsUEBCgJUuWVNv/lVde0d13362YmBh169ZNL774oioqKpSdnd3AlQMAAG/kFSGnrKxM+fn5SkxMtLf5+PgoMTFRubm5tdrGqVOndPbsWbVu3bra5aWlpbLZbA4vAABgXl4Rck6cOKHy8nKFhoY6tIeGhqqwsLBW23jwwQcVERHhEJR+LSMjQ0FBQfZXZGSky3UDAADv5RUhx1WZmZlasWKF3n77bfn7+1fbZ+bMmTp58qT9dfjw4QauEgAANKQmni5AkkJCQuTr66uioiKH9qKiIoWFhV1w3Tlz5igzM1Pr1q1T7969a+xntVpltVrdUi/MjVtWAcAcvOJMjp+fn2JjYx0GDZ8fRJyQkFDjerNnz9bjjz+uNWvWKC4uriFKBQA0IP7mgCu84kyOJKWlpem2225TXFyc+vfvr3nz5qmkpEQTJ06UJI0fP17t27dXRkaGJOmpp57SrFmz9OqrryoqKso+dqdFixZq0aKFx74HzIN5OgDPYZ4quIPXhJwxY8bo+PHjmjVrlgoLCxUTE6M1a9bYByMfOnRIPj7/PvH03HPPqaysTDfeeKPDdtLT0/XnP/+5IUsHAABeyGtCjiSlpqYqNTW12mU5OTkO7w8ePFj/BQEAgEbLK8bkAAAAuBshBwAAmBIhBwAAmBIhB6jE4KZVADAFQg4AwGsxOSdcQcgBasI0HYDHcPjBHQg5AADAlAg5AADAlAg5AADAlAg5AADAlAg5AADAlAg5QCXcsgoA5kDIAQB4LSbnhCsIOUANLMzUAXiMhcMPbkDIAQAApkTIAQAApkTIAQAApkTIAQAApkTIAQAApkTIASrhhlXAezBvFVxByAEAAKZEyAFqwDwdgCdxAMJ1hBwAAGBKhBwAAGBKhBwAAGBKhBwAAGBKhBygEm5ZBQBzIOQAALwWf3TAFYQcAABgSoQcoAbM0gF4DvNUwR0IOQAAwJQIOQAAwJQIOQAAwJQIOQAAwJQIOUAlhrhnFQDMgJADAPBa/NEBVxBygBpwCyvgORx+cAdCDgAAMCVCDgAAMCVCDgAAMCVCDgAAMCVCDgAAMCVCDlCJwR2rAGAKhBwAgNfijw64gpAD1MDCTB2AxzBPFdyBkAMAAEyJkAMAAEyJkAMAAEyJkAMAAEyJkAMAAEyJkAMAAEyJkAMAAEyJkAPUgHk6AM9hniq4AyEHAACYEiEHAACYEiEHAACYkleFnAULFigqKkr+/v6Kj49XXl7eBfu/8cYb6tatm/z9/dWrVy+tXr26gSoFAADezmtCzsqVK5WWlqb09HRt2bJF0dHRSkpK0rFjx6rt/9lnn2ns2LGaNGmStm7dqtGjR2v06NHasWNHA1cOAAC8kcUwvONB9vHx8erXr5/mz58vSaqoqFBkZKTuuecePfTQQ1X6jxkzRiUlJXrvvffsbb/73e8UExOjRYsW/ebn2Ww2BQUF6eTJkwoMDHTb9yg9V67jxaVu2x4a3t9zv9ULG77Rzf0ilXlDb0+XA1yUfvdktgptZ/TSbXG6PKylp8tBHfk18VG7lv5u3aYzv7+buPWT66isrEz5+fmaOXOmvc3Hx0eJiYnKzc2tdp3c3FylpaU5tCUlJWnVqlXV9i8tLVVp6b/Dh81mc73wanz1vU1/WPhZvWwbAC42k5Zv9nQJcEHfjsF66+6BHvt8rwg5J06cUHl5uUJDQx3aQ0NDtWvXrmrXKSwsrLZ/YWFhtf0zMjL02GOPuafgC7BIsjbxmquAqKNmfr66pls7T5cBXLSuj4nQ33MPyjuuNaCumvp69vehV4SchjBz5kyHMz82m02RkZFu/5w+HVtp91+Gu327AHAxefi67nr4uu6eLgONnFeEnJCQEPn6+qqoqMihvaioSGFhYdWuExYW5lR/q9Uqq9XqnoIBAIDX84rrKn5+foqNjVV2dra9raKiQtnZ2UpISKh2nYSEBIf+kvThhx/W2B8AAFxcvOJMjiSlpaXptttuU1xcnPr376958+appKREEydOlCSNHz9e7du3V0ZGhiRp6tSpGjx4sObOnasRI0ZoxYoV2rx5s1544QVPfg0AAOAlvCbkjBkzRsePH9esWbNUWFiomJgYrVmzxj64+NChQ/Lx+feJpwEDBujVV1/VI488oocfflhdu3bVqlWr1LNnT099BQAA4EW8Zp6chlZf8+QAAID648zvb68YkwMAAOBuhBwAAGBKhBwAAGBKhBwAAGBKhBwAAGBKhBwAAGBKhBwAAGBKhBwAAGBKhBwAAGBKXvNYh4Z2fqJnm83m4UoAAEBtnf+9XZsHNly0Iae4uFiSFBkZ6eFKAACAs4qLixUUFHTBPhfts6sqKir0/fffq2XLlrJYLA362TabTZGRkTp8+DDPzWok2GeNC/ur8WGfNS6e3F+GYai4uFgREREOD+6uzkV7JsfHx0cdOnTwaA2BgYEczI0M+6xxYX81PuyzxsVT++u3zuCcx8BjAABgSoQcAABgSoQcD7BarUpPT5fVavV0Kagl9lnjwv5qfNhnjUtj2V8X7cBjAABgbpzJAQAApkTIAQAApkTIAQAApkTIAQAApkTIqSelpaWKiYmRxWJRQUGBw7Ivv/xSgwYNkr+/vyIjIzV79uwq67/xxhvq1q2b/P391atXL61evdphuWEYmjVrlsLDw9WsWTMlJiZq79699fmVTOfgwYOaNGmSOnfurGbNmunSSy9Venq6ysrKHPqxvxqfBQsWKCoqSv7+/oqPj1deXp6nSzK9jIwM9evXTy1btlS7du00evRo7d6926HPmTNnlJKSojZt2qhFixa64YYbVFRU5NDn0KFDGjFihAICAtSuXTvNmDFD586dc+iTk5Ojvn37ymq1qkuXLlq2bFl9fz3Ty8zMlMVi0bRp0+xtpthfBurFvffeawwfPtyQZGzdutXefvLkSSM0NNQYN26csWPHDuO1114zmjVrZjz//PP2Phs3bjR8fX2N2bNnG19//bXxyCOPGE2bNjW2b99u75OZmWkEBQUZq1atMrZt22Zcf/31RufOnY3Tp0835Nds1D744ANjwoQJxtq1a439+/cb77zzjtGuXTvjvvvus/dhfzU+K1asMPz8/IwlS5YYX331lZGcnGwEBwcbRUVFni7N1JKSkoylS5caO3bsMAoKCozrrrvO6Nixo/Hzzz/b+0yePNmIjIw0srOzjc2bNxu/+93vjAEDBtiXnzt3zujZs6eRmJhobN261Vi9erUREhJizJw5097nm2++MQICAoy0tDTj66+/Np599lnD19fXWLNmTYN+XzPJy8szoqKijN69extTp061t5thfxFy6sHq1auNbt26GV999VWVkLNw4UKjVatWRmlpqb3twQcfNC6//HL7+5tuuskYMWKEwzbj4+ONu+66yzAMw6ioqDDCwsKMp59+2r78p59+MqxWq/Haa6/V07e6OMyePdvo3Lmz/T37q/Hp37+/kZKSYn9fXl5uREREGBkZGR6s6uJz7NgxQ5Lx8ccfG4bxy3/zTZs2Nd544w17n507dxqSjNzcXMMwfvm308fHxygsLLT3ee6554zAwED7MfjAAw8YPXr0cPisMWPGGElJSfX9lUypuLjY6Nq1q/Hhhx8agwcPtoccs+wvLle5WVFRkZKTk/Xyyy8rICCgyvLc3FxdddVV8vPzs7clJSVp9+7d+vHHH+19EhMTHdZLSkpSbm6uJOnAgQMqLCx06BMUFKT4+Hh7H9TNyZMn1bp1a/t79lfjUlZWpvz8fIeftY+PjxITE/lZN7CTJ09Kkv14ys/P19mzZx32Tbdu3dSxY0f7vsnNzVWvXr0UGhpq75OUlCSbzaavvvrK3udCxxuck5KSohEjRlT5mZplfxFy3MgwDE2YMEGTJ09WXFxctX0KCwsd/oOQZH9fWFh4wT6/Xv7r9arrA+ft27dPzz77rO666y57G/urcTlx4oTKy8v5WXtYRUWFpk2bpoEDB6pnz56SfjkO/Pz8FBwc7NC38rFS1+PNZrPp9OnT9fF1TGvFihXasmWLMjIyqiwzy/4i5NTCQw89JIvFcsHXrl279Oyzz6q4uFgzZ870dMkXtdrur187cuSIhg0bpj/+8Y9KTk72UOWAOaSkpGjHjh1asWKFp0tBDQ4fPqypU6fqlVdekb+/v6fLqTdNPF1AY3DfffdpwoQJF+xzySWX6KOPPlJubm6VZ3nExcVp3LhxWr58ucLCwqqMTj//PiwszP6/1fX59fLzbeHh4Q59YmJinP5+ZlPb/XXe999/r6uvvloDBgzQCy+84NCP/dW4hISEyNfX94L7A/UrNTVV7733njZs2KAOHTrY28PCwlRWVqaffvrJ4exA5WOl8p1wtT3eAgMD1axZs/r4SqaUn5+vY8eOqW/fvva28vJybdiwQfPnz9fatWvNsb8aZOTPReLbb781tm/fbn+tXbvWkGS8+eabxuHDhw3D+PdA1rKyMvt6M2fOrDKQ9T/+4z8ctp2QkFBlIOucOXPsy0+ePMlA1jr47rvvjK5duxo333yzce7cuSrL2V+NT//+/Y3U1FT7+/LycqN9+/YMPK5nFRUVRkpKihEREWHs2bOnyvLzA1nffPNNe9uuXbuqHcj66zvhnn/+eSMwMNA4c+aMYRi/DGTt2bOnw7bHjh3LwGMn2Ww2h99X27dvN+Li4oz/+q//MrZv326a/UXIqUcHDhyocnfVTz/9ZISGhhq33nqrsWPHDmPFihVGQEBAlVuSmzRpYsyZM8fYuXOnkZ6eXu0tycHBwcY777xjfPnll8aoUaO4JdlJ3333ndGlSxfj2muvNb777jvj6NGj9td57K/GZ8WKFYbVajWWLVtmfP3118add95pBAcHO9wBAvebMmWKERQUZOTk5DgcS6dOnbL3mTx5stGxY0fjo48+MjZv3mwkJCQYCQkJ9uXnb0keOnSoUVBQYKxZs8Zo27Zttbckz5gxw9i5c6exYMECbiF3k1/fXWUY5thfhJx6VF3IMQzD2LZtm3HllVcaVqvVaN++vZGZmVll3ddff9247LLLDD8/P6NHjx7G+++/77C8oqLCePTRR43Q0FDDarUa1157rbF79+76/Dqms3TpUkNSta9fY381Ps8++6zRsWNHw8/Pz+jfv7+xadMmT5dkejUdS0uXLrX3OX36tHH33XcbrVq1MgICAoz//M//dPijwjAM4+DBg8bw4cONZs2aGSEhIcZ9991nnD171qHP+vXrjZiYGMPPz8+45JJLHD4DdVc55Jhhf1kMwzDq/6IYAABAw+LuKgAAYEqEHAAAYEqEHAAAYEqEHAAAYEqEHAAAYEqEHAAAYEqEHAAAYEqEHAAAYEqEHACohYMHD9qfYl8fD1YdMmSIffsFBQVu3z5wMSLkAKjRhAkT7L94f/3at2+fp0vzmHXr1ik7O9v+/s9//nO1oed8KKptYHnrrbeqPNEZgGuaeLoAAN5t2LBhWrp0qUNb27Ztq/QrKyuTn59fQ5XlMW3atFGbNm3cvt3WrVvLZrO5fbvAxYwzOQAuyGq1KiwszOHl6+urIUOGKDU1VdOmTVNISIiSkpIkSTt27NDw4cPVokULhYaG6tZbb9WJEyfs2yspKdH48ePVokULhYeHa+7cuRoyZIimTZtm72OxWLRq1SqHOoKDg7Vs2TL7+8OHD+umm25ScHCwWrdurVGjRungwYP25RMmTNDo0aM1Z84chYeHq02bNkpJSdHZs2clSTk5OdWepZowYYK7f4T2eqr7vJycnHr5PACEHAAuWL58