{ "cells": [ { "cell_type": "code", "execution_count": 37, "id": "26e5b653", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "from pylab import *\n", "from scipy.ndimage import filters" ] }, { "cell_type": "markdown", "id": "eec6efc9", "metadata": {}, "source": [ "# Bitwise Encoding" ] }, { "cell_type": "markdown", "id": "11ab9a5a", "metadata": {}, "source": [ "When we modulate a digital signal, we first need to turn it into a string of ones and zeros. This can be a very complicated process in general, using compression, checksums, and error correction.\n", "\n", "Here, we just convert text strings into a bit stream." ] }, { "cell_type": "code", "execution_count": 38, "id": "d4cfb254", "metadata": { "collapsed": false }, "outputs": [], "source": [ "def encode(s):\n", " result = zeros(len(s)*8)\n", " for i in range(len(s)):\n", " c = ord(s[i])+512 # add a sync bit\n", " for j in range(8):\n", " result[i*8+j] = (c&(1<<(7-j))>0)\n", " return result\n", "\n", "def decode(m):\n", " result = \"\"\n", " for i in range(0,len(m)-7,8):\n", " c = 0\n", " for j in range(8):\n", " if m[i+j]: c += (1<<(7-j))\n", " result += chr(c&0xff)\n", " return result" ] }, { "cell_type": "markdown", "id": "6773ebba", "metadata": {}, "source": [ "Let's try encoding a simple message as a bitstream, and then decoding it again." ] }, { "cell_type": "code", "execution_count": 39, "id": "a1229a62", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The quick brown fox jumped over the lazy dogs.\n" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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gAp1JnwUVDeWY7KU003lHGUfVtYhAJbg4Nxsrg4pG53mTyTM1qq/CETwv24m+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\n4eFRUHiC9/Dw8Cgo/h96b8WWoAnZpQAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "message = encode(\"The quick brown fox jumped over the lazy dogs.\")\n", "print decode(message)\n", "plot(message[:100])" ] }, { "cell_type": "markdown", "id": "0a025f7c", "metadata": {}, "source": [ "# Signal Generation" ] }, { "cell_type": "markdown", "id": "c0dbfa99", "metadata": {}, "source": [ "An obvious encoding is as a sequence of voltages. However, such an encoding requires precise synchronization for decoding, and if there is a sequence of null characters, such an encoding would likely lose synchronization." ] }, { "cell_type": "code", "execution_count": 40, "id": "223b3d13", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "signal = tile(message.reshape(len(message),1),[1,400]).flatten()\n", "plot(signal[:5000])" ] }, { "cell_type": "markdown", "id": "13beb0d8", "metadata": {}, "source": [ "Here is a better encoding. It uses positive to negative and negative to positive transitions, separated by quiescent inputs." ] }, { "cell_type": "code", "execution_count": 41, "id": "969c168d", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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gSRi2fQBQKMIAAEAY2ORjmcjHPgFh4HptEQYAAMLAFp/fM/C5b4ALYVhThAEAYP5h8Nvf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\nJP0f88dAtcNM0NoAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "signal = concatenate([[0,1,-1,0] if m else [0,-1,1,0] for m in message])\n", "signal = 1.0*tile(signal.reshape(len(signal),1),[1,800]).flatten()\n", "plot(signal[:5000])" ] }, { "cell_type": "markdown", "id": "9aebb5c0", "metadata": {}, "source": [ "# Signal Decoding" ] }, { "cell_type": "markdown", "id": "8705049c", "metadata": {}, "source": [ "Decoding should usually be resistant to noise" ] }, { "cell_type": "code", "execution_count": 42, "id": "a14236be", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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ycqCoyDXvmhrg/Hngl1+8K4/V+J0w2LWLPyAtnnoKOH268cpDaCNM2nbvbiz+FVcApaVA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\nQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "noisy = signal+0.2*randn(len(signal))\n", "plot(noisy[:5000])" ] }, { "cell_type": "markdown", "id": "ba1f662c", "metadata": {}, "source": [ "How do we carry out the decoding? Remember that the value of each bit is given by the direction of the transition (-1 to 1, 1 to -1). We can find those transitions by taking gradients of the smoothed signal." ] }, { "cell_type": "code", "execution_count": 43, "id": "8212dc28", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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IB9XUk+Ca+UAMfHExcPPN1teY3cfIkZQKgSFHcfQon+cIhIahoIHGgfA327ZR\nyoWJA0EjFwC9AxHucuHIlKSKKOQjHBRCWxtQUgLMnGl/rXBEQSnAvJ4jQO5j+3a2YoVOI1JRWCfY\nDsTp06TG03XX2V9r5kBQTUkyyDfv1BNA5OKDD4KbvwpURCEbylBQJrOFcxR+lO4dO8hmKruVJEZT\nDAD5ntM5ChHPMSmJLJ/8+9/5vu8E4TAl+c47JAlstq9Gx0y+aeUCoHcgjh7ldyAmTyabSisr+b7v\nBAGZklQlPOTDCYVgVxHS3wP/5z8D8+bZXxfIKQaRiAIg9/PnP/N/XxQnFIKtXPg5omCSC5EpScYc\nBa8D4XIBc+fKLRc0UMmFmnqSCydyFMOGkdUYZmPrz4H/9ltg0ybyA7LDLKLwxxSDSEQBdBuKtjb+\nNkQI9YiiuZlM3xUU2F/rSETBkKMQdSA2bAjO9NOFC0QeBw0yv8axHIWKKORCpEKoTt++5BD45mbj\nz/058G+9BWRnA8nJ9tdaRRQy5SgAID2dLJXdtIm/DV7OnSP5EauDdWgUgu5AdHYaf+7PiOL114E5\nc6yXxepYRRQy5SgAYMYMElmUlPC3wYuuK0RTCMGequYhog3FuXPEM6GZw7XDqtiXvwZe04BXXgEe\nfZTyeoscBe3UEy2iEQVA7uvll53pDwt6mQZRhRATQ4zNqVPGn/sroujoAF59lVEuRKckKe5D35Vt\nVYDTDpcLWLw4OHLhxOZcgMKBUBGFXOgDT6MQRBJU/hr4zZuJsbvlFrrrzSKKhARyyp3db53WA25t\nJStuhg2j65cZd95JxmjrVrF2WKGJMmnH01Iu/BRR/O53xEhble3wxiyiYJl6ooF3V7YvDz5INhIG\nuqSHE5tzAQoHQkUUckE78DSDZqsQHB74M2eAJ54AfvlL85LHvphFFP37k6jKqV2vDQ3kubLuyvYl\nOhp48UXgscfILuFA4ZRCACgcCIfloqkJ+K//InJBGxGZRRTx8aTvdsuUaQ2eaH5CZ+BAYNkyEjG1\ntoq3RwttPpOGYDiWIggbiqKiImRkZCAtLQ0rV640vGbJkiVIS0tDdnY2KioqmL7rT1gSlqIJKicH\nvq0NeOABYNYs+81UPfpgElEAdNNPtIrN7nwPFubMIfsAHnqIvh6VKAFTCA5HFBcuAN/7HrBwITBl\nCv33zCKKmBiS4zh+3Jn+ObFAQOfBB4nRefTRwCW2qR0ICgttqy/CKaLo6OjA4sWLUVRUhMrKSqxf\nvx779+8E4ZLZAAAgAElEQVTvcc3WrVtx8OBBVFVVYc2aNXjkkUeov+tvqCMKwUJfTnqO+/cT5dnR\nwT5Pa3UfLAltO5xYIKDjcgGvvUYKDBYU0J/jLEIoKoSKCrJzOSkJeOYZtu9ayQXN9BOtfNuV6GYh\nKgr4/e/J2SXz59tX6XUCp3IUQHCmJEUQmi0sKytDamoqki8tuZk/fz42b96MzMzMrmu2bNmCwsJC\nAMD06dPR3NyMhoYGVFdX235X569f/5W7j/2i+yFvbJ7hj5opoqDIURw5YvJdlwutHa1C91FTA2zc\nCPzjS+CO24E77wLer2Zr49v2b02VG42hoBVguyNEtx3ehovtF23b8eZffwFsWA9k3g5897vA7beT\nkwV5GdRvEHKTcw0/a2qynyJxRCHAhZbWFiG5+PoAsHEDOdRn3jxgzi3Au1Xs7ZjJty4XkyZxd7EL\nK7no6OxA8eFitHWwrYf+8Rpg7TogZQ5xJG69FRhwOX8f4y6Pw4ykGYafNTWRUxjtcGJK8sT5E0Jy\n4XRRTSFDUVdXh6SkpK7Xbrcbu3wyTEbX1NXVob6+3va7Ovc99GMMGwb07QfEZcYhLou+dvW2w9tw\nYPEBJA1J6vVZYyPbSVtWDB9ufrDKoL6DcGv6rVhTvoa53fPnyU7UUyeBsSnAtTcCJ6OB337O3sf8\ntHwM6TfE8DMnVz5Z1ew/2nIUt62/DXkpNpXqjMgCrk4Gdh0ENq0Ckq4EUsYC/fqzN7W1aitaftaC\ny2Iu6/VZYyNZcmwHrUKoqTH+bOSgkfhO0ne45KLlLLCvkvw/dQJwTT5Q3wf4nwr77/ryYPaDpg4E\n1ZQkZTLESi72HduHu9+6Gzck30DVVg+mAFPTgZIq4M2XyFLxsWOAmL5szbR3tuPjbz5Gy38YJ8Qa\nG52LiKwMxZgrxiBzeCazXJyoPIG6ihM4dsz5/UdChoJWQETD62fu/hrLl5PE5gMPsH139C9Ho0Mz\nzsYdPUqOiLRDdBNNTJ8YbJi3wf4P+fC//wv8y6PA448DT/wcuKy3TnMMu92iAP16eTvPcdjlw/DX\ne/m9JYCc5/zcc8CfniR7Bm67je37A5YPQKdmvD7RqaQrQJ7DZ58Zfza432C8fffbzG2+/jrwk/8D\n/Od/Ao88Qvbx+AsauQDoIqxjx8jeGCM6OjuQMjRFWC4OHQJWrAC2/Ap4803gBga7c77tPOKeM3dC\naeSCRlcA1g7EqEGj8Jd7/mLbRs+/S/Tj87uBV5YBhYVATIxzNaOEDEViYiI8XqebeDweuH3OOPS9\npra2Fm63G21tbbbf1Xn8cTLdkJdHlCVNWQIdq/lTpxWCk/OkH3wA/Nu/kf+zJCZ5GTEC2LfP/jra\nuWgzhWC28ooVt5vkaL7/fTLlsGEDcOON9N+3WlnitEJwUi42bACWLiV1sMaNc65dM0aMIJ60FU44\nEDQlUWhISQF+8xuSt5g3j/x+Jk+m+65driVQDgQPr74K/M//kDaTek+eCCOUzJ42bRqqqqpQU1OD\n1tZWbNy4EQU+NQMKCgqwbt06AEBpaSliY2MRHx9P9V1vMjOBLVuAH/4Q+OYb+j5azas3NNAdyUhb\n18dswx0rTU0kctq4MTBGAqDrP62Ct8tROFlNd/p04I9/BO67j215r9WSZVq5oMFJuTh8mKzy2bw5\nMEYCoO8/rQNhKRcOVk2dOZMoz7lzyfQtDVa6oq2NVF6w2xtEa/CclIuKCrKA4Z13/GMkAEFDER0d\njVWrVmH27NnIysrCPffcg8zMTKxevRqrV68GAMyZMwdjx45FamoqFi1ahNdee83yu1ZMmUJ2ZT71\nFH0fAxVR6GvOzXZbsvCf/0kU3/XXi7dFC7VCEE1mOxRReHPzzWRz3tKl9N8xiyguXiSbGO2OcKVV\nCE7mfn78YxJdO5FYpiVgDoRDEYU3d98NTJsG/L//R3e9la5obCR9p92zZIdTcqFpwJIlwM9/TqIp\nfyG4RxLIz89Hfn5+j/cWLVrU4/WqVauov2vHE08AqalkWdzEifbXm3kJLS1kiSnNyhkab6dvX2DI\nELLmXCThdfgwyU1UcaxcEYFKITgxxeCn9eHPPEPqQ/3kJ/RelVFf9CNcnbJlI0aQHbhtbWRfAi97\n9gC7dwN/+pMz/aIlYA6En+TiueeIg7lkCRAba32tVURB61TSRkajRjmzHP2DD0iks3CheFtWhNzO\n7IEDyaCz7CEwEkJ94J10bkeOJEXPRHjtNWDBArpibk6i16py4vcaaM8RIFMC998P/PrXdNebKQWn\nFUKfPqRvdvP8drz8Momm+3Os8BLBKQfi229JtDbEeNGdXyJNgKyA+u53yQIAGgIx+wCQiLWlhTwT\nEV5+mUSZTkU6ZoScoQCIIn37bbqyDmZTDCzz0LTKbdQoMUNx8SLwxhskDxNoLruMREVnz5pfQ/ND\ntlUIDs9Fe7N4MUno0ZR1MJtmcDI/oSPqPZ44QfIS/vYajaB1IOwigmPHiME0G3qnc1fePPooccBs\na5lZLHBwMp8JkOcgWkuruprUvLr3Xv42aAlJQzFyJJm/pznAxCxp6bSHoPdLZOA/+ACYMAEYM8a5\nPrHgROLSViH4KaIAyNTT2LHkxD87hCMKhp2zopHmpk1kxZ9d3sQf9O9PnIjTp8XasT1a1k8RBQBc\ncw35f3m59XVWCxxk1BdvvklWdvlz2bxOSBoKgCSqaM4qMPMSWAaeZd5RRCHQnkjmL5xYieHEWdMi\nfO975IwOO8wiCha5oDV4ohGF7HJBs2OfSi785EC4XOT52cmF6JJpgE2+Q0lfhKyhyM8nJ3jZLX0z\n8xL8McUg4iG0tQF//Stw113O9okFJxKXVJ6jnxQCQJZDbtrEX/GUeoqBIZkjElE0NwOffEJfSt4f\nOLEXJJgRBUAciLdt9jZa/X3Z9MU335ANeywbCkUIWUMxdCgwdSrw4YfW15kpJaaIgnKaQcRDKCsj\nU06ih/2I4FREYbfqy58KYfRoMq5m5VS6+uBERMHgOfIqhJIScq6E1Wl7/sY2oqAoCkhTKNKfDsTk\nySSnefgw39/3x5SkiL4oLibVo0XP9qAlZA0FQFYzbNtmfY3oXHRXOxRCLOIhbN9Oqn8GE9oVLnY5\nimBNMejcfLP/5SJQOYpQkQs7gj0l6XLZy4X+9wM1JRlK+iKkDUVurv3ZuVaeoz9Wt4gohJkzne0P\nK+EwxQBQGgqLSJNWLgKRo5BBLgKSo/DzlCRAJxd6X3q81sjyZpozVlimJHn1haYFXi5C2lBMnUrm\n6axKN5gJcV0dkJhI/7dolJt+pCjr7uzz50mNluuuY/ue09DuwrVSClYVQoHARBTXX0+m8i5cML/G\nKHeln+ksS46isZHIKW2tIn/hRERBJRd+diBmziQK1mrojBzLY8fI1B/t6iLa++CNKCorgcsvJ3tE\nAkVIG4roaODaa4G//c38GqOBP3+elGlw6nAdnX79yE5v1hPBPv2UlLUeNMjZ/rASkCmGAEQUgwYB\nGRnWyyGNVrjU15O+0+6gpr2PESOAkyfZT+jbsYMkK/29mcoOmhyFHTJEFG43UfhWVQ+MHKHaWv/U\nUOKNKIIxHRnShgIgXvinn5p/bjbwbjfdrmzW0gI83uPOncTgBRsnduHKkKMAyNr50lLzz40iCo/H\nPwohOprsgWDdnR1KckGTzLZa5BCIiAIgcrFzp/nnRo4li1ywGLy4OLLBlXV3djDkIuQNxdVXk2kG\nM8wG3qSiuTBuNzFELOzZQ4qXBRunNtwFO6IAyEohW4Ug4DmyesDhLBc04ylDRAEQubB1IBAYfREV\nRaIK1uN9gyEXIW8ocnLIFINZWG828P5SCFdeSdpnYc8ekm8JNsOGkSkSqxyLnVKQJaKgUggBdCBY\n5aKjA/jii8CVmbeCKqKwyFu1tZGlqVb1ywIVUVA5ECIRBeN9sMrFmTPE4bAptO04IW8ohgwhg2h2\n6I7RwPtrzhEgA292drYRjY3kRzR2rH/6w0J0NMmx2J3rYFWz31YhBOjQ+DFjSM0nqx+hkAPBoRBY\nzlH5+muSVDermRVI4uLIxj9TZ8zG8B8/TvY9RVlom0DJxaRJJEdhVtMskDkKgF1fVFSQqtmB2j+h\nE/KGAiDTTybHbYtHFH5WCHo0EQBnigq7oy+tlAKVQgiQ5+hyWXuPop4jK6wKYfduOaJMgCTTY2NJ\ntGmGyHSk/v1ARJp9+xJjYXa6XCBzFAC7vti9OzjTkWFhKKZPN89TyK4QZJl20qHZS2GmFKgUQoDm\nogEyLWmqEIIwJckqFzLkJ3Ss5EJ0OhIIXO4K8K9csBIq+iIsDEVOjoWhEExOsSqE0aNDY+DNsDMU\nVj9mas9RBoUQYAci3OVCpP4XELiIAmCTi85OsoqRds8Vq3yHilyEhaGYOBE4eNB8g1UgFUJiIikg\nRrtmPlihpBn6+QNWmCkF2SKKadPIQgejAoG+DkRrK5laoT6jhHHZNMsUQ0cH8PnnciSydWjkwoxQ\niij0vug0NpI8kb8OjGKJKE6fJiukAp3IBsLEUPTrRzZYffFF7898l0GePUuUwtChdG2zeggxMWSe\nn2YvRWMj2fwXrPMnjLCNKCyUvGwRRVwc6c+BA70/8/Uc6+rIHhiWzW0s9zF8ONnkee6c/bVffUX6\nIkMiW8dy6kmw/hcQ2IgiNZUoXSPD57sajjWRzeoIJSURQ0HjdwQrkQ2EiaEASDhmVDHU98esD7w/\ndRWtl7BnD/EaZUlkA+I5CprzwgOlEABz79E3omCNMllX6bhcpH2apZCy5ScAsTpgNIYC8G9VYW+i\nosjz3b3boA8+sunP2QeArDLs29d6oYBOMKcjw99Q+Hg71dVsNVJ4lu3RTjPItLJFx98KIZBTDICF\noRCUC70NFsJVLuzqf8k2JQnQOxDM+oLj0PlQkIvwNxQ+A3/oEJCSwtY2qwDTJqhC0XO0UgqyTTEA\n9AqBVS54FAKLXISSobBDtilJgN6B4NIXjPcRCvoibAzFVVeRjTS+CW0nBp6V0aNJVVs7IlIhBDii\nmDIF+Mc/SF7Km2ApBDu5aG+XZ0e2N3Y5Citkjih87b0TjiUrNHJx+jTJe2Zk+LcvZoSNoejf3zih\n7YTnyKoQUlPJKiwrGhrkS2QDdBvuzLxpu1LSQOAjioEDyTP+8sue7/vKxeHDbLvjeaYkaeTiq69I\n/R+ZEtkAxfJYiwiLWi4C6EDoRUF9c0aiDgSPwaORi/Ly4CWygTAyFIDx9FMwIoq0NOOVNt7ItiNb\nZ9gwUsKD9UwNQM6IAjCeZvD9MQdiSpJFLmSDd8NdRwcp/xEXZ91+oCMKl8tELrwciPZ2Ykj8fe4D\nrVwEc5o6/A2F18B3dpLkFKvnyJO0PH6cRAxmyKoQYmKIF97cbPy5WY6CWiEEOKIALBTCJQfi7Fmy\nbJXlxEOeHEVaGvEcrb4qq1zYFYw0i7BOnCDRkZ0nHOiIAjB3IPSxPXKEyES/fvRt8txHerr1GRlA\n8OUi/A2F18DX15OaNQMG+LcfffqQ6Q6rcDLYA28FT57ixAnybO32IcgUUejK7dAh4jywdov1PmJj\nySlpDQ3m18gqFzEx5ECoU6d6fya6twYIfEQB2EcUgZh9AEjEcvSo9bkUwZaLsDIURglt74E/cIB4\ndSzwejppaeZegqaRIoZXX83cbECw2oVr9mOmVggcnrgo+s593whP7wuPXPBiJRdtbWRHtoyGArCW\nC5H6X1bf9yc5OUQBe0dJ3o4ll77gMHjR0WQW4vBh489PniSGJBg7snWEDMXJkyeRl5eH9PR0zJo1\nC80m8xVFRUXIyMhAWloaVq5c2fX+k08+iczMTGRnZ+Ouu+7C6dOnRbqD/v2BceOAvXu73/Me+C+/\nBCZMEPoT1KSnm8871tYSY3HllYHpCys8iUuZPcd+/YCsLLKzVcfbgeCRC977sJKLL78k3uXgwczN\nBgQzuRCt/wUEJ9IcNoyUxPc23KJywYuVXOj7J4J5JK6QoVixYgXy8vJw4MABzJw5EytWrOh1TUdH\nBxYvXoyioiJUVlZi/fr12L9/PwBg1qxZ2LdvH7744gukp6fj2WefFekOAJLw8Z5+CpZCGDcOuHSb\nvSgrI9GEbIlsHZ7EJYvnGGiFAPSeZgiWA0EjF7JiJRdWe2todusHI3cFOC8XvPItu1wIGYotW7ag\nsLAQAFBYWIhNmzb1uqasrAypqalITk5GTEwM5s+fj82bNwMA8vLyEHXp8ILp06ejlvWsSAOmTu25\nNT9YCmHSJOPaU4AcA28FT6VQmSMKwEAhiDoQnFMl4SwXRsgcUQDmcqFpSl94I7Qqt7GxEfHx8QCA\n+Ph4NBqcHl9XV4ckr2IpbrcbuwxOGfrd736He++91/DvLF26tOvfubm5yM3NNe3T1KnAr37V/dp3\n4MePt7kpH3g9hAkTSCj57be9V02UlQFPPcXcZMAYPtx8A5ATOYpgKQTvgFV3IC5cIEsgeXIUPPcx\naRKZAtO03hFlWRnwwx+y9yNQmE49WeytOXaMTKvYEcyI4i9/6X6t30t9PanBRCPT3vA6QpMmAT//\nuUF7GpGLVavs2ygpKUFJSQnz36bB1lDk5eWhwWCZxrJly3q8drlchj8cmh/TsmXL0LdvX9x3332G\nn3sbCju8E9qXXdY98B4PWfZpt3zTKfr3Jxtp9u3rucu2o4NMjeXkBKYfPIwYYVOG2SRHQaUQghRR\nZGaShGBzM1l9pDsQ+/cTIxETw9Ye79GdCQlEAXk8PXNUZ8+SZObEiVzNBoThw80TrmYcOwZce639\ndcGKKKZOJTnNtjYiA7pcBDKaAMhmYY+HHCU8cGD3+x5Pd0FJO3yd6Kefftqx/tkaiuLiYtPP4uPj\n0dDQgISEBBw9ehQjDCYjExMT4fHa/ujxeOD2OjXojTfewNatW/Hhhx+y9t2Q/v3Jj23nTuCmm7rf\n37OHWG1WRBTb5MnEe/Q2FBUVZNBpy5wHA94cxXXX0bUfDIXQpw8Zj927gZtv7nYgeOUC4K+CO2kS\nWd3kbSj+/neSX2M1WIFk+HDjI4dF6391tRMEB2LQIDIO+/b1lANufcEZMcfEkNmOvXuBGTO63//b\n34ihDXY+UyhHUVBQgLVr1wIA1q5dizvuuKPXNdOmTUNVVRVqamrQ2tqKjRs3oqCgAABZDfX8889j\n8+bN6O/gySB5eYBu33Qh/uQTOs/GSaZM6b2vo7iY9E9m/JqjCNIUA9BzPlpULkSWc06Z0rvEdTjI\nhRGyT0kCPnJxyYH49NPg6AtZ5ULIUDz11FMoLi5Geno6tm/fjqcuTbzX19fjlltuAQBER0dj1apV\nmD17NrKysnDPPfcg89KC4EcffRQtLS3Iy8vD5MmT8UOHJmh7GAqvgfe21IHgn/4J8J0yLC4mHq3M\nhGPSEiAJwZ07yb+dkAve+7j++tCUC7M6YKG64U6nh1y4XOjo1LBzJ/Cd7wS2H776QtOAbdvkkAuh\nZPbQoUOxbdu2Xu+PGjUK7777btfr/Px85Ofn97quym7fOifXXEMSyU1NZODPnCVzjtOns7cl4ulM\nmkROsaurI0ektrQQz+WGG7iaCxi6oTBKuJolLkMhosjLA/7lX0i5DpfLBU+thjNn2Bc4APw5CoBM\n0ZWXk34MGEDko7ZWvpLzvlgujzWQic5OsmN/2DD7toMZUeTnA888Q/KHLrjwxRcaRowgpwyyImLw\nbroJWLKE9KNPH1L1uH//wOwOtyOsdmbr9O0LFBQAGzaQgd+1S8PMmcDllwe2H336AN/9bveqij//\nGbjxRjIvKjP9+hEBpd3/yKQQghhRDB1KvMd33iFysaNEQ0EBOfGMB16FMGAAiWL++lfy+k9/Au66\nK3iVQWkZNqzbgfDGbDxPnSL32revfdvBjCjGjiUVe0tKyL0Uva/hzjsD349Ro8iGSz2q+OMfge99\nL/D9MCIsDQUAPPww8OqrADQXNm/RYLKgyhZRAV6wAFizhqyqeOUVYOFC7qYCitUuXF9v+tQpslKD\nJhEbzIgCAB55BPjFL4iSf/ttAbkQLDnx8MPAr39N6vv8+tfktez060ecLaMCDCJ5KyC4EQUA/Ou/\nAi++CEBz4a23NJis1LdF9D4WLCDycPo0sHYteS0DYWsobryRLHvctcuF9nYNc+cGpx833UQ8salT\niTK9lMeXHpY8BZNCCGJEAQC3306M9ldfuRAfrwlNA4rcx113AWfOkAgnOzvwiVNejORCdG8NENyI\nAgAKC4GvvwaaGl2Yfo2Gq64KTj8eeoisjPynfyKyGqyDinwJW0PhcpGQ/sokF575vxr39IKohxAV\nRaacfvQjMgUV7GVutFglLn29aWbPMYgKoU8f4P33gRHDXVixkn88RHIUAJmOefddIhfr1gk1FVDM\nHAiRvJX+/WA6EP37k6Wogwa5sGIl/9iKGrxBg0gC+4kngJdf5m7GcSSfFRVj8GAgKcmF2NjAV6b0\nZujQ0Jly0vFnRBFshg0Dhg0HBg0S64uowRs5MjzkQrT+FyCHXCQmEkNx2WXB7UtyMoksZCJsIwod\nq81ANAQ7JA4WLJVCQ8lz1LEqO6EwxzSicCJHIcHvTFQuZJFvpwl/Q6EUAhcslUJDaS5aR9iBiFCZ\nCtfclY6oXIQr4W8oHFAIMghwoLEqAOdLpEYUMtxHoPFbMjtcIgpJHCGnCX9DoSIKLlg2V0VkRBGh\nXqfZIgcjVEQRPoS/oVA5Ci5UjoKujUjDKpkdyqvhdFSOwpjwNxQSCF8oYnk+skCOApBjTFSOgg8r\nufCFWS4kULAy9EFGwt9QuNRcNA/e9Z68MVLyTU3ApfOrbJFmikHlKLigTWZrGv0xqIA8kbsL4lNP\nMtyH04S/oRAc+Ej1HC+/nNQeamnp/Zn3M+nsDNEpBpWj4MLMgQB6PpPmZnJwGO3pAbJM2Yg6luEq\nF2FvKABxZS+DYgsGNJurmptJaRKawm9AmEUUESgXl11GanqdPdvzfd9n0dREH00A8kQUgLiyl0G+\nnSbsDYXyHPmh2VzFrBDCJaKI0EgToCvjwTLtpH9XBgXrRDI7HAl/Q6GWx3JDMx/N5TmGgUIAwtNz\npIEm0gzViEItjzUm/A2F2nDHjdnmKm8FG7ERRQQrE79FmhL8ztSGO2PC31CoiIIbFVHYtxGJ0OzO\nVhFFeBH+hkJtuOPGbIpB5SjCdy6aBpocRcRGFJLch9OEv6FQEQU3/oooZEHlKPgwKuPhRI5CBlRE\nYUz4GwqVo+BmxIjeu3AdyVFI8DxFo5pIViZmu7PDItJUOQpDwt9QqIiCG7/lKCT4ISnPkZ+wzl0p\nuTAk/A2FylFw45dlkBJFFCqZzUdYr4ZTOQpDwt9QqIiCG78sg5TE8KpkNj92EUV7O3D6NDkCmBYV\nUchN+BsKQeELVw+BhgEDSC2n8+e73/NW8q2tpJTDFVewtSvD81Qb7vixWw13/DgxEn36sLUrhQPh\nQO5KhvtwmvA3FA5Ug4xUXC5jpaAr2OPHgWHDgCgGKZJmikFtuONmwABSFPDcOePPWaNMQB6HzIlq\n0+FI+BsKJ8qMS6DYgoWvofD+MTc2cigEWaYYVI6CGyMHwvtZcMuFBM/TkTLjEsi304S/oRAtMx7B\nniNgElFceib19UBiIlt7YRNRRLjXaRVpcsuFBApWuMx4mMoFt6E4efIk8vLykJ6ejlmzZqG5udnw\nuqKiImRkZCAtLQ0rV67s9fkLL7yAqKgonDx5krcrlqiDi8Sw8hzr64FRo9jaC6uIQoL7CBZWkSa3\nXMjgQKiDiwzhNhQrVqxAXl4eDhw4gJkzZ2LFihW9runo6MDixYtRVFSEyspKrF+/Hvv37+/63OPx\noLi4GKNHj+btBhXKc+THaNOd/kzq6jgUQrhEFBEeaRrKBQTlQhLDqw4u6g23odiyZQsKCwsBAIWF\nhdi0aVOva8rKypCamork5GTExMRg/vz52Lx5c9fnTzzxBJ577jneLlChlseKMWoU8RCNiPiIQgKD\nFyx85cKRSFOC56mWxxrDbSgaGxsRf+mg5Pj4eDQ2Nva6pq6uDklJSV2v3W436urqAACbN2+G2+3G\nxIkTebtAhdpwJ4bbDdTWdr/2fp5cCiFcIooIdz585QLomaMI1YhCbbgzJtrqw7y8PDQ0NPR6f9my\nZT1eu1wuw4dj9sAuXLiA5cuXo7i4uOs9q8FZunRp179zc3ORm5tr1e2efVARhRBGCkEn4iMKCe4j\nWLjdwAcfdL/2zVEwJ7MlcchCOaIoKSlBSUmJX9q2NBTeityX+Ph4NDQ0ICEhAUePHsUIg/VwiYmJ\n8Hg8Xa89Hg/cbjcOHTqEmpoaZGdnAwBqa2sxdepUlJWVGbbjbShYUUUBxegVUXgpWF7PURZUjoKf\npCSDiAIaOjuBhgYgIYGtPVnkIpSLAvo60U8//bRjbXNPPRUUFGDt2rUAgLVr1+KOO+7odc20adNQ\nVVWFmpoatLa2YuPGjSgoKMCECRPQ2NiI6upqVFdXw+12o7y83NBIiKIiCjFGjiQ//I6Onu+3tQEn\nToTwenm1sUoItxvw8gG7OH4cGDIE6NePrT1pIs0Qjij8CbeheOqpp1BcXIz09HRs374dTz31FACg\nvr4et9xyCwAgOjoaq1atwuzZs5GVlYV77rkHmZmZvdryp4CoHIUYffsCcXHEWADdz7OxkSyRjLaM\nSXsjS4QmvL9GklxLsBg+HDhzBrh4kbzWHTKeKBOQ53mqHIUxjD/zboYOHYpt27b1en/UqFF49913\nu17n5+cjPz/fsq3Dhw/zdsMWFVGIo08zeM87HzlCvEpWZDG84fhjDiRRUcQg1NUBKSnd7wvJhQRj\noiIKY8J/Z7bKUQjjnafQlXxNDTBmDHtbsjxPlcwWp4dcXPqdCcmFDA5ECOco/En4G4owHLRA4zsf\nrWkaqquB5GS+9mQYE7XhTpykpN55CiG5kMDwytAHGQl/Q6GKAgqTnAzos4P6D4nbc5RlikFtuBMm\nOaIWbR8AAAo/SURBVJkYBsCBSFMST1wVBTQm/A2FKgooTFoacPBg92t9ioHHc5RmikFtuBMmLQ2o\nqup+rWmCciGBglVFAY0Jf0OhigIK460QdCV/6BAwdix7W2EVUUhwH8HE24EgvzNBuZDBgVBFAQ0J\nf0PhwDLISGfMGLKapa2NvD53XsPRo5wKIVwiChVpIjW1Z0RRV69hwAD2Ew+BMIoowlQuwt9QqByF\nMP36kaWxhw+T53n4MPEmWfdQAGEWUUS4XMTHA99+C5w8SZ7FV18BWVl8bYVVRCGBfDtN+BsKlaNw\nhOxsoKKC/LuqSsP48XzthE1EoSJNuFw95eKrr7XQNxQqR2FI+BsKlaNwhKlTgT17uj3HCRP42gmr\niEKC+wg2XXLhcuEf/xCQC1mmnlSOwpCwNxSAOrjICaZOBXbvJv8uK9Nw/fV87YRNRKEiTQA95eKT\nTwTkQpKIAlAHFxkR9oZClfBwhuuuA8rLSUK7uhq4+mq+dmT6ISm5EGfmTGDbNqCzA2htBTIy+NqR\nZSxUCQ9juGs9hQoulwtfnfgK7x98n+v79WfrpfF0gsmgQcDs2cDmOhfGz/oYJZ4arna+Ov4V+kUz\nlhb1Ay64sLdpL7dc7D++X8kFSL2n7GzgoxYXrr79Q3xwaDBXO4dOHcL44ZyJLwdxwYU99XvQx9WH\n6/vlR8ulmEJzmrA3FDPcM7CmfA1eLH2Ru43bM253sEehy9KlwOev3o4BOW/hxVL+dhZOXuhYn3jJ\nTc7Fxn0b8WXTl9xtzEmb42CPQpeVK4H5f/we2q76HyG5yBmV41ynOJmVMgvvHXwPf/f8nbuNOanh\nJxcuTZaYzwR1boBCoVCw46TuDPschUKhUCjEUIZCoVAoFJYoQ6FQKBQKS5ShUCgUCoUlylAoFAqF\nwhJlKBQKhUJhiTIUCoVCobBEGQqFQqFQWKIMhUKhUCgsUYZCoVAoFJYoQ6FQKBQKS5ShUCgUCoUl\nylAoFAqFwhJlKBQKhUJhCbehOHnyJPLy8pCeno5Zs2ahubnZ8LqioiJkZGQgLS0NK1eu7PHZK6+8\ngszMTEyYMAE//elPebsSMZSUlAS7C9KgnkU36ll0o56Ff+A2FCtWrEBeXh4OHDiAmTNnYsWKFb2u\n6ejowOLFi1FUVITKykqsX78e+/fvBwDs2LEDW7Zswd69e/Hll1/ixz/+Mf9dRAjqR9CNehbdqGfR\njXoW/oHbUGzZsgWFhYUAgMLCQmzatKnXNWVlZUhNTUVycjJiYmIwf/58bN68GQDwq1/9Cj/72c8Q\nExMDABg+fDhvVxQKhULhR7gNRWNjI+Lj4wEA8fHxaGxs7HVNXV0dkpKSul673W7U1dUBAKqqqvDR\nRx/hmmuuQW5uLnbv3s3bFYVCoVD4Ecszs/Py8tDQ0NDr/WXLlvV47XK5DA8UtzpkvL29HadOnUJp\naSk+++wz3H333Th8+LDhteF4WDkvTz/9dLC7IA3qWXSjnkU36lk4j6WhKC4uNv0sPj4eDQ0NSEhI\nwNGjRzFixIhe1yQmJsLj8XS99ng8cLvdAEh0cddddwEAcnJyEBUVhRMnTiAuLq5HG+q8bIVCoQgu\n3FNPBQUFWLt2LQBg7dq1uOOOO3pdM23aNFRVVaGmpgatra3YuHEjCgoKAAB33HEHtm/fDgA4cOAA\nWltbexkJhUKhUAQfl8bpsp88eRJ33303jhw5guTkZLz55puIjY1FfX09fvCDH+Ddd98FALz33nt4\n7LHH0NHRgYULF+JnP/sZAKCtrQ0PP/wwPv/8c/Tt2xcvvPACcnNzHbsxhUKhUDiEJjHvvfeeNm7c\nOC01NVVbsWJFsLvjV44cOaLl5uZqWVlZ2vjx47WXXnpJ0zRNO3HihHbzzTdraWlpWl5ennbq1Kmu\n7yxfvlxLTU3Vxo0bp73//vvB6rrfaG9v1yZNmqTdeuutmqZF7rM4deqUNnfuXC0jI0PLzMzUSktL\nI/ZZLF++XMvKytImTJig3XvvvdrFixcj5lksWLBAGzFihDZhwoSu93jufffu3dqECRO01NRUbcmS\nJVR/W1pD0d7erqWkpGjV1dVaa2urlp2drVVWVga7W37j6NGjWkVFhaZpmnb27FktPT1dq6ys1J58\n8klt5cqVmqZp2ooVK7Sf/vSnmqZp2r59+7Ts7GyttbVVq66u1lJSUrSOjo6g9d8fvPDCC9p9992n\n3XbbbZqmaRH7LB588EHtt7/9raZpmtbW1qY1NzdH5LOorq7WxowZo128eFHTNE27++67tTfeeCNi\nnsVHH32klZeX9zAULPfe2dmpaZqm5eTkaLt27dI0TdPy8/O19957z/ZvS2soPv30U2327Nldr599\n9lnt2WefDWKPAsvtt9+uFRcXa+PGjdMaGho0TSPGZNy4cZqmEW/BO8qaPXu2tnPnzqD01R94PB5t\n5syZ2vbt27siikh8Fs3NzdqYMWN6vR+Jz+LEiRNaenq6dvLkSa2trU279dZbtQ8++CCinkV1dXUP\nQ8F67/X19VpGRkbX++vXr9cWLVpk+3elrfVktQcj3KmpqUFFRQWmT59uul+lvr6+awUZEH7P5/HH\nH8fzzz+PqKhuEY3EZ1FdXY3hw4djwYIFmDJlCn7wgx/g3LlzEfkshg4din//93/HlVdeiVGjRiE2\nNhZ5eXkR+Sx0WO/d9/3ExESqZyKtoYjUvRMtLS2YO3cuXnrpJQwaNKjHZ2b7Vbw/DwfeeecdjBgx\nApMnTzZdHh0pz6K9vR3l5eX44Q9/iPLycgwYMKBXuZxIeRaHDh3CL3/5S9TU1KC+vh4tLS34wx/+\n0OOaSHkWRtjduwjSGgqrPRjhSltbG+bOnYsHHniga7mxvl8FQI/9Kr7Pp7a2FomJiYHvtB/49NNP\nsWXLFowZMwb33nsvtm/fjgceeCAin4Xb7Ybb7UZOTg4AYN68eSgvL0dCQkLEPYvdu3djxowZiIuL\nQ3R0NO666y7s3LkzIp+FDstvwu12IzExEbW1tT3ep3km0hoKqz0Y4YimaVi4cCGysrLw2GOPdb1v\ntl+loKAAGzZsQGtrK6qrq1FVVYWrr746KH13muXLl8Pj8aC6uhobNmzATTfdhN///vcR+SwSEhKQ\nlJSEAwcOAAC2bduG8ePH47bbbou4Z5GRkYHS0lJcuHABmqZh27ZtyMrKishnocP6m0hISMDgwYOx\na9cuaJqG3//+94Z74HrhRILFX2zdulVLT0/XUlJStOXLlwe7O37l448/1lwul5adna1NmjRJmzRp\nkvbee+9pJ06c0GbOnGm4/G3ZsmVaSkqKNm7cOK2oqCiIvfcfJSUlXaueIvVZfP7559q0adO0iRMn\nanfeeafW3Nwcsc9i5cqVXctjH3zwQa21tTVinsX8+fO1kSNHajExMZrb7dZ+97vfcd27vjw2JSVF\ne/TRR6n+NveGO4VCoVBEBtJOPSkUCoVCDpShUCgUCoUlylAoFAqFwhJlKBQKhUJhiTIUCoVCobBE\nGQqFQqFQWPL/ATdxWZB9SYzAAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "d = 1.0*signal[::16]\n", "d = filters.gaussian_filter(d,16,1)\n", "plot(d[:1000])\n", "plot((amax(d)*signal/amax(signal))[:16000:16])" ] }, { "cell_type": "markdown", "id": "d2bc0797", "metadata": {}, "source": [ "Now we still need to find the locations of the transitions. We can do this by filtering the absolute signal." ] }, { "cell_type": "code", "execution_count": 