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Labor_Rechneruebung_zur_Signaluebertragung_II
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Labor_Rechneruebung_zur_Sig.../Versuch 1 - Fehlerwahrschei.../Versuch1.ipynb

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T1fTUDSBr9VXm3lRRa+atXTnFsX8ZL6qdNG0V2D70sgpsdUY0V53JhWBbBBCg\nRjVcfydg3ggggAACCCCAAAIIIBBaARLV0HrP3tFIVD2zj4S/n6quprXvfFH/4be7n3pTqejEM/JR\n0Q2fbHPzj7k6M/LVt9TL4/N/OiH+iKVl9z6bvvTCmINODHG2orRUhbHtyVl7fohRZ9Xk41bH/mVh\n8Q0PjpfNulyqZvU+pahoJaruYWOu1t+TE49ZEeKZczgEEIg8AWpUZ+/HNXtCAAEEEEAAAQQQQACB\nCBQgUQ3Xi0qiOinCmHeistSBmgbr5dQCUA2f/hB3xFJjpPqT9hRX7LzjyQO5kFNP7scftTzuyKX9\n1fVq3mqekdbLijvsZK+pTf7G21Vya554787daSevi7x8hzNCAIFQCpCohusvB8wbAQQQQAABBBBA\nAAEEQiJAohoS5iAchER14unUg+ZXPrdVFZrd+Ttbfk0cqGuyerfFp8cdvsQYrL6loYwkAj9WVHTm\nqsu1YtXY8IhxLjvvfNLr3jJXXj7c2W2MGR0YUGXuUEv7UGt77obNYXOys9qaNnBzpoEAAhYBEtUg\n/NxmlwgggAACCCCAAAIIIBA5AiSq4XotSVTN7Kz0tsddIyMKVY02o3GHLS6//7mR7p7xS+ty7Xrs\ntXAM2pRopJ50QcMn34/29ismLrpmYh0t43RSos9RKatxmhLYeedTaheQetL5PSUVYwODA3WN+Zfc\nFo4nzpwRQGC/C5CohusvB8wbAQQQQAABBBBAAAEEQiJAohoS5iAchETVSBwS/7VysHHPSGd33KGT\nHorPXXuTWbw5UNsQf8R4mep+zyn8nkBUdNqitY2f/1j14nvWbdXNoCu7yLyz6j/4Vh0DjAHpp1w0\n2ts3WN+sZqx+H44yPQQQQEAV/fNODMIPLnaJAAIIIIAAAggggAACCESIAIlquF5IElUjKyy9/XFd\nwsGGPZ7RYcnmR4yrq2fnFTKGe7YY8+cFO6JOyLvoloSjT1M1bvP3v0/cuy5XX0V1+rIL4/9vmcpa\nlb0qUc066+pwP2XmjwAC+0uARDVcfzlg3ggggAACCCCAAAIIIBASARLVkDAH4SAkqkbQUP/BN9LV\nIlSp88+zRQ+KINuTsgz7rDOv3F/BxCweN/bQRX1lleoAYI1Tu3KKci+4caC+ebijs7e8srtgZ/bq\nqwuuuGsWj8uuEEBgrgmQqAbh5za7RAABBBBAAAEEEEAAgcgRIFEN12tJojqeqH70nXEJGz7ZpgjA\nlnqU3OwuUx0bGkpfemGwAxE9dK+Foapeej/pP2cE71hJx55pxsQ6NfVRTTnxXB0ubfG64Y7uka6e\nzJWXBe/o7BkBBOaIAIlquP5ywLwRQAABBBBAAAEEEEAgJAIkqiFhDsJBSFSNXGPX468ZulqayV2Y\nGeX+pPnKOe/6vWOuvvKquL9O6rIajEwk9q+LjJlkn3OdvVr2oBNLNj/c+PlPhdfcm7t+k8JfTTv2\nkIWBTUM9Yes/+s41NuYaHc254EZjJ4VX36MFrAqvvtfLPqOiC6+6O3/j7YEdjq0QQGAOCpCoBuHn\nNrtEAAEEEEAAAQQQQACByBEgUQ3Xa0miamQcGcsu0rr2xlUc6e4tvOoea/ZR+ew7+nzpbY+HIBDx\nkajmX3yr0s99ua/LNeYyZlt+//MBz0r1sO4oecy156e4+COXaT/xRy7Nu/DmHVHRnvuMmRdd9+5X\nw20daUvWB3xENkQAgTklQKIarr8cMG8EEEAAAQQQQAABBBAIiQCJakiYg3AQElUz3ah9+3MTWMFl\n83e/ZZ99TdqiteUPvjg2NKzKUK3jFIIoxEeiuvOOJz1vAXWAneGsiq5/YKSruyurIPm41TnnXFfz\n5qdxh3ovxU067kzlzj2FZQlHLZ/hQdkcAQTmggCJahB+brNLBBBAAAEEEEAAAQQQiBwBEtVwvZYk\nqmaoofLM5m0xKv+05qqj/QPqA9DwyfcKOkMTf/hIVDNOu3Ssf7yQ1pxk4ZV3z3xi2WdfO1DbqNdo\nT19rTIrXk01fskHLVRnH1ZJWWrBr5sdlDwggENkCJKrh+ssB80YAAQQQQAABBBBAAIGQCJCohoQ5\nCAeZc4lqVHTp7U+kLrzAa4qhnqRl9zzTX1U3NjjkGhlVPWZXTpEiy5iD7GtVBS8E8ZGo7pgXXbv1\nS+td0J6QMVvJZuqC87sLSntLdyX+a5X97KKi8y+9bWhP20TWPOba/fRb6gMQPIc5u+fiG7dUPrfV\nfKlKes5S2E5cub9Vxt3v2NLsmH8/MAVIVIPwc5tdIoAAAggggAACCCCAQOQIkKiG67Wca4lq3obN\nY4PDJZse8pE+xBw0PyX6HC12n/TvVV47igY1ufCVqKrP6RFLu7KLjLttoK4p+b9nzeJk4v92Ssrx\nZ9t2qEBE4an6Hpi3eEdqTtXz7ypxzlu/aRaPzq4Mgba4NOt3k4LL7kDGENj91JtWmaavf0bmwBcg\nUQ3XXw6YNwIIIIAAAggggAACCIREgEQ1JMxBOMicSlSVPw42tnQXlsUdvsQziUg+fk3VS++Hplmq\njxzEd6KqDVPmnzvU0j7aP5hz/g1BylMS/nFa4r9WaueJR5/WvG2H2QnBNTZW9+6XcYctVkpSdN0D\n6pMQpAnM5d0eOImq+upWv/xB41c/77zzqala64bySpGohlJ7to5FohqEn9vsEgEEEEAAAQQQQAAB\nBCJHgEQ1XK/l3ElUlQMaWZViQaWERmJofeWcf70qMRs+/j72kBC1TPWaWUybqGqromvv3/Xoq1PW\nz0ZFF113v86x4uFXlLo2ffNLzRufJB5zusOIRCW62rYrtzj7rKvNxqlyG+3tL7v7aX3V4X7217C0\nk9ft2bZjzw8xgb1q3vxsf838gKpRTT72zP7dNePf11x7G7/cvt8vPYnq/r0zAzs6iWq4/nLAvBFA\nAAEEEEAAAQQQQCAkAiSqIWEOwkHmSqIaFV396kdWv75dNVroyZoR6P/86979SmNUlxdYdjArWzlJ\nVJWl+mjtmr70QtfoqPtkXa7xf9m7t+6Dr51PL23x+uG2Tj3Xb4oNNrUEryTW+cScjMw559q9YxPL\ni/n7puktq3RylOCNOUBqVCuffWcS3dhY6knnB++sneyZRNWJ0oE2hkTV329BjEcAAQQQQAABBBBA\nAIE5JUCiGq6Xe44kqkXXP6BlphSYDjY0m5dqtH9g5x1PmpV3Wmep5s1Px/oHss68cj+mEo4SVZ8L\n8uRdeLPn7dgWm+bXSbkbzv7RO7UzPS/5f7PZsNWvmfg7mETVXzGv4xs/+9F2F2WtvnpW9hzwTkhU\nA6bbjxuSqIbrLwfMGwEEEEAAAQQQQAABBEIiQKIaEuYgHGSOJKp6Erzs3mf1//ZJx57ZFp8+0Rh0\ndEzr28QftVyJg4JINSctu/uZWV+NSv1GCzbe4bDEb+aJauIxK0a6emw3S/n9z/ubqpRveck1OtYW\nmxp76P5sg+DvtElU/RXzOl69U6230Gh3X8LRK2ZlzwHvhEQ1YLr9uCGJahB+brNLBBBAAAEEEEAA\nAQQQiBwBEtVwvZZzJFG1BgpqqFr1wrtjwxOL1/cUlaskc6Cmofn732e9WWTMwSc1f/ubnqDPueBG\nJ7nGzBNVHUUNTxWGmjelmqIGsIqUFulSD9ahPa0pJ5ztZOYHyJi0hRc0fv5T4xf2V1tCxqSIsLfP\nc4w+o9XJ9u+JHCBP/Wv1traYVDUdFprquxWwzvpfGvx1JlH1V+xAGE+iGq6/HDBvBBBAAAEEEEAA\nAQQQCIkAiWpImINwkDmYqLpThqjo/EtuHW7vmhB1uXp37k74+6mznkEUXH6nmpk2ffOrw0BqVhLV\nmD9rdakY4+xGOrvTl10Y2HklHLW8O7+0O68k/qhTtIfU+edNdRZaxsq9WJbPdgT796u5F9xofQP1\nV9Xt3/lMdfQDJFHV9PTHgNx1m0pvfyJj+cUHghWJ6oFwFfydA4lqEH5us0sEEEAAAQQQQAABBBCI\nHAES1XC9lnM0Ud0X/CUfv6YzPde4csPtnQHHjj4iBiWbPYU7tf+GT7YVXXu/k2RqVhJVTUlhaE9J\nhWvMVXjl3f6GINbxKSeeo1WquvN3dmUXqVtCyeZHvO6t8Kq7RwcG1V1hJscK6rYkqkHlDcHOSVRD\ngDzrhyBRDddfDpg3AggggAACCCCAAAIIhESARDUkzEE4yFxOVJUdxB+xpD0hQ482F1//wEyiBCWn\nXjdPX3bR2NCQed2at+2Y9iizlajqQJkrL69+9UOHtbE+JpZ30S1asEuLepXe9rim5zlSoUn22deM\n9vQ2fv7jzA83LVFgA0hUA3M7cLYiUT1wroXzmZCoBuHnNrtEAAEEEEAAAQQQQACByBEgUQ3XaxnZ\niWrMwQsyV2wsveNJLUtVePU9if883Zb3pcw/b6ilveGT73fMi3aYEaQtWqtkp+Gj71R2WvPGJ/Uf\nfdeRnL3nx1gFB557UH2o9c7Y9dj0z8XPYqKqk52dtrBR0Vq2K+k/q7xkqX9ekHXmlS3b48f6B3Wm\nY0PD8nEoGeJhgSWqcYcvzl13k654/Yff6orXvftlxUMvZa2+ymuy7OWMoqITj15RdN191a98qM31\nqn3rs/IHX8hec3XcoSd7FfD61L9u3ZLND9e+84V7Du9/XfHIK5krL1OjW697iD9iqZZBG38tOD/2\nkIUapvtT/XB33vW0NndP450v9KZQTfFUfwzQzid2ctL5Kcef7TUr11ssbfH60jueqHntY+MEa978\nVE1X0xavm2p61jmrklptMapf+mAc5+3PKx5+OXftTXFHLPE8Na+JqhjzL77V4NWbcffTb+Wu3+x1\nc/sO3ZfmtIIr7qp8/l19BzBmXnbPM26TgxeE+OaM4MORqIbrLwfMGwEEEEAAAQQQQAABBEIiQKIa\nEuYgHCSCE1UlIx2pOcbSOsbHaE9f9csfxB02kWTpMfyWn+Pj/2+Zw0Qj9uCTBuqaPK9Dw2c/eM2b\niq5/0Bw80t2T7GCJp9lMVGe7q6nSq4R/nGZYxRx0YsFld3akZLuFXS7zNBs+/s4hZoiH+Zuo6kKU\nP/jiYMMer2+73vLKwivu8l2Qq7a8yhlHunu97kE3kmp+PfdgS1TVTkH56UhXj+dOurIK00+5yJNR\nkaJ1cMHG27UuWd17X48NTpRLGwN07Vp+S0o5YY3nTpSMW3fSt6vaSGYnXsrZ12/qzi22vsUmNhlz\n9RSXlz/w4lS9iRV6Vj73jrpteMUZam4tv//5mD9PSjbtieo3v+RdeIsm5rmHwfpm/QXFx9VJ+Mep\ntVu/8Kqq0+lIy808fWOI789IPRyJahB+brNLBBBAAAEEEEAAAQQQiBwBEtVwvZaRmqimL90w3GFZ\neMpyfVp/T7YufO+1ttSWbiT95wylWvUffKNaNncy29u3866n9Blzrz1F5VqayTMTyTrrKtfIqDGs\n6vl3nYQmB2yiKiiV4u75OV6hasnNj/SWVe4dcymkVnGfuhkY5zjaP3DA3lF+JaoqLG1PzLQmxZ7v\ncNfISMWWF6e6pkok+8qrfH9f0L0hSdsebIlq3+4aH9MY2tPmWRScumita3TiDwmNX27vLij1MZO+\nylozKDcnM22iqkJUCUz7ja/qBS+3vapluwvc/YV9fbhcKge24tgS1eHWDtfw8FR7kG3Rtfd5vTqK\nofur6n0ffLSvP+fc65y8YRnjW4BEddr3CAMQQAABBBBAAAEEEEBgLguQqIbr1T9g86+Z5BR66lkr\n1Cvd2/NTbPWrHzV//7t6gFpjqerXPvJr/1Uvvme9wHq2fefdT8f/3ynW8sPhjm7FuLbd6on4scFh\nVSNWv/axvcRvigLSAzZR1anlq6Hq8IjqB4Wpbgmy1bpV2auvFojbZ2xMj2z7BRvKwc4T1dhDF7Wn\nZHuJUIftAaLay3pdbSzxnyv7q+qcfFNQnanvRHXanTR/b2/Om3TcmdbqS+81pJP365l7+k5U005e\nP9LjvfbWNuHSWx6znaBKwntLdk17XhogQx+J6rR70ObxfzvFdvSU6HP6qz3iVJfLNTr+lw9zt9pc\nTQlCeYtG5LFIVKe9URmAAAIIIIAAAggggAACc1mARDVcr35EJqru6rnR0ZwLbtgRNf6QskIcFQMO\nNrUY10nPGrt7qjp+KF71p4oLrddYNYCekVnFo/Y2qXt+iFE1nGes4+PQB3KiqnBED0SPDQ6qWjDp\nXyt1Fnqm212suu+jbUfygdyA0nmiuuvx1ydd6+ERrbiVf9GtCk/1QL3+3Zq+eVmMa96JKgud9B3B\n5WqLT1cPgbL7nlOEav3SQE29o0TV5VJ831tSoZetMnS0t992g6k96NAft/qkExkb053fU1imJ+Vt\nMWtfhf2hft+JauWz71j3rEhdf7fQU/z6fP37X6v+VMm7McBe6RkVrU6yNhx151A5qvq6diRlWb80\n3N7lJFFVNwNV8nbnlaiw1LbnvA2bbZ0K1OXAOkb15urBmn3OtZmnXaqequ2agKWFhb6TOP8uwUiv\nAiSq4frLAfNGAAEEEEAAAQQQQACBkAiQqIaEOQgHibxEVWsxKVtpT8jw/N/7pH+v6szIdyu6XPao\nxSNdVbvVymfeTl14gfajujalNirK68ot7swsGKhp8Pogtpq0Wg+qrfRcfOXTb/kVtRzIiapOJG/d\nptH+QdXe6t/VSlV5onFXDtQ2qDTSrzMN8WCHiaqef7c199SCRZMWLouKrnv3K/O9ONzWGXfYYuu5\npC/ZYH3oXiMVMpotQTNOu8SaZjpJVMcGBrWYlbkWVtF191v3oH+3pZa6dft319q+W+ikiq57YHwd\nqnnRtifodT/r3WE9C9+JauMXP1n3ryDVdjXTFl5Q995XSlr1gP+kN8XxaxQBW7dt/u43cw2r1Pnn\nWVPR6RPVsbGmL7arRYNxiNQF59tao+otbD161pprrGn4vs4A91sH6DJ1ZU9E3moT7LtVbojv4XA8\nHIlqEH5us0sEEEAAAQQQQAABBBCIHAES1XC9lpGXqCb/b41SlbbYVK/pgzqiDja61xpSLOU7nlDl\nmoZlnHqJMSxzxUatZqPARZmUsq3CK+/2XOenLS5dIaO5Wy07rshGIZFfOUjQE9V50SLKXnNN3oU3\nm6/8S27b9cQbHam5XrvBToqcDl6gHgipC9wnVXzTQ0aXWAVneesnFwM6rv/1C2cmgx0mqiWbH7a+\nmdWs03NtpWy1x7XULJs3iTG96lc+8LEH1ZPqxqh64T3jVbFlUqtQbW7rozrS2aNmC9ZcTwXXA7WN\n1kMU3fCgVcYzUdXfAJTkWsfojWB7zj1r1eXOE9WGT7dZJ9CVU5T0n0mBrHtXUdGZZ1wxnuH+cT9o\nvSnrhgqLNRPzuPFHLFGBsImje9I6JVsKrPlXv/S+/oJiHbNne5x1/w2f/mD9av3H7j7I5kd7UqZt\n8SsNLt/yojlAVe2eHWZnchPOwW1JVMP1lwPmjQACCCCAAAIIIIAAAiERIFENCXMQDhJ5iWr6KRcr\n7VLcmbpwrdf8QiWH7hpVpVQ+U7+a1z+Rt1ouKrXRw78773hSSdZE9PO3U9ztRCd/6EnngsvuNMYo\nqenMLNQz2rGHLPIrRgl2oqpWp16XOHefisuVteoKh7NVUjzU2m4A1H/4rXIxFTnqpbBVT8frlbZ4\n/aTSzv2dsTpMVJu++XVSVphdmLfhZlU0W1/FN26xxpGT0vmo6M70POsemr762a86R1uiqo699isS\nFa02wdZD7Lxr0hh7oupymbeluSvV1Q42TbqBFbI7T1TVvsB28w82tigpVl229Y8KnvdSyy8J1g3d\nf4SIinZ4y9kS1baYFM881PhDiPmhq2nuXC0p1NzA+tXGz360XVn9Z+VzW80xY0P6NuKuUucVsACJ\nahB+brNLBBBAAAEEEEAAAQQQiBwBEtVwvZaRl6gq0RvtG9D16CkqS/7vas8gQBVwihSTjrU/oq7/\n80/428RCNMpPdz32mjIXrWVfds8zycevyVx52c57nlEiqSo2hUdeH/xXP0ejaE4FrTqK+qj6m0QE\nO1FV14Kpbtbe0l22ir+pJq/HtNX70tzPaE+v7Tl3fUntPjNOudjf0w/eeCeJqtLA6deg9+Arf+D5\niajdo4BU7VP9Oilbolpw2R2em6sE23miqj8w2NJS7VC3ma0zgF+Jqt4+WprM80bScnCtvyfrzxW2\n0tTxPzPMO7Hvj667xra2Rhm+oWyJatPXP3uO3/XEpB641kQ17vDFRkm1Xx9Zq6/y6/Ix2CZAourX\n/cZgBBBAAAEEEEAAAQQQmGsCJKrhesUjL1GN++sic62koZa20lsfizv0ZPN/8pUE9dc0NG+zL4+u\nAVrPp6+iSuFp/JFLPWMRrWQ13NYx7WVWsJh5+kZtrmpNDW76aru/CUuwE9WO5PHFf3Q6vaW7rbmw\nCnv1NHfq/HOnnXPehbdoqSXztefHWK3FZLxadySrss+A0ueVp0y7t9AMcJKoqrqzz6MD6bQXveqF\nd81TSDxmha142dapc9qTdZSoxqTMMFGNOfgkW6GrX4mqzkJ1r2P97j9deP1QOp938aRmBdok7ogl\nA3VN1vH6o8W0IOaAGSaq6ug67aX0HJC7fpPzGTLSU4BENYC7jk0QQAABBBBAAAEEEEBg7giQqIbr\ntY68RFX/S7/z7mfMoFAFelo0qf7j77SYuAri1IBSpaPpSy/0/D//zBWXGiVsde984SUZiYou2fxI\n4VX3qGFo5fNbbT0otZVW/lHPTf1L8Y3uppZJ/1qpdLUzLdfzwWTfscusJ6qqFsy54Iaq57dqNSG9\n+ivrNEmlfnpAW1lz09e/2O5dLbVUdP0Dfj2obpyRqnrVG2GwodnEV0SbuXJSd879GDkFlqgKSuGg\n75cWqQ+/RFVLMGVNLMGke8DfRFV3SM4517lrTl0ur9/+1F236uUPrJF6CBJV/UXEOhlrjapnoqr2\nstNe3KzV7kXYeAUsQKIarr8cMG8EEEAAAQQQQAABBBAIiQCJakiYg3CQiExUYw9ZqMftvWopMy29\n7XGv6YAWN1cGpK0G65sSjpp4/N82WA+823pBGgfKXb859aTz9/wUm322ux+lwsrenbv15Hvuupv8\nCiNmPVEtvOY+z4edlQgr/VTYocWpPKFcwyMlNz+yI2qaIElTNep5dbJapaqvvNK6q+GOLtUIq0z1\nAOmm6iRR1RnZWm369Vi6KHTnDNY3Wx0qHn7FrxsgkBrVO5+yHsLWR9XrU//7FrUvss7T70TViNGP\nXFp6+xM9xeW6Z7y841wu9430RyKpTqa2VgPVr37kHMdJjapq0qdKVI2ycetHwUYvHRWcz4eRTgRI\nVIPwc5tdIoAAAggggAACCCCAQOQIkKiG67WMyERV/58f+5eFWqNGK4lPyvhaO4quuc9WfakQLevM\nK+OPWh578IK2hAyNV9qYuuB8r2GBBjd/84vXorzdT7xu20TrF2lvQ3va8vx5cDiARDVj+SVxR3jp\nVGDMJ0sL0w+7k2LbhyKwPT/G9JRUeL13R/v63UtL+azOU4fZ9sTMwivvVqGfdScqTa3/6Lvk/51V\neMVd6mmbseJSJ8lLsMc4SVQ1h46UbOu5qJDTa0vQqWarwd2FZdY9tGyP96vgN4BEVZfA30R1hn1U\nbaev/rOq5dQCZSPdvbbbSQl13OFLzPHtyZN4OzPynfeFcJKoVjz6ylSJqk7ZNr26974O9l3H/klU\nw/WXA+aNAAIIIIAAAggggAACIREgUQ0JcxAOEqmJqjvIiHI3My25+dGaNz5RKVzxdQ/osXRbwFH7\n5mdaS0dFfCqoVFuAzBUbVVWqV9ridZ5RSMqJ53ZmTbmsk9akij9iIjnaN4FoVTgqn1V2qXjXR+hp\nPZbfiWpUtNYpUk1u/JH2szN2m77sIkWcAdw7ahHgOw/KOff6MWW1loe+dabqUZt28jojQ9Q6Vxmn\nXhJGNaqasy7ZJCuXK/+S26ZySDruzKqX3lfppXVA/cffW/cw2tufEn2294D+kIXZZ11t+1IAiWrB\nFXft30TVPLrayDZ/v2MS4JgrxdKZV1zWr6ozRsZy78uXqYpWXQWs5+UkUfWxMtWOeSe2J403ETbm\noHe96sqnurhqiGxdc4xsNDABEtUAvveyCQIIIIAAAggggAACCMwdARLVcL3WkZyoOuh+qACop2i8\nolC5andBqf6pa6kSS9uq94Lqr673dZldLmNNKutLtXvFN23Rw+/aUAsBKdycNpXwN1FV6aW7WYFr\nrzqixuzLMdX0oPLZt931d/Pc/6kKwf6qiZkr4TWaG0z7MdiwJ+Hvp/qYsOox22LTjP1ot4qrlA/a\n3KY935ANcFijmrXqcuMeMD/UGTZr1RW2HghqCaoHzPWA/0BdoxZDs56Fu5HC5Nai7fHpCf84zXam\nqoNu+TWxMz0vkEQ1NtU6w9AnqmrCW/v258n/Xe15+fR3C9utpRpqc5jeRzZevek896MC56Zvf+0r\nr5phoqpJWvdQdv9ztrl15ZYoFredReK/VlY+t1Vl2rpAIbs/I/VAJKrTfqdlAAIIIIAAAggggAAC\nCMxlARLVcL36kZOoRkXH/+0UFaXaCganzSlS55+n2re6975q/PxHs5ZT+WD5lhfNh7UzTrl4qNmd\nivr+cC/o5C3GVY1ee7K7OG6goTl9ukfp/U1UtSzSeKY5MpL4z9M1AffCXHv3uitM9wWseqlFZmdm\nfltcuhoRZJx2afqSDXkX3VL7zhfDbR3ez0iB4L5X5hlX+AbUnlVm2F9VV7DxdnWYnVZ7Pw5wmKiq\n+UNHSo6NZaSzu+aNT7PPuU5rmqmHQ9VLH/TtqjZiU+VuSlcnlYjua6Fr24PCwfIHX8hceZkKePMu\nurnu/a9HOrrct0RVXQCJaldu8awnqrYmD2orbD2EzldJvTnVnPOu11e1GlvdB9/odPS+iztssV7J\nx6/RGmjWDUd7+hRQmhvqJulIy7XhDFTXVzzyStbqq4STu36TisqNO3O4ozv24ImbKoAa1Zo3P7Xy\nKtc2/rxh/dBqdRVbXtKlUT11weV3Nnz8/WBTqzGgO6d4P96xkXFoEtXpfm7wdQQQQAABBBBAAAEE\nEJjTAiSq4Xr5IyNRVV1k5bPvGF1TFWYVXnWPlzBiX8Gm15cqSfVkd/P3v7ufYbd86All5Zsql1Pm\n4uMCDzbuMTacKlHVQfUIc9NXP2uMGo/6Dkp8J6qJR6/Iv/R25aHqZmA8sKwcylx4Kvvsa/WZ5u9+\n04HUzUDPLFsbHcQeskjxsZrGpi1ca8xBq58rzLKdmhJSRVdl9z+vppP5F93ie7Y6L5WpKoJUEHmA\nB0AOE1WdhZo/2Drw+n57J/3nDNu55224WaG8k28Kuky2rghOnvrvLthp3XkgNaqHnqyV7q07sfUO\n9p2o2haA8nGmLT/He5Z7e1/GymMvo719Sf+cSGOdJKrVr31k3Y0tUdVl0sJ0Di+N9tO3q+YA/zvB\nAf6mc3/rm3eikzcCYxBAAAEEEEAAAQQQQACBuSlAohqu1z0yElWtJ64c0LwGisOyJhdXKhZp+uYX\nrXrvGUDoofjW35PdTyKPueo/+Ga4rXPiWrpcWrjJVg9ou9JdOcWqjd1511PaPHuNvSfmpPo4rQLf\nsEdP3Ccdaw/grMN8J6rJx612LyVvVEf29ivYilU09kfgm3/Jre4a1TufGp+kyzXS06e2Bnq0vKdk\nl+r+BuqaFBL1V9aaGVzZPc/YzkgzVDWlUjCVHDpZNUhP+mvPmthU4U7i0aflnH+9Yuv9m/44T1Q1\nTwXWyjodvqvTT/HoBBoVvevRV82k28d+VBadeIy7