ufz8/LRx40YtWrRIP/30k6655hr16dNHmzdv1po1a1RUVKSbbrrJvs6MGTP08ccf65133tE///lP5eTkaMuWLU597tmzZ5WUlKSWLVvqk08+0caNG9WiRQsNGzZMZWVl9n7r16/X/v37tX79ei1fvlzLli2zB6UBAwbo6NGj9tdHH30kf39/XXXVVW752VT2zDPPOHze1KlT1a5dO3Xr1q1ePg8Al6sA/Ib33ntPLVq0sL8fPny43njjDUlS165dNXv2bPuyv/zlL+rTp4+efPJJe9uSJUsUGRmpPXv2KCIiQi+99JL+53/+R9dee62kX4JShw4dnKpp5cqVqqio0IsvviiLxSJJWrp0qYKDg5WTk6OhQ4dKklq1aqX58+fL19dX3bp104gRI5Sdna3k5GT5+fkpLCxMkvR///d/uuOOO3T77bfr9ttvd/pntH37doefkSQZhuHwPigoSEFBQZJ+GX/z/PPPa926dfYaALgfIQfABV199dV67rnn7O+bN29u//+xsbEOfbdt26b169dX+YUvSfv379fp06dVVlam+Ph4e3vr1q11+eWXO1XTtm3btG/fPrVs2dKh/cyZM9q/f7/9fY8ePeTr62t/Hx4eru3btzusc/bsWd1www3q1KmTnnnmGafqOO/yyy/Xu+++69B25MgRDRkypErfrVu36tZbb9X8+fM1cODAOn0egNoh5AC4oObNm6tLly41Lvu1n3/+WSNHjtRTTz1VpW94eHit78qyWCxVzoScH0tz/nNiY2P1yiuvVFn314OimzZtWmW7FRUVDm1TpkzR4cOHlZeXpyZN6vZPop+fX5WfUXXbKiws1PXXX6877rhDkyZNqtNnAag9Qg4At+nbt6/+8Y9/KCoqqtpf8pdeeqmaNm2qzz//XB07dpQk/fjjj9qzZ48GDx5s79e2bVsdPXrU/n7v3r06deqUw+esXLlS7dq1U2BgYJ3rzcrK0uuvv67PPvusXu6Y+rUzZ85o1KhR6tatm7Kysur1swD8goHHANwmJSVFP/zwg8aOHasvvvhC+/fv19q1azVx4kSVl5erRYsWmjRpkmbMmKGPPvpIO3bs0IQJE+Tj4/hP0TXXXKP58+dr69at2rx5syZPnuxwVmbcuHEKCQnRqFGj9Mknn+jAgQPKycnRvffeq++++65Wta5bt04PPPCAnn76aYWEhKiwsFCFhYU6efKkW38m59111106fPiw/va3v+n48eP2z/v1QGkA7kXIAeA2ERER2rhxo8rLyzV06FD16tVL06ZNU3BwsD3IPP300xo0aJBGjhypxMREXXnllVXG9sydO1eRkZEaNGiQbrnlFt1///0KCAiwLw8ICNCGDRvUsWNH/eEPf1D37t01adIknTlzptZndj799FOVl5dr8uTJCg8Pt7+mTp3qvh/Ir3z88cc6evSorrjiCofP++yzz+rl8wBIFqPyhW8AaGBDhgxRTEyM5s2b5+lSanTw4EF17txZW7durZfHOjTUZwAXE87kAIATBgwYoAEDBrh9u8OHD1ePHj3cvl3gYsbAYwCohQ4dOmjv3r2SfpkF2t1efPFFnT59WpLsg7IBuIbLVQAAwJS4XAUAAEyJkAMAAEyJkAMAAEyJkAMAAEyJkAMAAEyJkAMAAEyJkAMAAEyJkAMAAEzp/wF78vE/wH3jAgAAAABJRU5ErkJggg==",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"n = 8192\n",
"f_s = 2080 * 4\n",
"f = np.roll(np.fft.fftfreq(n, d = 1/f_s), -n//2)\n",
"\n",
"def rect(f):\n",
" return np.where(np.abs(f) < 0.5, 1, 0)\n",
"\n",
"fig, ax = plt.subplots()\n",
"ax.plot(f, rect(1/4160 * f));\n",
"ax.set_xlabel(\"Frequenz [Hz]\");\n",
"ax.set_ylabel(\"$rect(f/4160)$\");"
]
},
{
"cell_type": "markdown",
"id": "515f4212",
"metadata": {},
"source": [
"Hier haben wir das Rechteck bereits so skaliert, dass es für Frequenzen zwischen -2080 und 2080 den Wert 1 hat und sonst 0.\n",
"Das erreichen wir folgendermaßen:\n",
"```{math}\n",
"\\text{rect}\\left(\\frac{1}{4160} \\cdot f\\right) = \\left\\{\\begin{array}{rcl}\n",
" 1 && -\\frac{1}{2} < \\frac{1}{4160} \\cdot f < \\frac{1}{2} \\Leftrightarrow -2080 < f < 2080 \\\\\n",
" 0 &:& \\text{sonst} \\\\\n",
"\\end{array}\\right.\n",
"```\n",
"\n",
"In der Zeit-Domain entspricht das Rechteck der sogenannten $\\text{sinc}$ Funktion.\n",
"Sie ist definiert als\n",
"```{math}\n",
"\\text{sinc}(t) \\mathrel{\\vcenter{:}}= \\left\\{\\begin{array}{ccl}\n",
" \\frac{\\sin(\\pi t)}{\\pi t} && t \\neq 0 \\\\\n",
" 0 &:& t = 0 \\\\\n",
"\\end{array}\\right.\n",
"```\n",
"\n",
"Mit der Skalierung auf den Bereich von -2080 bis 2080 Hz (wegen $x[at] \\,\\circ\\!\\!-\\!\\!\\bullet\\, \\frac{1}{|a|} X \\left[\\frac{f}{a}\\right]$):\n",
"```{math}\n",
"\\text{rect}\\left(\\frac{1}{4160} \\cdot f\\right) \\,\\bullet\\!\\!-\\!\\!\\circ\\, 4160 \\cdot \\text{sinc}(4160 \\cdot t)\n",
"```\n",
"\n",
"Um das Signal zu filtern wollen wir also eine Faltung mit der $\\text{sinc}$ Funktion implementieren.\n",
"Dabei haben wir allerdings ein Problem:\n",
"Die $\\text{sinc}$ Funktion hat einen *unendlichen Träger*, also wir müssten sie an unendlich vielen Stellen auswerten.\n",
"\n",
"Damit unser Programm in endlicher Zeit fertig wird, können wir nur ein endlich großes Fenster an Samples für die Faltung benutzen.\n",
"Damit ist die Berechnung nicht mehr exakt.\n",
"Den so entstehenden Fehler können wir aber mit Hilfe einer sogenannten *window function* klein halten.\n",
"Eine häufig verwendete window function ist das sogenannte [Hamming-Window](https://de.wikipedia.org/wiki/Fensterfunktion#Hamming-Fenster):\n",
"```{math}\n",
"w[n] \\mathrel{\\vcenter{:}}= 0.54 - 0.46 \\cdot \\cos\\left(\\frac{2 \\pi \\cdot n}{N - 1}\\right), \\quad n = 0,\\dots,N-1\n",
"```\n",
"wobei $N$ die Größe des Fensters ist.\n",
"\n",
"Wir gehen also folgendermaßen vor:\n",
"- Als erstes wählen wir die Größe des Fensters.\n",
" Je mehr Samples das Fenster umfasst, desto besser wird das Ergebnis, aber die Laufzeit wird schlechter.\n",
" Für dieses Projekt können wir ein Fenster mit 64 Samples benutzen.\n",
"- Wir berechnen die sogenannten *Filter-Koeffizienten*. Für jeden Eintrag $a[n]$ setzt er sich zusammen aus $w[n]$ und einem Funktionswert $\\text{sinc}(t)$.\n",
" Der Zeitpunkt $t$ hängt von $n$ ab:\n",
" Wie schon beim Frequenz-Shift ist der Zeitabstand $1/f_S$.\n",
" Der Zeitbereich den wir abbilden wollen ist symmetrisch um die 0.\n",
" Gegeben $n$ und $N$ haben wir also\n",
" ```{math}\n",
" t = \\frac{1}{f_S} \\cdot \\left(n - \\frac{N-1}{2}\\right)\n",
" ```\n",
" Und insgesamt\n",
" ```{math}\n",
" a[n] = w[n] \\cdot \\text{sinc}(4160 \\cdot t)\n",
" ```\n",
"- Wir skalieren $a$ noch so, dass\n",
" ```{math}\n",
" \\sum_{n=0}^{N-1} a[n] = 1\n",
" ```\n",
" Deshalb haben wir auch den konstanten Faktor vor der $\\text{sinc}$ Funktion weg gelassen.\n",
" \n",
"Hier sehen wir die $\\text{sinc}$ Funktion:"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "949bb97c",
"metadata": {
"tags": [
"remove-input"
]
},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ntaps = 64\n",
"M = ntaps - 1\n",
"n = np.arange(ntaps)\n",
"\n",
"window = 0.54 - 0.46 * np.cos(2 * np.pi * n / M)\n",
"\n",
"M //= 2\n",
"t = (M - n).astype(np.float64)\n",
"t /= f_s\n",
"\n",
"taps = np.sinc(4160 * t)\n",
"\n",
"fig, ax = plt.subplots()\n",
"ax.plot(t, taps)\n",
"ax.set_xlabel(\"Zeit [s]\")\n",
"ax.set_ylabel(\"$sinc(4160 t)$\");"
]
},
{
"cell_type": "markdown",
"id": "9808b2f0",
"metadata": {},
"source": [
"Und hier das Hamming-Window:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "f1c92eaf",
"metadata": {
"tags": [
"remove-input"
]
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAkQAAAGwCAYAAABIC3rIAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAABe00lEQVR4nO3dd1yVZeMG8OsM9kYEZMgBceFOUwFn4qgcZZlpubW0YUX1Uyv1taVvmdVrlmU5WmqWaaW5xRw4wZyI7KFs2fuc5/cHSpKoHDyH+4zr+/nwefNwDlw3r8LF/dz3c8skSZJAREREZMbkogMQERERicZCRERERGaPhYiIiIjMHgsRERERmT0WIiIiIjJ7LERERERk9liIiIiIyOwpRQdoahqNBleuXIGDgwNkMpnoOERERNQAkiShqKgIXl5ekMt1P59jdoXoypUr8PX1FR2DiIiIGiE1NRU+Pj46/7hmV4gcHBwA1HxBHR0dBachIiKihigsLISvr2/tz3FdM7tCdOMymaOjIwsRERGRkdHXchcuqiYiIiKzx0JEREREZo+FiIiIiMweCxERERGZPRYiIiIiMnssRERERGT2WIiIiIjI7LEQERERkdljISIiIiKzx0JEREREZk9oIfrrr78wYsQIeHl5QSaTYcuWLXd9TUREBO677z5YWVkhMDAQa9eu1XtOIiIiMm1CC1FJSQm6dOmCFStWNOj5iYmJePjhhzFw4ECcPn0aL7/8MqZPn46dO3fqOSkRERGZMqGHuz744IN48MEHG/z8lStXwt/fHx999BEAoH379jh06BA+/vhjDB06VF8xiciA5RZXoKxKfdv3u9lbwdpC0YSJiMgYGdVp95GRkQgLC6vz2NChQ/Hyyy/f9jUVFRWoqKio/XNhYaG+4hGRnmk0Ei5nFeNEUh5OJV/DiaQ8pF0ru+NrLBVydPZxQneVC+73c0V3Pxe42Fk2UWIiMhZGVYgyMjLg4eFR5zEPDw8UFhairKwMNjY2t7xm8eLFWLRoUVNFJCIdyygox6/R6TiRlIeTSXkoLK+u836ZrKb01EeSgEq1BieTr+Fk8jV8iQQAQGt3e/RQuaJ/GzcMDvKEQi7T+ziIyLAZVSFqjHnz5iE8PLz2z4WFhfD19RWYiIgaIi6rCF8eSMCW0+moUku1j9tYKNCtpTN6qFxxv8oFXX2d4WBtUe/HkCQJybml18vUNZxMzkN8dgkuZxXjclYx1h9PQUtXW8zoF4Ax3X14aY3IjBlVIfL09ERmZmadxzIzM+Ho6Fjv7BAAWFlZwcrKqiniEZEOnEq+hpUH4rH7wj//1u9XuWBYxxa4X+WC9i0cYXGbGaF/k8lkULnZQeVmhzE9an4Ryi2uwKnkaziWmIdfotKQkleK+VvO4dM9sZgcosKE3io42dZfsIjIdBlVIQoODsb27dvrPLZ7924EBwcLSkREuiBJEvbFZGHlgXicSLpW+/jgIA/M7N8K3f1cdPa5mtlbYUgHTwzp4IlXh7TBxhOp+PpgItLzy7B0Vyy+iIjHuJ4tMa2vP1o41f+LFhGZHpkkSdLdn6YfxcXFiIuLAwB069YNy5Ytw8CBA+Hq6oqWLVti3rx5SE9Px7fffgugZtt9x44d8fzzz2Pq1KnYt28fZs+ejW3btjV4l1lhYSGcnJxQUFAAR0dHvY2NiBomPb8Mr/30NyITcgEAFgoZHu3mjWf6tUKgu32TZKhSa/DHmSv48kACYjKKAACWSjnmDGuHKSEqyLnGiEg4ff/8FlqIIiIiMHDgwFsenzRpEtauXYvJkycjKSkJERERdV7zyiuv4MKFC/Dx8cH8+fMxefLkBn9OFiIiwyBJEjZHpeM/v51HUUU1bCwUmBDsh6mh/vB0shaWKSI2G5/vj6udqQoOaIalT3SBtzNni4hEMulCJAILEZF4ucUVePPXc9hxPgMA0K2lM5Y90RX+bnaCk9WQJAk/HEvBe9suoqxKDQcrJRaO7IDH7vOGTMbZIiIRWIh0jIWISKy9FzMx55ezyCmugFIuwyuD2+DZfgFQNnChdFNKzClB+E+nEZ2SDwAY2sED7z/aCc3suVGDqKmxEOkYCxGRGMUV1Xj3jwvYcCIVANDGwx7LnuiKjt5OgpPdWbVagy//SsAne2JRpZbgZm+JJaM7IyzI4+4vJiKdYSHSMRYioqZ3taAMk1YfR2xmMWQyYEbfAIQPbmNU9/05f6UAr2w8jdjMYgDAK2FtMHtQIC+hETURff/8Nrw5aiIyKXFZRXjs8yOIzSyGh6MV1s/ojTceam9UZQgAOng54bcX+mBqqD8A4OM9sVj423moNWb1OyWRyWIhIiK9iU65hsdXRuJKQTkCmtth83Oh6B3QTHSsRrO2UGDBiCC8PaoDZDLg28hkzF4fjYrq2x8uS0TGgYWIiPQi4lIWxq86hvzSKnTxdcbPM0NMZuv6xGAVlo/rBguFDNvOXsWUNSdQVF4lOhYR3QMWIiLSuV+j0zB93UmUVanRr01zrJ/RC64mdsL88M5eWDulJ+wsFTgSn4txq44iu6hCdCwiaiQWIiLSqa8PJuCVjX+jWiNhVFcvfD2xB2wtjeqUoAYLDXTDhmeC0czOEufSC/H4yiNIyS0VHYuIGoGFiIh0QpIkfLAjBu9uuwgAmBrqj4+f6ApLpWl/m+nk44SfZ4XA19UGybmlGP3FEVy6fvwHERkP0/5ORURNZtXBBHweEQ8AmDOsHeYPb282Z4D5u9nhl5khaN/CETnFFZi0+jiu5JeJjkVEWmAhIqJ7tvV0Ot7fHgMAePOh9pg1oJXZ3Z/H3dEaG2b0RhsPe2QUlmPS6uPIL60UHYuIGoiFiIjuyeG4HLy26W8AwLQ+/pjRL0BwInGcbC2wdkpPeDpa43JWMWZ8exLlVdyST2QMWIiIqNHOXynAs9+dQpVawvDOLfDmQ+1FRxLOy9kG66b2hIO1EieSruHlDad580YiI8BCRESNkppXislrTqC4ohq9A1zx0RNdzGbN0N209XTAqok9YKmQY8f5DCz6/TzM7JQkIqPDQkREWrtWUolJa44ju6gC7Twd8NXEHrBSGtdRHPrWO6AZPh7btfaO1l8ciBcdiYjugIWIiLRSVqnGtHUnkJBdAi8na6yd0hOO1haiYxmkhzu3wILhQQCAD3Zcwi+n0gQnIqLbYSEiogZTayTM3hCNqJR8ONlYYN3UnvB0shYdy6BNCfXHs9cXms/55Qz+is0WnIiI6sNCREQNtmJ/HHZfyISVUo6vJ/VAaw8H0ZGMwpxh7fBIVy9UayS8uD4aadd4N2siQ8NCREQNcjguBx/viQUAvPdoJ9yvchWcyHjI5TL89/HO6OLjhIKyKrzwYzQqqzWiYxHRTViIiOiusgrL8dKGaEgSMLaHLx7v7iM6ktGxUirw2fj74GitxOnUfCz5M0Z0JCK6CQsREd1RtVqDF9ZHI6e4Eu08HbBoVAfRkYyWr6stPnqiKwBg9eFE7Dh3VWwgIqrFQkREd7RsdyyOJ+bB3kqJz5+6D9YW3F5/LwYHedQusn590xkk55YITkREAAsREd3B/pis2gNblzzWCQHN7QUnMg2vDW2LHn4uKKqoxnM/RPF4DyIDwEJERPVKzy/DKz+dBgBMCvbD8M5eYgOZEAuFHMvHd4OrnSXOXynEO39cEB2JyOyxEBHRLSqrNXjhxyjkl1ahs48T3niYZ5TpWgsnG3xy/U7WPxxLwdbT6aIjEZk1FiIiusWSP2MQnZIPR2slVoy/j8dy6Em/Ns3x4sBAAMC8zWcRl1UkOBGR+WIhIqI69sdkYfXhRADAR090ha+rreBEpu2lsDYIDmiG0ko1709EJBALERHVKiirwtzNZwAAU0JVGBzkITiR6VPIZfh0XFe42lkiJqMIn+2PEx2JyCyxEBFRrXf/uIDMwgr4u9nh/4a2Ex3HbLg7WOPt6/d3+nx/HM6lFwhORGR+WIiICACw/1IWNp1Kg0wGfPh4Z9hYct1QUxre2QsPdfJEtUbC6z+f4aUzoibGQkREKCyvwrxfzgIApob6owfPKRPi7VEd4WJrgYtXC/F5BC+dETUlFiIiwnt/XERGYTlUzWzx2pC2ouOYLTd7K7w9qiMA4LN9cbhwpVBwIiLzwUJEZOYiLmVh48lUyGTAB4934aUywYZ3boFhHWounb226W9UqXnpjKgpsBARmbHC8irM21xzqWxyiAo9/XmpTDSZTIZ3HukIZ1sLXLhaiM/3x4uORGQWWIiIzNj72y7iakE5/JrZ4vWhvFRmKJo7WGHRyJpdZ8v3XealM6ImwEJEZKb+is3GhhOpAIAPHusMW0ul4ER0s5FdvDAkyOP6rjNeOiPSNxYiIjNUVF6Fub/U3IBxcogKvQKaCU5E/yaTyfDuox3hZGOB81cKsTKCl86I9ImFiMgMfbQrFlcKytHS1Rb/N4yXygyVu4N17aWz/+27jITsYsGJiEwXCxGRmbl4tRDfRiYBAN57tCMvlRm4UV290K9Nc1SpJSz6/QIkSRIdicgksRARmRFJkrBg6zloJODBjp7o27q56Eh0FzKZDP8ZEQQLhQwHYrOx60Km6EhEJomFiMiMbD19BSeSrsHGQoG3hgeJjkMNFNDcHjP6BgAA3v79Asqr1IITEZkeFiIiM1FUXoX3tl8EALzwQCC8nW0EJyJtvPBAILycrJGeX4bPucCaSOdYiIjMxKd7LiO7qAKqZraY3tdfdBzSkq2lsnZWb+WBeCTnlghORGRaWIiIzEBsZhHWHEkCACwc2QFWSh7PYYwe7OiJ0MBmqKzW4J0/LoiOQ2RSWIiITJwkSVi49TzUGgmDgzwwsK276EjUSDKZDItGdoBSLsOei1nYF8MF1kS6wkJEZOL+OHMVkQm5sFLKsYALqY1eoLsDpvWpueT5n9+4wJpIV1iIiExYSUU13ttWs5D6uQGB8HW1FZyIdOHFQa3h4WiFlLxSrPorQXQcIpPAQkRkwpbvi0NGYc0dqZ/tHyA6DumIvZUSbz5cM9u3IiIOaddKBSciMn4sREQmKj67GN8cqpk9WDA8CNYWXEhtSkZ0boFe/q4or+ICayJdYCEiMlHvbbuIKrWEB9q5IyzIQ3Qc0jGZTIa3R3WEQi7DzvOZOBKXIzoSkVFjISIyQZHxudgXkwWlXIa3Hm4vOg7pSVtPBzzdqyUAYPGfMdBoeM4ZUWOxEBGZGI1GwuI/axZSj+/VEgHN7QUnIn16cVBr2FspcTa9AH+cvSo6DpHRYiEiMjHbzl7FmbQC2FkqMHtQa9FxSM/c7K0w8/qC+Q93xqCimtvwiRqDhYjIhFRUq/HBzhgAwLP9W8HN3kpwImoK0/oEwMPRCql5Zfj+aIroOERGiYWIyIT8cDQFqXllaO5gxfPKzIiNpQLhg9sAAJbvu4yCsirBiYiMDwsRkYkoLK/C8n2XAQDhg9vA1lIpOBE1pcfu80Frd3vkl1bhi4h40XGIjA4LEZGJWBkRj2ulVQh0t8eY7j6i41ATUyrkmPtgOwDA6sOJSM8vE5yIyLiwEBGZgKsFZfjmUCIAYO6wdlAq+E/bHD3Qzh29/F1RWa3Bsl2xouMQGRV+1yQyAct2xaKiWoOeKlcMas/T7M2VTCbDvIdq7ju1OToNF64UCk5EZDxYiIiMXExGIX6OSgMAzHuoHWQymeBEJFJXX2cM79wCkgT8d0eM6DhERoOFiMjI/ffPGEgS8HCnFujW0kV0HDIArw9tCwuFDAdis3HoMo/0IGoIFiIiI3YkLgf7L2VDKZfh9aFtRcchA+HXzA5P9/YDACz+8yKP9CBqAOGFaMWKFVCpVLC2tkavXr1w/PjxOz7/k08+Qdu2bWFjYwNfX1+88sorKC8vb6K0RIZDkqTaSyJP9WoJlZud4ERkSF58oDUcrJQ4f6UQv5+5IjoOkcETWog2btyI8PBwLFy4EFFRUejSpQuGDh2KrKysep//448/Yu7cuVi4cCEuXryIb775Bhs3bsQbb7zRxMmJxNsXk4W/0wpgY6HAizyig/7F1c4Sz/SrOdLj072XoeYsEdEdCS1Ey5Ytw4wZMzBlyhQEBQVh5cqVsLW1xerVq+t9/pEjRxAaGorx48dDpVJhyJAhGDdu3F1nlYhMjSRJWLa7Zlv1pBAVj+igek0OVcHZ1gIJ2SX47e900XGIDJqwQlRZWYlTp04hLCzsnzByOcLCwhAZGVnva0JCQnDq1KnaApSQkIDt27fjoYceuu3nqaioQGFhYZ03ImO383wmzl8phJ2lAs9enwUg+jcHa4t/Zon2XEa1WiM4EZHhElaIcnJyoFar4eHhUedxDw8PZGRk1Pua8ePH4+2330afPn1gYWGBVq1aYcCAAXe8ZLZ48WI4OTnVvvn6+up0HERNTaOR8MmemtmhqX384WJnKTgRGbJJwSo0s7NEUm4pNkdzlojodoQvqtZGREQE3n//fXz++eeIiorC5s2bsW3bNrzzzju3fc28efNQUFBQ+5aamtqEiYl0789zGYjJKIKDlRLT+3B2iO7MzkqJmf1bAQD+t/cyqjhLRFQvYac/urm5QaFQIDMzs87jmZmZ8PT0rPc18+fPx4QJEzB9+nQAQKdOnVBSUoJnnnkGb775JuTyW/udlZUVrKy4voJMg/qm2aFpff3hZGshOBEZg6d7++HLvxKQdq0MP59Kw7ieLUVHIjI4wmaILC0t0b17d+zdu7f2MY1Gg7179yI4OLje15SWlt5SehQKBYCaRaZEpu6PM1dwOasYTjYWmNrHX3QcMhI2lgo8N6BmluizfXGoqFYLTkRkeIReMgsPD8eqVauwbt06XLx4EbNmzUJJSQmmTJkCAJg4cSLmzZtX+/wRI0bgiy++wIYNG5CYmIjdu3dj/vz5GDFiRG0xIjJV1WoNPt1zGQDwTL8AOFpzdogabnyvlvBwtEJ6fhl+OpkmOg6RwRF2yQwAxo4di+zsbCxYsAAZGRno2rUrduzYUbvQOiUlpc6M0FtvvQWZTIa33noL6enpaN68OUaMGIH33ntP1BCImszW01eQkFMCF1sLTApRiY5DRsbaQoHnBwZiwdbzWLEvDmO6+8Dagr9IEt0gk8zsWlNhYSGcnJxQUFAAR0dH0XGIGqRKrUHYsgNIzi3F3Afb1S6SJdJGRbUaAz6MwNWCcvxnRBAmh/KyKxkPff/8NqpdZkTm6teodCTnlqKZnSUmBvuJjkNGykqpwAsPBAIAVkTEo6ySa4mIbmAhIjJwldUafLq3Zu3QrAGtYGsp9Eo3Gbkx3X3h42KD7KIK/HAsWXQcIoPBQkRk4DadSkV6fhmaO1jVnmBO1FiWSjlmP1Bz9t0XEfEorawWnIjIMLAQERmwymoNVuyLAwA8P6AVF8GSTjx6nzf8mtkit6QS30VylogIYCEiMmi/RqfhSkE53B2s8CRvpkc6YqGQ44WBNWuJVh1MRHkV1xIRsRARGahqtQZfRMQDqLnvEGeHSJce6eYNb2cb5BRX4KeTPNKIiIWIyEBtP5eBpNxSONta8KgF0jkLhRzP9q85C+/LAwk844zMHgsRkQHSaCR8vr9m7dDUUH/YWXFnGeneEz184WZfc/fqX6PTRcchEoqFiMgA7Y3JQkxGEeytlJgUrBIdh0yUtYUCM/rW3Jzxi4h4qDVmdZ9eojpYiIgMjCRJ+Oz67NCEYD+eaE969VRvPzjZWCAxpwR/nrsqOg6RMCxERAbmcFwu/k7Nh7WFHNN4oj3pmb2VElNCVQCAFfvjYWanORHVYiEiMjCf7a+5K/WT97eEm72V4DRkDiaHqGBnqcDFq4XYF5MlOg6RECxERAbkVHIejibkwUIhwzP9AkTHITPhbGuJp6+fkffZ/jjOEpFZYiEiMiAr9tfcd2h0Nx94OdsITkPmZFoff1gq5YhOyUdkfK7oOERNjoWIyECcv1KAfTFZkMtqDnElakruDtZ48n5fAKhd1E9kTliIiAzE59dnh4Z39oLKzU5wGjJHz/ZvBaVchiPxuYhKuSY6DlGTYiEiMgBxWcXYfn3L8/PXz5giamrezjZ4tJs3ANQeKkxkLliIiAzAFxHxkCRgcJAH2no6iI5DZmzWgFaQy2puDnrhSqHoOERNhoWISLD0/DJsPV1zbMILnB0iwQKa2+OhTi0AAF8ciBechqjpsBARCbb6UCKqNRJCWjVDF19n0XGIahf1bz97Fal5pYLTEDUNFiIigQpKq7D+eAqAmgWtRIagg5cT+rZ2g1oj4ZtDiaLjEDUJFiIigb4/lozSSjXaeTqgX2s30XGIaj3br6agbzyRimsllYLTEOkfCxGRIOVVaqw5nAQAeLZ/AGQymdhARDcJDWyGoBaOKKtS47ujyaLjEOkdCxGRIFui05FTXAEvJ2sM7+wlOg5RHTKZDM/2rzk+Zt2RJJRXqQUnItIvFiIiATQaCV8dTAAATO3jDwsF/ymS4XmoUwt4O9sgt6QSP59KEx2HSK/4XZhIgD0XM5GQXQIHayWe7NlSdByielko5JjWxx8A8PXBBKg1PPSVTJfWhai8vFwfOYjMyld/1cwOTejtB3srpeA0RLc39n5fONlYICm3FLsvZIiOQ6Q3WhciZ2dn9OvXD/Pnz8fevXtRVlamj1xEJutUch5OJl+DpUKOySEq0XGI7sjOSokJvf0AACsPJECSOEtEpknrQrRnzx4MGzYMx44dw6hRo+Di4oI+ffrgzTffxO7du/WRkcikfHmgZnbo0W7ecHe0FpyG6O4mhahgqZTjdGo+TiTx0FcyTVoXoj59+uCNN97Arl27kJ+fj/379yMwMBAffPABhg0bpo+MRCYjPrsYuy9mAgBm9AsQnIaoYZo7WOGx+3wAAF/yOA8yUY1avBAbG4uIiIjat4qKCgwfPhwDBgzQcTwi0/L1wQRIEhDW3gOB7vai4xA12Iy+/thwIgV7Y7JwObMIrT14CDGZFq0Lkbe3N8rKyjBgwAAMGDAAc+bMQefOnXlTOaK7yCoqxy+nag5xndmfs0NkXAKa22NIkAd2ns/EV38l4MMxXURHItIprS+ZNW/eHKWlpcjIyEBGRgYyMzO5sJqoAdYdSUKlWoP7Wjqjh8pVdBwirT1z/TiPLafTkVnIHcdkWrQuRKdPn0ZGRgbmzp2LiooKvPHGG3Bzc0NISAjefPNNfWQkMnolFdX4LrLm+IMbP1SIjE13Pxf08HNBlVrC6sM89JVMi0y6hz2Uubm5iIiIwNatW7F+/XpoNBqo1YZ9e/fCwkI4OTmhoKAAjo6OouOQmVh7OBH/+f0C/N3ssCe8PxRyXmIm47T7QiZmfHsSDtZKHJ03CHa8jxY1EX3//NZ6hmjz5s2YPXs2OnfuDA8PD8yaNQvFxcX46KOPEBUVpfOARMZOrZGw+vohrlP7+LMMkVEb1M4d/m52KCqvxqaTqaLjEOmM1tV+5syZ6NevH5555hn0798fnTp10kcuIpOx+0ImUvJK4Wxrgcfu8xYdh+ieyOUyTA1VYf7W81hzJAkTglUs+WQStC5EWVlZ+shBZLJWH6pZa/FUr5awteTlBTJ+j3X3wdJdsUjOLcWei5kY2sFTdCSie9ao785qtRpbtmzBxYsXAQBBQUEYNWoUFAqFTsMRGbszafk4npQHC4UME4NVouMQ6YStpRLje7XEFxHx+OZgIgsRmQSt1xDFxcWhffv2mDhxIjZv3ozNmzdjwoQJ6NChA+LjeQdTopt9c312aERnL3jwmA4yIZOCVVDKZTielIczafmi4xDdM60L0ezZs9GqVSukpqYiKioKUVFRSElJgb+/P2bPnq2PjERG6Up+GbaduQqgZjE1kSnxdLLG8M4tAPxT/ImMmdaF6MCBA/jggw/g6vrPjeWaNWuGJUuW4MCBAzoNR2TM1kUmoVojoXeAKzp6O4mOQ6Rz0/rU3HF925mruFrAG/SScdO6EFlZWaGoqOiWx4uLi2FpaamTUETGrqSiGuuPpQD454cGkanp5OOEnv6uqNZIWHckWXQconuidSEaPnw4nnnmGRw7dgySJEGSJBw9ehQzZ87EyJEj9ZGRyOj8fCoNheXVUDWzxaB27qLjEOnN9OuXg388loySimrBaYgaT+tC9L///Q+tWrVCcHAwrK2tYW1tjdDQUAQGBuLTTz/VR0Yio1JzI8aaNRXT+vhDznu0kAkb1N4Dqma2KCyvxi9RaaLjEDWa1tvunZ2dsXXrVly+fBkxMTEAgPbt2yMwMFDn4YiM0d6LmUjOLYWTjQUe6+4jOg6RXinkMkwJ9cfC385j9aFEPN3Lj78EkFFq9F3iWrdujdatW+syC5FJ+Pr6jpvxvBEjmYnHu/vgo12XkJRbir0xWRgc5CE6EpHWGvTdOjw8vMEfcNmyZY0OQ2TszqYV4HhiHpRyGSbxRoxkJuyslBjXqyW+PJCArw8msBCRUWpQIYqOjq7z56ioKFRXV6Nt27YAgNjYWCgUCnTv3l33CYmMyDeHEgAAwzu3gKcTb8RI5mNyiArfHEzEscQ8nEsv4K0myOg0qBDt37+/9r+XLVsGBwcHrFu3Di4uLgCAa9euYcqUKejbt69+UhIZgYyCcvxx/UaM3GpP5qaFkw0e6tQCv/19Bd8cSsTHY7uKjkSkFa13mX300UdYvHhxbRkCABcXF7z77rv46KOPdBqOyJh8e/1GjD1Vrujkw9+OyfxM71uzBf+PM1eQVVguOA2RdrQuRIWFhcjOzr7l8ezs7Hpv2EhkDsqr1Fh/vOZGjDymg8xVZx9n9PBzQZVawvdHeaNGMi5aF6JHH30UU6ZMwebNm5GWloa0tDT88ssvmDZtGkaPHq2PjEQGb0t0Oq6VVsHHxYYLSsmsTQmt+YXgh2MpKK9SC05D1HBa7wleuXIlXnvtNYwfPx5VVVU1H0SpxLRp0/Dhhx/qPCCRoZMkCWsOJwGoOQFcwXuwkBkb2sEDXk7WuFJQjt//voIxPXxFRyJqEK1niGxtbfH5558jNzcX0dHRiI6ORl5eHj7//HPY2dnpIyORQYuMz8WlzCLYWirwxP385k/mTamQY8L1W06sOZwESZLEBiJqIK0L0Q12dnbo3LkzOnfuzCJEZm319dmhx+7zgZONhdgwRAZgXE9fWFvIceFqIY4n5omOQ9QgWl8yKykpwZIlS7B3715kZWVBo9HUeX9CQoLOwhEZuuTcEuyNyQQATA5ViQ1DZCCcbS3xaDcfrD+egjWHk9AroJnoSER3pXUhmj59Og4cOIAJEyagRYsWkMm4XoLM17ojyZAkoH+b5mjV3F50HCKDMSVUhfXHU7DrQgZS80rh62orOhLRHWldiP78809s27YNoaGh+shDZDSKK6qx6WQqgJpv/kT0jzYeDugT6IZDcTn47