sth8+Zuoulyu3HWbJhXJHnZy/+5a86C6t1VK\nbMOPP2KpuogGnKja2qFOdYJ6N6XMP8/zupfe8YST1hNjQ0PpizeYmztJVFV57TtR1X2ocmNb54Gp\n5r+v8cXy/XvfhvvRSVQdfhthGAIIIIAAAggggAACCMxNARLVcL3uEZCoxvzlJFu1nS6Gwpe4Q1Ve\nuqbg8rtqt36hxejHhkcKLrvTM55QGmVcvD3b49zPsI+M6N97yyodXlGjUaNKNVXYGHvINI+9d2UX\nKWVLX3ahj5Rk2qf+Cy67w8yDlMcpKGz8crsxWz2LrT0rPt71+GsKUpW96sRbfkuqevE9baUiRPWN\nVZSWcNRyc/n13HU3eZ6p4mmt0+V0hfqo6OT/nuVjcOGVd4109Xg2Eg1xVORXoqq6UZUtT9s5d7Cp\npeLRV+MOPdnzXBRJK+gf2uOrWYS+uvupt6xP02s/fieqHoFpXECJqmqxrWfhu0a18Kq7Pd90k26k\nfX+NyFx5uferPO/Ewivv8V36rZjevZ7bYYtnkqhWPr/Vy6U5eIHKt3VP+niP6y2m+Rdde/9+/0tA\niN8ms344ElWHP0oYhgACCCCAAAIIIIAAAnNTgEQ1XK97BCSq6mupms2unKLyB16offNTVWXqYigL\n0+P/qnEzL0x3bonCSs+8QO1T22JSlTmqG2b9+9+MR5MX3NiZWeDkorb+nuQlTIyKVqCmh8FVv5m3\nYXPu2pvca+9ERXfnlSqxVVY1k0RVYZ9SPLXvNCpV9Wz+aN94NaV6pE6556jo3LU36pno2rc+06vi\noZdzzr9BcZXZhtV2stp/6sILZiFeiYrWPaadq9vmLOzNwWpjUx1FPTobPv3BfFW//MG081EKrHLd\n7rwSFVTuq2Ie0z8VNw+1tOthdtWxThsT6x5QuK9sTs+5m3tQ9av6JKjdrbXBqDkZHdE6z4xT7QWw\nWhCs6oV3J8Z88r3tgX1F6tUvve9jgDt2P2SRyjmtB7K9O9Qa1fpVvUH0ZwOrmHL5ks0Pt/ySoOhT\nJpPOLjlb1dPxRy7zLay2vwruewrL1DTD3Fx/JOjKLlRjU88Fo1SCbZ1S6W2Pee6/6Lr7rWP07ptq\nDiqerX71o/7dNe7y9omLO6pvHfoThXpreP12Me09wwCbAImqk58jjEEAAQQQQAABBBBAAIE5K0Ci\nGq6XPgIS1bp3v9LDxUnHji/YrV6itiaYSkza4tPVQnTasEPLi+tCDjW3qpYz4ejT+nbXTHtdFQBp\nDSstyJP471Xpp1ykp+kV1alZqhbtsW3bkZLtTj8HBq1ld55TmrZG1dhEcVXOudeV3Ttp7XLV9E11\njmqoqkPbpjTWP6DXVOdY++6X04oZA/RkdOE191rPS6lf5ukbdz/5hlbEMsp+tfaXw70dgMNUharU\nMn3Jev1TTR4CmKGKgo09qJ7XFk0GsLcDa5Oo6IS/n6rA2n12/wvk7HTPK9/U5mrs6+/KcjOn0FtD\n68W5J3/82b7fmzM/1hzcA4nqtD9EGIAAAggggAACCCCAAAJzWYBENVyvfrgnqnpiWh1Ch1o7dj3y\navryixXNKGrU0+4qedOC3R2puZXPvK2g02GGpXXGh5pa9E8j+EiJPkePdU9/aV0uVXSO9PQ6aQ3Z\nU7jTd6riJFFVbaMK9Oo//q49Kcs6PXXGnKqwVDWzalDQ+NkPqstTcWJnRv60s+0rq3RYpqdl4lUn\nq/Wy1BI0/+JbtZC9FryyLfOlxe7V8nUOJkqcMgJzWYBEdfqfIIxAAAEEEEAAAQQQQACBOSxAohqu\nFz/cE1U9m2yuG64IT0/6N339S9+uaj1on3j0Cj1on750Q+aqyx22BNWD/1lnXWWNPzqSJ0WWM7/M\nDZ98P8NEVaWpg417jJkoOB7a02qdVVtcupM6OwWseo7b9+mMdHWblb/GnBWJ6nFsz0pYhSY9xRWD\nDc1TtQ1VJa8CXLWancvREueOwBwUIFGd+U8N9oAAAggggAACCCCAAAIRLECiGq4XN9wTVS025ZVe\n0V7z978X37SlPTlLz+Cr92hgWUb1ax/P7qVVqeZMElW1yOxIzTHjVIWbJbc8NmmGLlf9h996nq82\nzDnnWj2Gr8rWhk+37XridWWgvk9ttLfPveTUH61L1QrW6C2rBdA9Q1stAeS5t9He/pbfErWwe/rS\nCwfqm3Y/83ZgV4GtEEAgTAVIVGf3Jwh7QwABBBBAAAEEEEAAgQgTIFEN1wsa7olqzZufKuBri00b\n7uye6hrsvPvpgMOIrFVXGG1AZ+tDpZpJx57hYz6+n/ovuPxOreSjItzu/J1aSj5tyQb3ElX6cLkm\nnrJ3uRq/+Cn+iCXjR4mKLr39CSkZK1lN+9FdUFp0zX1ayd1ao6oumeqlYGxb/9F3nvNXIbBrdNQ9\nkbExTa/+g2/yLrzZHbxGjWfZugqltz0e8IVgQwQQCEcBEtVpv+UyAAEEEEAAAQQQQAABBOayAIlq\nuF79sE5UtfxRV06xljzS/7Rr3fCCy+5o+OyHgdpG14g72jM+RvsHtdxNwEmE1slp/T054Ks71j+o\ntFdTmtjD2FjuBTcEnKjG/mWhWscqqdQ/FVY2/xBj7Hmgpr72rc+s8+zKLFBlqA6kNdkH6iwTmO5k\nmrft0J5zzr2+5o1P3Ef50wlap6u3dJexXVtMavz/eVmaKf7IpeqdqtW31LXWSduBgK8IGyKAQBgJ\nkKhO9x2XryOAAAIIIIAAAggggMCcFiBRDdfLH9aJqp5kL9/yYvaaa6z5ghZVzzrzKjUJdT/VPubq\nziuZYfqQcuK5A7UNAVxglYWqnavSyZT5545Xku7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AAQQQQAABBBBAYA4KkKiG60WPpETV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\nPWcdk/zf1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}
},