mgy3niovehIRHek9RoiFxcXuLq66iMLkVH5+WQqiiqqEdDcDv1aNxcdh8jg3PhFYcPxFJRWVosNQ3QXWheid955BwsWLEBpaak+8hAZBY1GwrrImhvPTQlRQc6t9kS3GNjWHapmtigsr8YvUemi4xDdkdaXzD766CPEx8fDw8MDKpUKFhZ1d9VERUXpLByRoYqIzUJiTgkcrJUYfZ+P6DhEBkkul2FSiAqLfr+ANYcT8VTPlvzlgQyW1oXokUce0WmAFStW4MMPP0RGRga6dOmC5cuXo2fPnrd9fn5+Pt58801s3rwZeXl58PPzwyeffIKHHnpIp7mI7mT1oSQAwJP3+8LOSut/RkRm4/HuPvhoVywSskvw1+VsDGjrLjoSUb20/k6+cOFCnX3yjRs3Ijw8HCtXrkSvXr3wySefYOjQobh06RLc3W/9R1NZWYnBgwfD3d0dP//8M7y9vZGcnAxnZ2edZSK6m9jMIhyKy4FcBky8fgM6Iqqfg7UFxvTwwZrDSVhzOImFiAxWo2/MqAvLli3DjBkzMGXKFAQFBWHlypWwtbXF6tWr633+6tWrkZeXhy1btiA0NBQqlQr9+/dHly5dmjg5mbMbx3QMDvLgVmKiBpgcooJMBhyIzUZcVrHoOET1alAhcnV1RU5ODoB/dpnd7q2hKisrcerUKYSFhf0TRi5HWFgYIiMj633Nb7/9huDgYDz//PPw8PBAx44d8f7770Otvv0BghUVFSgsLKzzRtRY+aWV+DU6DcA/h1gS0Z35NbPDoHY1M0PrjiSJDUN0Gw26ZPbxxx/DwcGh9r91cTPGnJwcqNVqeHjUPRncw8MDMTEx9b4mISEB+/btw1NPPYXt27cjLi4Ozz33HKqqqm57KW/x4sVYtGjRPeclAoANJ1JRXqVB+xaO6OXP208QNdSUUH/suZiFX6LS8NrQtjzmhgxOgwrRpEmTUFFRAQCYPHmyPvPckUajgbu7O7766isoFAp0794d6enp+PDDD29biObNm4fw8PDaPxcWFsLXlwdwkvaq1Rp8d9NWe96lnajhQlo1Q1sPB1zKLMKmk6mY3jdAdCSiOhq8hsjJyQkDBw7E22+/jUOHDqGqquqePrGbmxsUCgUyMzPrPJ6ZmQlPT896X9OiRQu0adMGCoWi9rH27dsjIyMDlZWV9b7GysoKjo6Odd6IGmPPxSyk55fB1c4SI7t6iY5DZFRkspot+ADwbWQy1BpJbCCif2lwIVq5ciX8/PywevVq9OvXD87Ozhg8eDAWL16Mo0eP3nEdT30sLS3RvXt37N27t/YxjUaDvXv3Ijg4uN7XhIaGIi4urs6BsrGxsWjRogUsLS21+vxE2lp7JBFAzVZ7awvFXZ5NRP/2SDcvOForkZJXiohLWaLjENXR4EI0efJkrF27FklJSYiLi8Py5cvh5eWFlStXIjQ0FC4uLnj44Ye1+uTh4eFYtWoV1q1bh4sXL2LWrFkoKSnBlClTAAATJ07EvHnzap8/a9Ys5OXl4aWXXkJsbCy2bduG999/H88//7xWn5dIWxevFuJoQh4Uchme7u0nOg6RUbK1VOLJni0BAGu5uJoMTKPuKBcQEICAgABMnToViYmJ+Oabb7B8+XLs2LFDq48zduxYZGdnY8GCBcjIyEDXrl2xY8eO2oXWKSkpkMv/6Wy+vr7YuXMnXnnlFXTu3Bne3t546aWXMGfOnMYMg6jBvo1MAgAM6+AJL2cbsWGIjNiE3n74+mACDl7OQVxWEQLdHURHIgIAyCRJ0upCbkpKCvbv34+IiAhEREQgJycHvXv3Rr9+/dC/f3/069dPX1l1orCwEE5OTigoKOB6ImqQ/NJK9F68F+VVGvz0bDB6cncZ0T2Z8e1J7L6QiQm9/fDOIx1FxyEjoe+f3w2eIZo6dSoiIiKQl5eH0NBQ9O3bF8888wzuv/9+KJU8uoBM18brW+2DWjjifpWL6DhERm9KiAq7L2Til6g0vD6sLRytuQWfxGtwk1m7di1atmyJN998E4MGDUK3bt247ZhMXrVag2+vb7WfHMqt9kS6ENyqGdp42CM2sxibTqZhWh/e5JTEa/Ci6osXL2Lu3Lk4deoUHnroIbi6umLEiBFYunQpTp48WWfnF5GpuLHV3sXWAiO7cKs9kS7U3YKfBA234JMBaHAhatu2LWbOnIkNGzYgIyMDhw8fxkMPPYTjx49j+PDhcHV1xfDhw/WZlajJ3ThmYFzPltxqT6RDj3bzhqO1Esm5pYiI5RZ8Eq/Rh7sGBQVh9OjRGD16NEaNGgVJkvDnn3/qMhuRUDEZhYhMyOVWeyI9uHkL/o0Dk4lE0mo1dFZWFiIiImp3mcXGxsLS0hI9e/bEK6+8goEDB+orJ1GTuzE7NLSDB7faE+nBhN5+WFW7Bb8Yge72oiORGWtwIWrfvj1iY2OhVCpx//334/HHH8eAAQMQGhoKa2trfWYkanI1p9qnAwAmh3DBJ5E++LraIqy9B3ZfyMS3kUl4exS34JM4DS5EjzzyCAYOHIg+ffrA1tZWn5mIhONWe6KmcWML/s+n0vDaUG7BJ3EavIZo8eLFGDJkCMsQmTy1Rvpnqz1PtSfSqxtb8Esr1fj5ZJroOGTGGr2omshU7bmY+c9We55qT6RXN2/BX8ct+CQQCxHRv6y9vuOFW+2Jmga34JMhYCEiusmljCJutSdqYraWSoy93xcAsPZIsuA0ZK5YiIhusu76qfZDgrjVnqgpTeitgkwG/BWbjfjsYtFxyAxpfSrrmTNn6n1cJpPB2toaLVu2hJWV1T0HI2pqBaVV+DXqxlZ7ldgwRGamZTNbDGrngT0XM/HtkSQs4hZ8amJaF6KuXbvecdeNhYUFxo4diy+//JL3JyKj8tPJVJRVqdHO0wE9/V1FxyEyO5NDVNhz8Z8t+A7cgk9NSOtLZr/++itat26Nr776CqdPn8bp06fx1VdfoW3btvjxxx/xzTffYN++fXjrrbf0kZdIL9QaCd8eTQLArfZEooQGNkOguz1KKtX4+RS34FPT0nqG6L333sOnn36KoUOH1j7WqVMn+Pj4YP78+Th+/Djs7Ozw6quvYunSpToNS6Qv+2KykJpXBmdbC4zq6i06DpFZurEFf/6Wc/g2MhmTglWQy/nLCTUNrWeIzp49Cz+/W3ff+Pn54ezZswBqLqtdvXr13tMRNZEb55aNvd8XNpbcak8kyuhu3nCwViIxpwQHLmeLjkNmROtC1K5dOyxZsgSVlZW1j1VVVWHJkiVo164dACA9PR0eHh66S0mkR5czi3AoLgdyWc1hk0Qkjp2VEmO612zBv/GLClFT0PqS2YoVKzBy5Ej4+Pigc+fOAGpmjdRqNf744w8AQEJCAp577jndJiXSkxtb7QcHecDHhUfTEIk2MdgPa44kIuJSNhJzSuDvZic6EpkBrQtRSEgIEhMT8cMPPyA2NhYAMGbMGIwfPx4ODg4AgAkTJug2JZGeFJRVYfP1rfaTuNWeyCCo3OwwsK079sVkYd2RJPxnZAfRkcgMaF2IAMDBwQEzZ87UdRaiJrfpZCpKK9Vo6+GA4IBmouMQ0XWTQlTYF5NVuwXf3qpRP66IGqxRf8MuX76M/fv3IysrCxqNps77FixYoJNgRPqm0Uj47mjNMQGTuNWeyKD0DXRDQHM7JGSX4JdTaZzBJb3TuhCtWrUKs2bNgpubGzw9Pev8EJHJZCxEZDQiYrOQnFsKR2slHunGU+2JDIlcLsOkYBUW/nYe6yKTMKG3H7fgk15pXYjeffddvPfee5gzZ44+8hA1mTXXT7V/smdL2FpyOp7I0DzW3Qcf7ryEhOwSHIzLQf82zUVHIhOm9bb7a9euYcyYMfrIQtRk4rKKcfByDmTcak9ksOytlHi8uw8AbsEn/dO6EI0ZMwa7du3SRxaiJvPt9a32g9p5wNeVW+2JDNXE4JpfWPZfykJSTongNGTKtL5OEBgYiPnz5+Po0aPo1KkTLCzqHr43e/ZsnYUj0ofC8ir8cv2cJJ5qT2TYAprbY0Db5oi4lI1vI5OxYESQ6EhkomSSJEnavMDf3//2H0wmQ0JCwj2H0qfCwkI4OTmhoKAAjo6OouOQAKsPJeLtPy6gtbs9dr3Sj7vLiAxcxKUsTF5zAg5WSkS+MYhb8M2Uvn9+a/23KjExUechiJqKWiPV3pl6cii32hMZg36tmyPAzQ4JOSXYHJWGicEq0ZHIBGm9hojImEVc+mer/aPdeKo9kTGQy2W19yFaeyQJGo1WFzaIGqRBM0Th4eF45513YGdnh/Dw8Ds+d9myZToJRqQPa6/vVOFWeyLj8lh3Hyy9vgX/r8vZGNDWXXQkMjEN+okQHR2Nqqqq2v++HV5+IEN2ObMIBy/zVHsiY2RvpcSYHr5YfTgRa48ksRCRzjWoEO3fv7/e/yYyJjefas+t9kTGZ2KwH9YcSUTEpWwkZBcjoLm96EhkQriGiMxCQWkVfjlVc6r95JDb75QkIsOlcrPDA9dnhr6NTBachkyN1osoysvLsXz58tse7hoVFaWzcES68tPJVJRVqdHO0wG9A1xFxyGiRpocqsLemCxsOpmKV4e0gYO1xd1fRNQAWheiadOmYdeuXXj88cfRs2dPrhsig1dnqz1PtScyan0C3RDobo+4rGL8fCoNU0I540u6oXUh+uOPP7B9+3aEhobqIw+Rzu29mIm0a2VwtrXAI9xqT2TUZDIZJoeo8NaWc1h3JAmTglWQy/lLDt07rdcQeXt7w8HBQR9ZiPTixlb7cT1bwtpCITYMEd2z0fd5w8FaiaTcUkTEZomOQyZC60L00UcfYc6cOUhO5oI2MnyXMopwJD4XCrkMT3OrPZFJsLVU4sn7fQEAaw4niQ1DJkPrQtSjRw+Ul5cjICAADg4OcHV1rfNGZEjWHqk5amZoBw94O9sITkNEujIxWAWZDDh4OQdxWUWi45AJ0HoN0bhx45Ceno73338fHh4eXKBKButaSSV+jeZWeyJT5Otqi7D2Hth9IRPrjiTjnUc6io5ERk7rQnTkyBFERkaiS5cu+shDpDMbT6aivEqDDl6OuF/lIjoOEenYlFAVdl/IxC9RaXhtaFs42XALPjWe1pfM2rVrh7KyMn1kIdKZarUG312/cRu32hOZpuCAZmjr4YDSSjU2nUwVHYeMnNaFaMmSJXj11VcRERGB3NxcFBYW1nkjMgS7LmQiPb8MrnaWGNHFS3QcItIDmUyGyaEqADW7SdUaSWwgMmpaXzIbNmwYAGDQoEF1HpckCTKZDGq1WjfJiO7B6kM1i6mf7sWt9kSm7NFu3vhgRwzSrpVh94VMDOvoKToSGSmtCxEPdyVD93dqPk4mX4OFglvtiUydtYUC43u1xIr98Vh9KJGFiBpN60LUv39/feQg0pnVh2tmh0Z08YK7o7XgNESkbxODVfjyQAKOJ+XhbFoBOvk4iY5ERkjrQgTUHPB65syZeg93HTlypE6CETVGRkE5tp25CgCYyjOOiMyCh6M1hndugS2nr2DN4UQsG9tVdCQyQloXoh07dmDixInIycm55X1cQ0SifXc0CdUaCT39XdHRm78lEpmLqX38seX0Ffx+5grmPtiOs8OkNa13mb344osYM2YMrl69Co1GU+eNZYhEKqtU48djKQA4O0Rkbjr7OKOHnwuq1BK+P8qjpUh7WheizMxMhIeHw8PDQx95iBpty+l0XCutgo+LDQYH8e8nkbmZ2qfmF6Hvj6WgvIq/oJN2tC5Ejz/+OCIiIvQQhajxJEmq3Wo/OUQFhZw3YiQyN0OCas4szCupxNbT6aLjkJHReg3RZ599hjFjxuDgwYPo1KkTLCzq3ip99uzZOgtH1FAHL+fgclYx7CwVeOL6KdhEZF6UCjkmhfjh/e0xWH0oCU/08OVd6qnBtC5E69evx65du2BtbY2IiIg6f9lkMhkLEQlxY6v9mB6+cLTmeUZE5mrs/S3xyZ7LuJRZhCPxuQgNdBMdiYyE1pfM3nzzTSxatAgFBQVISkpCYmJi7VtCQoI+MhLdUVxWMSIuZUMmqznskYjMl5ONBcZ09wHwzx3riRpC60JUWVmJsWPHQi7X+qVEerH2SM03vbD2HvBrZic4DRGJNvn6LtO9MVlIzCkRnIaMhdatZtKkSdi4caM+shBpLb+0Er+cqlk8ya32RAQA/m52GNTOHQCw9jBniahhtF5DpFar8cEHH2Dnzp3o3LnzLYuqly1bprNwRHez/ngqyqrUaN/CEb0DXEXHISIDMbWPP/bGZGHTqTSED2kLJxuuLaQ707oQnT17Ft26dQMAnDt3rs77uJqfmlKVWoNvI5MAAFNDVfz7R0S1Qlo1Q1sPB1zKLMKG4yl4tn8r0ZHIwPG0ezJa289exdWCcrjZW2JEFy/RcYjIgMhkMkzto8KcX85i3ZEkTO3jDwsF177S7fFvBxklSZKw6mDNrsYJvVWwtlAITkREhmZUV2+42VviSkE5tp+9KjoOGbhGFaKTJ0/i//7v//Dkk09i9OjRdd4aY8WKFVCpVLC2tkavXr1w/PjxBr1uw4YNkMlkeOSRRxr1ecl4HU3Iw7n0Qlgp5ZgQ7Cc6DhEZIGsLBSYGqwAAqw4mQJIksYHIoGldiDZs2ICQkBBcvHgRv/76K6qqqnD+/Hns27cPTk7any6+ceNGhIeHY+HChYiKikKXLl0wdOhQZGVl3fF1SUlJeO2119C3b1+tPycZv6+vzw493t0HrnaWgtMQkaF6urcfrC3kOJdeiKMJeaLjkAHTuhC9//77+Pjjj/H777/D0tISn376KWJiYvDEE0+gZcuWWgdYtmwZZsyYgSlTpiAoKAgrV66Era0tVq9efdvXqNVqPPXUU1i0aBECAgK0/pxk3OKyirE3JgsyGTCtD7faE9HtudpZ4vHrN2q8cZmdqD5aF6L4+Hg8/PDDAABLS0uUlJRAJpPhlVdewVdffaXVx6qsrMSpU6cQFhb2TyC5HGFhYYiMjLzt695++224u7tj2rRpd/0cFRUVKCwsrPNGxu2bQzXf1MLaeyCgub3gNERk6Kb1CYBMBuyLyUJcVpHoOGSgtC5ELi4uKCqq+Qvl7e1du/U+Pz8fpaWlWn2snJwcqNVqeHh41Hncw8MDGRkZ9b7m0KFD+Oabb7Bq1aoGfY7FixfDycmp9s3Xlwd/GrOc4gr8ElVzI8YZfTk7SER35+9mh7D2NT9nvuFxHnQbWheifv36Yffu3QCAMWPG4KWXXsKMGTMwbtw4DBo0SOcBb1ZUVIQJEyZg1apVcHNr2IF98+bNQ0FBQe1bamqqXjOSfn0XmYzKag26+DrjfpWL6DhEZCSe6VfzC9QvUenILqoQnIYMkdb3Ifrss89QXl4OoOagVwsLCxw5cgSPPfYY3nrrLa0+lpubGxQKBTIzM+s8npmZCU9Pz1ueHx8fj6SkJIwYMaL2MY1GUzMQpRKXLl1Cq1Z1b75lZWUFKysrrXKRYSqvUuO7o8kAgBl9/XkjRiJqsB5+Luji64y/U/Px3dFkhA9uIzoSGRitC5Gr6z/HI8jlcsydO7fRn9zS0hLdu3fH3r17a7fOazQa7N27Fy+88MItz2/Xrh3Onj1b57G33noLRUVF+PTTT3k5zMT9EpWGvJJKeDvbYFiHWwszEdHtyGQyzOjrjxd+jMb3R5Mxq38r2Fjy/mX0jwYXooYuRnZ0dNQqQHh4OCZNmoQePXqgZ8+e+OSTT1BSUoIpU6YAACZOnAhvb28sXrwY1tbW6NixY53XOzs7A8Atj5Np0WgkfHOw5tr/tD7+UPKOs0SkpWEdPOHjYoO0a2X4JSoNT/fmPczoHw0uRM7Ozne8RCFJEmQyGdRqtVYBxo4di+zsbCxYsAAZGRno2rUrduzYUbvQOiUlBXI5f/iZu30xWUjIKYGDtRJP3M+ZQCLSnlIhx9RQf7z9xwWsPpSI8T1bQi7npXeqIZMaeOvOAwcO1P63JEl46KGH8PXXX8Pb27vO8/r376/bhDpWWFgIJycnFBQUaD2bReI88WUkjifm4dn+AZj3YHvRcYjISBVXVCN48V4UlVdj1cQeGBzkcfcXkUHQ98/vBs8Q/bvoKBQK9O7dmzdGJL07k5aP44l5UMplmBLCGzESUePZWynxVC8/rDwQj1V/JbAQUS1eiyKDt+r62qGRXbzg6WQtOA0RGbvJISoo5TIcT8rD6dR80XHIQLAQkUFLu1Zae0r1dN6IkYh0wNPJGiO7eAHgcR70j3sqRLwPDOnb1wcTodZICA1shiAvrvkiIt248QvWn2evIjm3RHAaMgQNXkM0evToOn8uLy/HzJkzYWdnV+fxzZs36yYZmb28kkpsOJECAJjVP1BwGiIyJUFejujfpjkOxGbjq78S8N6jnURHIsEaXIicnJzq/Pnpp5/WeRiim609koTyKg06eTshNLCZ6DhEZGJmDWiFA7HZ2HQqDS+FtYa7A9comrMGF6I1a9boMwdRHSUV1Vh3JAlAzTctXp4lIl3r5e+Kbi2dEZ2SjzWHkzBnWDvRkUggLqomg7T+eAoKyqrg72aHoTymg4j0QCaTYVb/mvMvv49MRmF5leBEJBILERmcymoNvr6+1f7ZfgFQ8E6yRKQnYe09EOhuj6KKavx4LEV0HBKIhYgMzpbT6cgoLIe7gxUevc/77i8gImokuVyGmddnib45lIjyKu2OnyLTwUJEBkWjkbDyQDwAYHpff1gpeRo1EenXyC5e8HKyRnZRBTZHpYuOQ4KwEJFB2XUhEwnZJXC0VmJcz5ai4xCRGbBUymvvS/TlX/FQaxp0xCeZGBYiMhiSJOGL67NDE4NVcLC2EJyIiMzFkz194WxrgeTcUvx57qroOCQACxEZjMiEXPydmg8rpRyTQ1Wi4xCRGbG1VGJyiAoA8EVEPCSJs0TmhoWIDMYXETWzQ0/08IWbvZXgNERkbiYFq2BjocD5K4U4eDlHdBxqYixEZBDOpRfg4OUcKOQyPNOPh7gSUdNzsbPEkz19AfzzCxqZDxYiMgg31g4N79wCvq62gtMQkbma3jcASrkMkQm5iE65JjoONSEWIhIuKacEf56tWcR4434gREQieDvbYFTXmvuf3bgFCJkHFiISbuWBeGgkYEDb5mjfwlF0HCIyczP711y233k+E7GZRYLTUFNhISKhUvNK8fOpNADAiw8ECk5DRAS09nDAsOtnKC7fFyc4DTUVFiIS6osD8ajWSOgT6Ibufq6i4xARAQBeHFTzC9ofZ64gLqtYcBpqCixEJMyV/DJsOpkKAJg9qLXgNERE/+jg5YTBQR6QJGDFfs4SmQMWIhJm5YF4VKkl9A5wRU9/zg4RkWGZ/UDNL2pbT6cjMadEcBrSNxYiEiKjoBwbjnN2iIgMVycfJzzQzh0azhKZBRYiEmLlgXhUqjXoqXJFcEAz0XGIiOp14xe2X6PTkZzLWSJTxkJETS6rsBzrj6cAqPlmI5PJBCciIqpfV19n9G/THGqNhM/3875EpoyFiJrcV38loKJag/taOiM0kLNDRGTYbswS/RKVhtS8UsFpSF9YiKhJ5RRX4PtjyQA4O0RExqG7nwv6BLqhWiPVHjNEpoeFiJrUqoMJKK/SoMv1aWgiImPwUljNLNGmk6m4kl8mOA3pAwsRNZm8kkp8F1kzO/TSoEDODhGR0bj/+gaQKrWELyI4S2SKWIioyXx9MAGllWp09HbEwLbuouMQEWnlxlqijSdSkVFQLjgN6RoLETWJ/NJKrDuSBKDmZmecHSIiY9M7wBU9Va6oVGuwkmuJTA4LETWJbw4loqRSjfYtHDE4yEN0HCIirclkstq1ROuPpyCzkLNEpoSFiPQup7gC3xxKBMC1Q0Rk3EJaNUMPPxdUVGuwfN9l0XFIh1iISO8+3x+P0ko1Ovs4YWgHT9FxiIgaTSaT4bWhbQEAG46nIiWX9yUyFSxEpFfp+WX4/mjNzrLXh7bl7BARGb3eAc3Qr01zVGskfLwnVnQc0hEWItKrT/fEolKtQXBAM/QJdBMdh4hIJ14fUjNLtOV0OmIyCgWnIV1gISK9icsqxs+n0gAArw/j7BARmY5OPk54qJMnJAlYupOzRKaAhYj05uPdsdBIQFh7D9zX0kV0HCIinQof3BZyGbDnYiaiUq6JjkP3iIWI9OJcegG2nb0KmQx4bWgb0XGIiHQu0N0ej3f3AQB8uOMSJEkSnIjuBQsR6cUHOy8BAEZ18UI7T0fBaYiI9OOlsDawVMgRmZCLQ3E5ouPQPWAhIp07mpCLv2KzoZTL8Mpgzg4RkenydrbBU71bAgA+3MlZImPGQkQ6JUkSPrw+O/RkT1/4NbMTnIiISL+eHxgIW0sFzqQVYOf5DNFxqJFYiEin9sVk4VTyNVhbyPHiA61FxyEi0js3eytM6+MPAFi6KxZqDWeJjBELEemMRvPP7NCkEBU8HK0FJyIiahoz+gXA2dYCcVnF+DU6XXQcagQWItKZ389cQUxGERyslJjVv5XoOERETcbR2qL2+97Hu2NRUa0WnIi0xUJEOlFRrcZHu2puTvZMvwA421oKTkRE1LQmBqvg7mCF9PwyfBeZLDoOaYmFiHRizeEkpOSVwt3BClOvX0snIjInNpYKhF/fWfvp3svIK6kUnIi0wUJE9yy7qAKf7YsDAPzfsHaws1IKTkREJMaYHr5o38IRReXV+IQHvxoVFiK6Z8t2x6K4ohqdvJ0wupu36DhERMIo5DLMH94eAPDDsRTEZhYJTkQNxUJE9+TClUJsPJECAFgwIghyOQ9wJSLzFtLKDUM7eECtkfDOHxd4s0YjwUJEjSZJEt7ddgEaCXi4cwvcr3IVHYmIyCC88VB7WChkOHg5BxGXskXHoQZgIaJG23MxC0fic2GplGPusHai4xARGQy/ZnaYElqzweTdbRdQpdYITkR3w0JEjVJZrcF72y4AAKb38Yevq63gREREhuWFBwLRzM4S8dkl+OEot+EbOhYiapRvI5OQlFsKN3srPDcwUHQcIiKD42htgfAhNdvwP95zGfml3IZvyFiISGu5xRX4dO9lAMD/DW0Le26zJyKq19gevmjn6YCCsip8suey6Dh0ByxEpLWP98SiqLwaQS0c8Vh3H9FxiIgMllIhx1sPBwEAvjuajLisYsGJ6HZYiEgrlzKK8OOxmm3284cHQcFt9kREd9SntRvC2rtDrZHw/vaLouPQbbAQUYPdvM1+WAdPBLdqJjoSEZFReOOh9lDKZdgXk4WIS1mi41A9WIiowX4/cxUHL+fAUiHHvIe4zZ6IqKECmttjUogKALDwt/Mor1KLDUS3YCGiBikorcLbv58HADw/MBB+zewEJyIiMi4vh7WGp6M1knNL8b+9XGBtaFiIqEGW7IhBTnElWjW3w8wBAaLjEBEZHQdrCywa1QEA8NVfCYjJKBSciG5mEIVoxYoVUKlUsLa2Rq9evXD8+PHbPnfVqlXo27cvXFxc4OLigrCwsDs+n+7diaQ8rD9es5D6/Uc7wUqpEJyIiMg4De3gicFBHqjWSHhj81loNDznzFAIL0