"cell_type": "markdown",
"id": "05b9058b-97d5-4516-ba1e-79a0afb7c726",
"metadata": {},
"source": [
"| |\n",
"|------------------------------------------------------------------------------------|\n",
"| <img src=\"attachment:media/image1.png\" style=\"width:8.26778in;height:1.87209in\" /> |\n",
"\n",
"<img src=\"attachment:media/image2.emf\" style=\"width:2.42103in;height:0.56977in\" />** \n",
"Rechnerübung zur Signalübertragung II**\n",
"\n",
"***Versuch 1: Fehlerwahrscheinlichkeit***\n",
"\n",
"Es wird ein Empfänger betrachtet, der zunächst nur entscheiden soll, ob\n",
"der Sender ein bestimmtes Signal gesendet hat oder nicht. Diese\n",
"Entscheidung soll durch einen Schwellwertdetektor getroffen werden, der\n",
"den empfangenen Wert mit einer geeignet gewählten Schwelle vergleicht.\n",
"Da die Übertragung durch Rauschen gestört wird, treten am Empfänger mit\n",
"einer bestimmten Wahrscheinlichkeit Fehlentscheidungen auf.\n",
"\n",
"**Teil 1.1 Verteilungsdichtefunktion von weißem, gaußverteiltem\n",
"Rauschen**\n",
"\n",
"Die Gleichung für die Verteilungsdichtefunktion der Gaußverteilung\n",
"lautet:\n",
"\n",
"$$p{}_{}$$\n",
"\n",
"Dabei bedeutet die Standardabweichung bzw. Leistung, der Mittelwert des\n",
"Rauschens.\n",
"\n",
"> Öffnen Sie die Datei „Versuch1.m“ und führen Sie das Programm aus.\n",
"> Betrachten Sie \n",
"> „Figure 1“. Man kann erkennen, dass mit wachsender Rauschleistung die\n",
"> Verteilungsdichtefunktion breiter (und niedriger) wird.\n",
"\n",
"**Teil 1.2 Sendestatistik bei unipolarer Übertragung**\n",
"\n",
"$U_{0} = 0$wird mit der Wahrscheinlichkeit $p_{0}$ und\n",
"$U_{1} = + 2\\ $mit der Wahrscheinlichkeit $p_{1}$ gesendet.Bei optimal\n",
"kodierter Quelle gilt:\n",
"\n",
"$$p_{0} = 0.5$$\n",
"\n",
"$p_{1} = 1 - p_{0}$ $p_{1} = 0.5$\n",
"\n",
"Betrachten Sie nun „Figure 2“.\n",
"\n",
"Hier entspricht die Fehlerwahrscheinlichkeit der Größe der Schnittfläche\n",
"der beiden \n",
"Kurven, unter der Voraussetzung, dass die\n",
"Entscheiderschwelle$x = U_{E} = + 1$ ist.\n",
"\n",
"Betrachten Sie nun „Figure 3“.\n",
"\n",
"Es ist zu erkennen, dass mit zunehmender Rauschleistung die\n",
"Fehlerwahrscheinlichkeit \n",
"zunimmt. Diese kann wieder verringert werden, indem die Sendeleistung\n",
"erhöht \n",
"wird $(x = U = + 4)$.\n",
"\n",
"Die Verteilungsdichtefunktionen mit erhöhter Sendeleistung sind in\n",
"„Figure 4“ \n",
"dargestellt.\n",
"\n",
"** \n",
"**\n",
"\n",
"**Teil 1.3 Symbolfehlerwahrscheinlichkeit bei mehrstufiger Übertragung**\n",
"\n",
"Aus den oben eingeführten Verteilungsdichtefunktionen lassen sich durch\n",
"Summierung der Fehlerbereiche die Symbolfehlerwahrscheinlichkeiten für\n",
"bestimmte Signal-zu-Rausch-Verhältnisse bestimmen. Für die\n",
"Symbolfehlerwahrscheinlichkeiten von m-stufigen Systemen ergeben sich\n",
"dann für gegebene Signal-zu-Rausch-Verhältnisse SNR\n",
"\n",
"Darin stecken folgende Annahmen:\n",
"\n",
"- Alle möglichen Amplitudenstufen sind gleichwahrscheinlich\n",
"\n",
"- Die Entscheiderschwellen sind optimal, d. h. bei\n",
" gleichwahrscheinlichen Amplitudenstufen liegen diese exakt zwischen\n",
" zwei Amplitudenstufen\n",
"\n",
"- m ist gerade\n",
"\n",
"„Figure 5“ zeigt die Symbolfehlerwahrscheinlichkeit für m=2; 4; 6; 8; 16\n",
"\n",
"**Aufgabenstellung:**\n",
"\n",
"Gegeben sei ein AWGN-Kanal und eine Quelle mit folgender Statistik:\n",
"\n",
"$U = - 1$ wird mit der Wahrscheinlichkeit $p_{0} = 0.6$und $U = + 1$\n",
"wird mit der Wahrscheinlichkeit $p_{1} = 0.4$ ausgegeben. Über ein\n",
"zweistufiges System (m=2) sollen die Daten übertragen werden."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "54f0e2d2-b7d7-474d-8242-d6474e5c13f1",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"xvals = -4:0.01:4;\n",
"\n",
"p0 = 0.6;\n",
"U0 = -1;\n",
"\n",
"p1 = 1 - p0;\n",
"U1 = 1;"
]
},
{
"cell_type": "markdown",
"id": "ebaab31d-c835-40f4-ac61-8b833b644ec1",
"metadata": {},
"source": [
"1. Stellen Sie die Verteilungsdichtefunktionen am Kanalausgang grafisch\n",
" dar."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "da057a07-be69-4275-9072-dd621e0420e1",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"figure(1)\n",
"hold on;\n",
"grid on;\n",
"func0 = @(x) (p0) * gauss_pdf(x, 1, U0);\n",
"func1 = @(x) (p1) * gauss_pdf(x, 1, U1);\n",
"plot(xvals, arrayfun(func0,xvals));\n",
"plot(xvals, arrayfun(func1,xvals));"
]
},
{
"cell_type": "markdown",
"id": "cd2d50ef-eda7-4f59-9a25-ce0f38badd35",
"metadata": {},
"source": [
"2. Berechnen Sie die Fehlerwahrscheinlichkeit für eine beliebige\n",
" Entscheiderschwelle$U_{E}$.Skizzieren Sie diese mit $U_{E}$als\n",
" Variable.\n",
"\n",
"> Hinweis: Für Integralrechnung in Matlab können Sie „function handles“\n",
"> und die Funktion „integral“ benutzen. Beispiel: Der function handle\n",
"> von $f\\left( x \\right) = x^{2}$ ist f = @(x)x.^2. \n",
"> Das Integral $\\int_{0}^{1}{f\\left( x \\right)\\text{dx}}$ kann\n",
"> überintegral(f,0,1) bestimmt werden."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "0f175b17-8365-4a6a-b10e-d70c59b4a362",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"figure(2);\n",
"hold on;\n",
"grid on;\n",
"errfunc = @(Ue) fehlerwahrscheinlichkeit(Ue,func0,func1);\n",
"errvals = arrayfun(errfunc, xvals);\n",
"ylim([0 1]);\n",
"plot(xvals, errvals);"
]
},
{
"cell_type": "markdown",
"id": "76a7bacc-3477-4410-880b-4aeb3d3b8e55",
"metadata": {},
"source": [
"3. Für welche Schwelle $U_{E0}$ ist die Fehlerwahrscheinlichkeit am\n",
" geringsten?"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "ab4bf3ce-8797-4576-a0fa-6f09bc879320",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/html": [
"<html><body><pre>Uemin = 0.2027</pre></body></html>"
],
"text/plain": [
"Uemin = 0.2027"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Uemin = fminbnd(errfunc,-4,4)"
]
},
{
"cell_type": "markdown",
"id": "2bf7a7ac-bd8a-44ea-8f2a-6a6bcdf6e93e",
"metadata": {},
"source": [
"4. Wie groß ist die Fehlerwahrscheinlichkeit für $U_{E0}$?"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "07b41fa2-77dd-450f-b87a-0b90aa938ea5",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/html": [
"<html><body><pre>ans = 0.1538</pre></body></html>"
],
"text/plain": [