QbN25EeHg4Fi5ciKioKHTp0gVDhw5FVlb9i84iIiIwbtw47N+/H5GRkfD19cWQIUOQnp7exMnNQ2W1Bm9sPgug5n4avQK4kJqI6F4sGtkBdpYKRKXk48frv2ySeDJJ8DG8vXr1wv3334/PPvsMAKDRaODr64sXX3wRc+fOvevr1Wo1XFxc8Nlnn2HixIl3fX5hYSGcnJxQUFAAR0fHe85v6j7bdxlLd8WimZ0l9r7aH862lqIjEREZvTWHE7Ho9wtwsFZib3h/uDtai45k8PT981voDFFlZSVOnTqFsLCw2sfkcjnCwsIQGRnZoI9RWlqKqqoquLrWf9J6RUUFCgsL67xRwyTmlOB/++IA1NxziGWIiEg3Jgar0MXHCUXl1Vj0+wXRcQiCC1FOTg7UajU8PDzqPO7h4YGMjIwGfYw5c+bAy8urTqm62eLFi+Hk5FT75uvre8+5zYEkSXjz17OorNagb2s3jOrqJToSEZHJUMhleH90JyjkMmw7exX7YjJFRzJ7wtcQ3YslS5Zgw4YN+PXXX2FtXf9047x581BQUFD7lpqa2sQpjdPmqHQcic+FlVKOdx/pCJmMd6QmItKlDl5OmNbHHwAwf8t5lFZWC05k3oQWIjc3NygUCmRm1m3GmZmZ8PT0vONrly5diiVLlmDXrl3o3LnzbZ9nZWUFR0fHOm90Z3kllXh3W80U7kthrXnPISIiPXk5rDW8nW2Qnl+Gj3fHio5j1oQWIktLS3Tv3h179+6tfUyj0WDv3r0IDg6+7es++OADvPPOO9ixYwd69OjRFFHNyvvbL+JaaRXaejhgRl/ec4iISF9sLZV495GOAIDVh5NwLr1AcCLzJfySWXh4OFatWoV169bh4sWLmDVrFkpKSjBlyhQAwMSJEzFv3rza5//3v//F/PnzsXr1aqhUKmRkZCAjIwPFxTxBWBf2x2Th51NpkMmA90d3goVC+F8RIiKTNrCdOx7u3AJqjYTXNv2Nimoe6yGC8J92Y8eOxdKlS7FgwQJ07doVp0+fxo4dO2oXWqekpODq1au1z//iiy9QWVmJxx9/HC1atKh9W7p0qaghmIyc4gq8/vPfAIDJISp093MRnIiIyDz8Z0QHNLOzRExGET7ccUl0HLMk/D5ETY33IaqfJEmYtu4k9sVkoa2HA7a+EAprC96Rmoioqey5kInp354EAHw/rRf6tHYTnMiwmPR9iMhwfH8sBftismCplOPTcV1ZhoiImlhYkAee6tUSAPDqptO4VlIpOJF5YSEixGUV473ru8rmDGuHdp6cOSMiEuGth4MQ0NwOmYUVeOPXszCzizhCsRCZucpqDV7eGI3yqpobME4JUYmORERktmwsFfh0bDco5TL8eS4Dm06liY5kNliIzNyy3bE4l14IF1sLLB3TBXI5b8BIRCRSJx8nhA9pAwBY9Nt5JOeWCE5kHliIzFhkfC6+/CseALB4dGd48HBBIiKD8Gy/Vujp74qSSjVe3nga1WqN6Egmj4XITBWUVuHVn05DkoCxPXwxrOOd7wxORERNRyGX4eOxXeFgrUR0Sj6WXz9om/SHhcgMSZKEN7ecxZWCcqia2WLBiCDRkYiI6F+8nW1q72K9fN9lnEq+JjiRaWMhMkPfH0vBH2eu1v4GYmelFB2JiIjqMaqrNx7p6gWNBMxeH42c4grRkUwWC5GZiYzPxaLfzgMAXhvSFt1a8m7URESG7O1HOsLfzQ7p+WV47vsoVFZzPZE+sBCZkdS8Ujz3wylUaySM7OKFmf15cCsRkaFztLbAqok94GClxPGkPCz87RzvT6QHLERmoqSiGjO+PYlrpVXo5O2EDx7vDJmMW+yJiIxBoLs9/jeuG2QyYP3xVHx3NFl0JJPDQmQGNBoJ4T+dRkxGEZo7WOGrid15NAcRkZEZ2M4dc4e1AwAs+v0CjsTlCE5kWliIzMAney9j5/lMWCrk+HJCd7RwshEdiYiIGuGZfgF4tJs31BoJz/0YhZTcUtGRTAYLkYnbduYq/rf3MgDg/dGdcB8XURMRGS2ZTIbFozuhi68z8kurMP3bEyiuqBYdyySwEJmw81cK8NqmvwEA0/v44/HuPoITERHRvbK2UOCrCd3h7mCF2MxivLLxNDQaLrK+VyxEJiq7qALPfHsKZVVq9GvTHHMfbCc6EhER6YiHozW+nNAdlko5dl/IxEe7L4mOZPRYiExQbnEFnv76GNLzyxDgZofl47pBqeD/1UREpqRbSxcsGd0JALBifzy+PBAvOJFx409JE3OtpBJPfX0MlzKL4OFohdWT74eTjYXoWEREpAej7/PBa0PaAAAW/xmDrw8mCE5kvFiITEh+aU0ZurG9/scZvaFysxMdi4iI9OiFB1rjpUGtAQDvbruItYcTBScyTixEJqKgrAoTvjmOC1cL4WZvifUzeqFVc3vRsYiIqAm8HNYaLwwMBAD85/cL+C4ySWwgI8RCZAIKy6swcfVxnE0vgKudJX6c0RuB7g6iYxERURORyWR4dUgbzOzfCgAwf+t5/HgsRXAq48JCZOSKK6oxefVx/J2aDxdbC/wwvRfaeLAMERGZG5lMhjnD2mJGX38AwBu/nsVPJ1IFpzIeLERGrKSiGlPWHEdUSj6cbCzw/fReaN/CUXQsIiISRCaT4Y2H2mNKqAoAMGfzGfx8Kk1sKCPBQmSkUvNK8fjKSJxIugYHayW+n9YLHbycRMciIiLBZDIZFgwPwoTefpAk4LVNf+PTPZd588a7YCEyQocu52DEZ4dw8foC6u+n9UInH5YhIiKqIZPJsGhkB0wNrbl89vGeWDz7/SkUlVcJTma4WIiMiCRJWPVXAiauPob80ip08XHCby/0QRdfZ9HRiIjIwMjlMiwYEYQPH+9ce0frR1YcRnx2sehoBomFyEiUVarx0obTeG/7RWgk4PHuPtj4bDC8nHlyPRER3d6YHr7Y9GwwPB2tEZ9dgkc+O4w9FzJFxzI4LERGIDWvFKO/OILf/r4CpVyGt0d1wIePd4a1hUJ0NCIiMgJdfJ3x+4t90FPliqKKakz/9iTXFf0LC5EBkyQJuy9k1lkv9MP0XpgYrIJMJhMdj4iIjEhzByt8P70XJgb7AahZV/TMd6eQVVQuOJlhkEmSZFb1sLCwEE5OTigoKICjo+FuUY/LKsI7f1zEgdhsAEAXHyd88XR3XiIjIqJ79tPJVLz16zlUqjWwt1LixQcCMTlUBSul4V550PfPbxYiA1NQWoVP917Gt5FJqNZIsFDIMLWPP14Ja8NLZEREpDNn0wrw1paz+DutAACgamaLtx4OwqD27gZ5FYKFSMcMtRCpNRI2nEjBR7tikVdSCQAIa++BNx9uD38e0EpERHqg0UjYHJ2O/+6IQXZRBQCgb2s3LBgehNYGduoBC5GOGVohqqzW4EBsNj7adQkxGUUAgNbu9pg/PAj92jQXnI6IiMxBcUU1VuyPwzcHE1Gp1kAhl+HpXi0xOdTfYH4pZyHSMUMoRBqNhGOJefjt7yv489xV5JfW3CjL0VqJ8MFt8FRvP1gouN6diIiaVnJuCd7bdhG7btqW39nHCSO7eGFEFy94OFoLy8ZCpGOiCpEkSTiXXoitp9Pxx5mryCj8Z1W/m70VHu3mhVkDAuFqZ9lkmYiIiOpz6HIOvvwrHofjcnBjZ75MBvT2b4aRXb3wYEdPONs27c8rFiId09cXVKORkFtSiSv5ZbiSX4b0/DJcyS/HlfwyXC0oQ9q1MuReXxsEAA7WSjzY0RMju3gjuFUzKOSGt4CNiIjMW3ZRBbafvYrf/r6CU8nXah9XymXwcbGBl/NNb07WN/3ZGraWSp1mYSHSMX19QQ/EZmPS6uN3fI61hRyD2ntgVBcv9G/b3KC3NxIREd0sNa8Uf5y5iq2n02vXvN5Oa3d77A7vr9PPr+9CpNv6Zsa8na0hkwEeDtbwcq5pyd43NecWTtYIaG6n88ZMRETUFHxdbTFrQCvMGtAKV/LLkJpXiisFNVdD0q9fHbl6/b+9XYzvnnmcIdIRjUaCWpK4GJqIiMxeRbVa51dBOENkJORyGeTgOiAiIiJjXBLC6QwiIiIyeyxEREREZPZYiIiIiMjssRARERGR2WMhIiIiIrPHQkRERERmj4WIiIiIzB4LEREREZk9FiIiIiIyeyxEREREZPZYiIiIiMjssRARERGR2WMhIiIiIrNndqfdS5IEACgsLBSchIiIiBrqxs/tGz/Hdc3sClFRUREAwNfXV3ASIiIi0lZRURGcnJx0/nFlkr6qloHSaDS4cuUKHBwcIJPJGvy6wsJC+Pr6IjU1FY6OjnpMKJ45jRUwr/Ga01gB8xqvOY0V4HhN2e3GKkkSioqK4OXlBblc9yt+zG6GSC6Xw8fHp9Gvd3R0NPm/jDeY01gB8xqvOY0VMK/xmtNYAY7XlNU3Vn3MDN3ARdVERERk9liIiIiIyOyxEDWQlZUVFi5cCCsrK9FR9M6cxgqY13jNaayAeY3XnMYKcLymTNRYzW5RNREREdG/cYaIiIiIzB4LEREREZk9FiIiIiIyeyxEREREZPbMthDl5eXhqaeegqOjI5ydnTFt2jQUFxff8TXl5eV4/vnn0axZM9jb2+Oxxx5DZmZmneekpKTg4Ycfhq2tLdzd3fH666+jurq63o93+PBhKJVKdO3aVVfDqpeosR46dAihoaFo1qwZbGxs0K5dO3z88cd6GePNRI138+bNGDx4MJo3bw5HR0cEBwdj586dehnjDaLGevXqVYwfPx5t2rSBXC7Hyy+/rI/hYcWKFVCpVLC2tkavXr1w/PjxOz5/06ZNaNeuHaytrdGpUyds3769zvslScKCBQvQokUL2NjYICwsDJcvX67znMZ8TXVFxHjfe+89hISEwNbWFs7Ozroe0m019ViTkpIwbdo0+Pv7w8bGBq1atcLChQtRWVmpl/H9m4j/b0eOHImWLVvC2toaLVq0wIQJE3DlyhWdj+3fRIz1hoqKCnTt2hUymQynT5/WLrhkpoYNGyZ16dJFOnr0qHTw4EEpMDBQGjdu3B1fM3PmTMnX11fau3evdPLkSal3795SSEhI7furq6uljh07SmFhYVJ0dLS0fft2yc3NTZo3b94tH+vatWtSQECANGTIEKlLly66Hl4dosYaFRUl/fjjj9K5c+ekxMRE6bvvvpNsbW2lL7/8Um9jlSRx433ppZek//73v9Lx48el2NhYad68eZKFhYUUFRVlcmNNTEyUZs+eLa1bt07q2rWr9NJLL+l8bBs2bJAsLS2l1atXS+fPn5dmzJghOTs7S5mZmfU+//Dhw5JCoZA++OAD6cKFC9Jbb70lWVhYSGfPnq19zpIlSyQnJydpy5Yt0t9//y2NHDlS8vf3l8rKymqf05ivqTGPd8GCBdKyZcuk8PBwycnJSd/DlCRJzFj//PNPafLkydLOnTul+Ph4aevWrZK7u7v06quvmuR4JUmSli1bJkVGRkpJSUnS4cOHpeDgYCk4ONgkx3rD7NmzpQcffFACIEVHR2uV3SwL0YULFyQA0okTJ2of+/PPPyWZTCalp6fX+5r8/HzJwsJC2rRpU+1jFy9elABIkZGRkiRJ0vbt2yW5XC5lZGTUPueLL76QHB0dpYqKijofb+zYsdJbb70lLVy4UK+FyBDGerNHH31Uevrpp+91WLdlaOMNCgqSFi1adK/DqpehjLV///56KUQ9e/aUnn/++do/q9VqycvLS1q8eHG9z3/iiSekhx9+uM5jvXr1kp599llJkiRJo9FInp6e0ocfflj7/vz8fMnKykpav369JEmN+5rqiojx3mzNmjVNVohEj/WGDz74QPL397+XoTSIoYx369atkkwmkyorK+9lOHckcqzbt2+X2rVrJ50/f75RhcgsL5lFRkbC2dkZPXr0qH0sLCwMcrkcx44dq/c1p06dQlVVFcLCwmofa9euHVq2bInIyMjaj9upUyd4eHjUPmfo0KEoLCzE+fPnax9bs2YNEhISsHDhQl0P7Raix3qz6OhoHDlyBP3799fF0OplSOPVaDQoKiqCq6urLoZ2C0Maq65VVlbi1KlTdXLK5XKEhYXV5vy3yMjIOs8HanLfeH5iYiIyMjLqPMfJyQm9evWqM3Ztv6a6IGq8IhjSWAsKCvT27/MGQxlvXl4efvjhB4SEhMDCwuJeh1UvkWPNzMzEjBkz8N1338HW1rZR+c2yEGVkZMDd3b3OY0qlEq6ursjIyLjtaywtLW+5xu7h4VH7moyMjDo/RG68/8b7AODy5cuYO3cuvv/+eyiV+j9bV+RYb/Dx8YGVlRV69OiB559/HtOnT7+XId2RIYz3hqVLl6K4uBhPPPFEY4ZyV4Y0Vl3LycmBWq2uN8edxnan59/437s9R9uvqS6IGq8IhjLWuLg4LF++HM8++2yjxtFQosc7Z84c2NnZoVmzZkhJScHWrVvvaTx3ImqskiRh8uTJmDlzZp1fZrRlUoVo7ty5kMlkd3yLiYkRlk+tVmP8+PFYtGgR2rRpc08fy9DHerODBw/i5MmTWLlyJT755BOsX79e649hTOMFgB9//BGLFi3CTz/9dMsP2LsxtrESGZv09HQMGzYMY8aMwYwZM0TH0avXX38d0dHR2LVrFxQKBSZOnAjJxA6oWL58OYqKijBv3rx7+jj6n6JoQq+++iomT558x+cEBATA09MTWVlZdR6vrq5GXl4ePD09632dp6cnKisrkZ+fX+e368zMzNrXeHp63rKa/sbuHU9PTxQVFeHkyZOIjo7GCy+8AKDmsookSVAqldi1axceeOABkxjrzfz9/QEAnTp1QmZmJv7zn/9g3Lhxdx3jzYxpvBs2bMD06dOxadOmW6aCG8KYxqovbm5uUCgUt+x+uznnv3l6et7x+Tf+NzMzEy1atKjznBs7PRvzNdUFUeMVQfRYr1y5goEDByIkJARfffXVvQ7nrkSP183NDW5ubmjTpg3at28PX19fHD16FMHBwfc6tFuIGuu+ffsQGRl5y9lnPXr0wFNPPYV169Y1bABarTgyETcWTp48ebL2sZ07dzZoMerPP/9c+1hMTEy9i1FvXk3/5ZdfSo6OjlJ5ebmkVquls2fP1nmbNWuW1LZtW+ns2bNScXGxyYz1dhYtWiT5+fnd46huT/R4f/zxR8na2lrasmWLrod2C9FjvUGfi6pfeOGF2j+r1WrJ29v7joszhw8fXuex4ODgWxZnLl26tPb9BQUF9S6q1uZrqisixnuzpl5ULWKsaWlpUuvWraUnn3xSqq6u1uWQ7kj0/7c3JCcnSwCk/fv338No7kzEWJOTk+v8XN25c6cEQPr555+l1NTUBmc3y0IkSTVba7t16yYdO3ZMOnTokNS6des6W2vT0tKktm3bSseOHat9bObMmVLLli2lffv2SSdPnrxlC+ON7cpDhgyRTp8+Le3YsUNq3rx5vdvub9D3LjNJEjfWzz77TPrtt9+k2NhYKTY2Vvr6668lBwcH6c033zTJ8f7www+SUqmUVqxYIV29erX2LT8/3+TGKkmSFB0dLUVHR0vdu3eXxo8fL0VHR0vnz5/X2dg2bNggWVlZSWvXrpUuXLggPfPMM5Kzs3Pt7rcJEyZIc+fOrX3+4cOHJaVSKS1dulS6ePGitHDhwnq37zo7O0tbt26Vzpw5I40aNarebfd3+prqi6jxJicnS9HR0dKiRYske3v72v9fi4qKTGqsaWlpUmBgoDRo0CApLS2tzr9RfRMx3qNHj0rLly+XoqOjpaSkJGnv3r1SSEiI1KpVqzv+0mqMY/23xMREbrvXRm5urjRu3DjJ3t5ecnR0lKZMmVLnG8CNL+jNTbqsrEx67rnnJBcXF8nW1lZ69NFHb/nHlJSUJD344IOSjY2N5ObmJr366qtSVVXVbXM0RSESNdb//e9/UocOHSRbW1vJ0dFR6tatm/T5559LarXaJMfbv39/CcAtb5MmTTK5sUqSVO9YdT37t3z5cqlly5aSpaWl1LNnT+no0aO17+vfv/8tX9uffvpJatOmjWRpaSl16NBB2rZtW533azQaaf78+ZKHh4dkZWUlDRo0SLp06VKd59zta6pPIsY7adKkev+/1OcsgiQ1/VjXrFlT7zib6kJJU4/3zJkz0sCBAyVXV1fJyspKUqlU0syZM6W0tDS9jlOSxPw9vlljC5FMkkxsdRURERGRlkxqlxkRERFRY7AQERERkdljISIiIiKzx0JEREREZo+FiIiIiMweCxERERGZPRYiIiIiMnssRERERGT2WIiIyCgNGDAAL7/8stavk8lkkMlkdQ63vZOIiIja1zzyyCNafz4iMg4sRETUZG4uF/W9DRw4sMEfa/PmzXjnnXdq/6xSqfDJJ5806LVr1qxBbGxsg54bEhKCq1ev4oknnmhwNiIyPkrRAYjIfNwoF//222+/YebMmXjuueca/LFcXV0bncPZ2Rnu7u4Neq6lpSU8PT1hY2ODioqKRn9OIjJsnCEioiZzo1zc/Hbt2jW89tpreOONNzBmzJja5547dw4PPvgg7O3t4eHhgQkTJiAnJ6f2/TdfMhswYACSk5Pxyiuv1M42aePvv//GwIED4eDgAEdHR3Tv3h0nT57UyZiJyDiwEBGRMPn5+Rg1ahQGDBhQ5/JXfn4+HnjgAXTr1g0nT57Ejh07kJmZedvLVps3b4aPjw/efvttXL16td5ZqDt56qmn4OPjgxMnTuDUqVOYO3cuLCws7mlsRGRceMmMiITQaDQYP348lEolfvjhhzqzOp999hm6deuG999/v/ax1atXw9fXF7GxsWjTpk2dj+Xq6gqFQgEHBwd4enpqnSUlJQWvv/462rVrBwBo3bp1I0dFRMaKM0REJMQbb7yByMhIbN26FQ4ODnXe9/fff2P//v2wt7evfbtRVuLj43WeJTw8HNOnT0dYWBiWLFmil89BRIaNhYiImtyGDRuwdOlSbNiwod7ZmOLiYowYMQKnT5+u83b58mX069dP53n+85//4Pz583j44Yexb98+BAUF4ddff9X55yEiw8VLZkTUpE6fPo1p06ZhyZIlGDp0aL3Pue+++/DLL79ApVJBqWzYtylLS0uo1epG52rTpg3atGmDV155BePGjcOaNWvw6KOPNvrjEZFx4QwRETWZnJwcPPLIIxgwYACefvppZGRk1HnLzs4GADz//PPIy8vDuHHjcOLECcTHx2Pnzp2YMmXKbUuPSqXCX3/9hfT09Dq70e6mrKwML7zwAiIiIpCcnIzDhw/jxIkTaN++vU7GTETGgTNERNRktm3bhuTkZCQnJ6NFixa3vN/Pzw9JSUnw8vLC4cOHMWfOHAwZMgQVFRXw8/PDsGHDIJfX/3vc22+/jWeffRatWrVCRUUFJElqUCaFQoHc3FxMnDgRmZmZcHNzw+jRo7Fo0aJ7GisRGReZ1NDvGkREJkAmk+HXX3/V+hiOyZMnIz8/H1u2bNFLLiISi5fMiMjsjBs3Dj4+Pg167sGDB2Fvb48ffvhBz6mISCTOEBGRWYmLiwNQc6nM39//rs8vKytDeno6AMDe3r5R9zkiIsPHQkRERERmj5fMiIiIyOyxEBEREZHZYyEiIiIis8dCRERERGaPhYiIiIjMHgsRERERmT0WIiIiIjJ7LERERERk9v4f16JIK2KlqJcAAAAASUVORK5CYII=",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"ax.plot(t, window)\n",
"ax.set_xlabel(\"Zeit [s]\")\n",
"ax.set_ylabel(\"Hamming Window\");"
]
},
{
"cell_type": "markdown",
"id": "730a4714",
"metadata": {},
"source": [
"Und hier das Produkt von beiden:"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "0143e3d8",
"metadata": {
"tags": [
"remove-input"
]
},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"filt = window * taps\n",
"filt /= np.sum(filt)\n",
"\n",
"ax.plot(t, filt);"
]
},
{
"cell_type": "markdown",
"id": "4fe418dc",
"metadata": {},
"source": [
"Jetzt verarbeiten wir die Samples nach folgendem Schema:\n",
"```{figure} img/FIRodd.png\n",
"---\n",
"name: fig:FIRodd\n",
"---\n",
"Struktur des sogenannten *FIR-Filters*.\n",
"Er berechnet die Faltung des Signals mit den Koeffizienten.\n",
"```\n",
"\n",
"Wir iterieren über die Samples, wobei wir immer die letzten $N$ Stück als $x$ betrachten.\n",
"Hier kann man z.B. mit einem [Ring buffer](https://de.wikipedia.org/wiki/Ringpuffer) arbeiten.\n",
"Dann berechnen wir\n",
"```{math}\n",
"y = \\sum_{n=0}^{N-1} x[n] \\cdot a[N-1-n]\n",
"```\n",
"und speichern $y$ als neues Sample.\n",
"\n",
"Visualisieren wir die so erzeugten neuen Samples, erhalten wir folgendes:\n",
"```{figure} img/reference/filtered_detail.webp\n",
"---\n",
"name: fig:filtered_detail\n",
"---\n",
"Gefiltertes Signal.\n",
"Die vertikalen Streifen sind entfernt.\n",
"```\n",
"\n",
"Und auch im Spektrum können wir erkennen, dass nur noch die gewünschten Anteile vorhanden sind:\n",
"```{figure} img/reference/filtered_waterfall.webp\n",
"---\n",
"name: fig:filtered_waterfall\n",
"---\n",
"Gefiltertes Signal im Wasserfall-Diagramm.\n",
"```"
]
}
],
"metadata": {
"celltoolbar": "Tags",
"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": "3.11.8"
}
},
"nbformat": 4,
"nbformat_minor": 5
}