"ans = 0.1538"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"errfunc(Uemin)"
]
},
{
"cell_type": "markdown",
"id": "e37a9f91-a69c-4932-ad2a-e68cce251470",
"metadata": {},
"source": [
"5. Wie sieht die Kurve aus, wenn $p_{1}$ nur noch $p_{1} = 0.2$beträgt?\n",
" Wo liegt nun das Minimum?"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "8655a9f3-b1a5-4fe1-904c-86460530973e",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/html": [
"<html><body><pre>Uemin = 0.6932</pre></body></html>"
],
"text/plain": [
"Uemin = 0.6932"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"p0 = 0.8; % ???\n",
"p1 = 0.2;\n",
"figure(3);\n",
"hold on;\n",
"grid on;\n",
"func0 = @(x) (p0) * gauss_pdf(x, 1, U0);\n",
"func1 = @(x) (p1) * gauss_pdf(x, 1, U1);\n",
"errfunc = @(Ue) fehlerwahrscheinlichkeit(Ue,func0,func1);\n",
"errvals = arrayfun(errfunc, xvals);\n",
"ylim([0 1]);\n",
"plot(xvals, errvals);\n",
"\n",
"Uemin = fminbnd(errfunc,-4,4)"
]
},
{
"attachments": {
"media/image7.png": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAABkAAAAVCAIAAAA8SdJPAAAAAXNSR0IArs4c6QAAATNJREFUOE9j\n/PDhAwOVABOVzAEZw4jHXauX2+KxKTTyMJosAbPCopZiNW7VsmgWvppAb3dkWRb8fmRiYty+fSOa\nGk9Pf6y6UMJLRZwfTRHQLCcnPTQEFCRsFqYKJiamQ4euoiGgIHlmMbq7G6AhXO5CCa87Lz9aKvAf\nf/ARbi1Q2/79l9Fc4e6uiNVdOMPe2dmZgYEtKY3Rw8MQPe4ZiQsvoKOATkN2FzMzIxrC5Uec6cvG\nxgZoYnFl7Z9PLdh9hJG+0M0yNjbGqrOmqQ1THC2topulqamJ1ay2ngloOjGVYfHj+q07geoKstKA\n5IRps+B6yDELollMTAxIzpy/uCs7DMhATii4sh3OMucXGEBMgUQuBOHJv/jKCYhn0bwGNw7TpfjM\nwl+EYMm8pGrAo56aZTQAFUd3+7fry/IAAAAASUVORK5CYII=\n"
}
},
"cell_type": "markdown",
"id": "2c8c06a3-3623-4a16-a102-a467bfdaa6f0",
"metadata": {},
"source": [
"6. Die Quelle liefere nun vier Amplitudenwerte, die alle\n",
" gleichwahrscheinlich sind. Bei wie viel dB muss der\n",
" Signal-Störabstand mindestens liegen, damit eine Fehlerrate von\n",
" $10^{- 4}$ nicht überschritten wird?\n",
"\n",
"> Hinweis: Benutzen Sie den data coursor\n",
"> <img src=\"attachment:media/image7.png\" style=\"width:0.25591in;height:0.21654in\" />\n",
"> oder die Funktion „ginput“, um die Achsen abzulesen."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "65719ba9-6ea6-420d-ba9c-a2bbc8a4e65e",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"SNR = 0:1:100;\n",
"figure(4)\n",
"\n",
"wk4 = symbol_fwk(SNR,4);\n",
"semilogy(10*log10(SNR),wk4,'LineWidth',2.5,'Color',[0 0 1]);\n",
"grid on\n",
"xlabel('10*log10(SNR)')\n",
"ylabel('P(SNR,4)')"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "474ea438-17c9-48d8-9dd5-5e71bc0b8410",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/html": [
"<html><body><pre>SNR = 18.6923</pre></body></html>"
],
"text/plain": [
"SNR = 18.6923"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"fr=1e-4;\n",
"SNR = 10*log10(find(abs(wk4-fr)<0.00001))"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "MATLAB Kernel",
"language": "matlab",
"name": "jupyter_matlab_kernel"
},
"language_info": {
"file_extension": ".m",
"mimetype": "text/x-matlab",
"name": "matlab"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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