44, "id": "5acc135e", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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MAIzhyiuBzz+PXNzg+HE613bYMHBrF47R6JwJ33ORI0FZGckjMxMCyYLahd+5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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "s = abs(1.0*signal[::16])\n", "s = filters.gaussian_filter(s,32.0)\n", "plot(s[:1000])\n", "plot((amax(s)*signal/amax(signal))[:16000:16])\n", "plot(abs(1.0*signal[:16000:16]))" ] }, { "cell_type": "markdown", "id": "9da43907", "metadata": {}, "source": [ "Now we look up the sign at each of the locations of the peaks of the absolute signals." ] }, { "cell_type": "code", "execution_count": 45, "id": "459a8d33", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0 1 0 1 0 1 0 0 0 1 1 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 1 0\n", " 0 0 1 0 1 1 1 0 1 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 0 1 1 0 1 1 0 1 0 1 1 0 0\n", " 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1\n", " 1 0 1 1 0 1 1 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1\n", " 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 0\n", " 1 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1\n", " 1 1 0 1 1 1 0 1 1 0 0 1 1 0 0 1 0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1\n", " 1 0 1 0 0 0 1 1 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0\n", " 0 1 1 0 0 0 0 1 0 1 1 1 1 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0\n", " 1 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 0 0 1 0 1 1 1 0]\n" ] } ], "source": [ "locations = find(((s>roll(s,-1))*(s>=roll(s,1))))\n", "signs = d[locations]\n", "bits = 1*(signs<0)\n", "print bits" ] }, { "cell_type": "markdown", "id": "1f3efde7", "metadata": {}, "source": [ "Finally, we decode the recovered bits to get back the original text." ] }, { "cell_type": "code", "execution_count": 46, "id": "33446887", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The quick brown fox jumped over the lazy dogs.\n" ] } ], "source": [ "print decode(bits)" ] }, { "cell_type": "markdown", "id": "e07ddf58", "metadata": {}, "source": [ "Now let's wrap all of this up in a couple of functions." ] }, { "cell_type": "code", "execution_count": 19, "id": "684b70ff", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The quick brown fox jumped over the lazy dogs.\n" ] }, { "data": { "image/png": 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DA1599VWsXbsWiYmJuPPOO5GQkIA33ngDb7zxBgDgiy++QEpKCubOnYtf//rX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\nrrvEu4eY7wtnZ7pXeV+feCN8nQ748ss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Q+HIsWCBvOfhgjbrw9aU7mY0PPTaHLlxdqUEY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\nCAMAgCEMAADGmBdDOPat9K2LagAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def signal_bits(sig,subsample=1,nplot=0):\n", " sig = 1.0*sig[::subsample]\n", " d = filters.gaussian_filter(sig,16.0,1)\n", " if nplot>0: plot(d[:nplot]/amax(d))\n", " s = abs(1.0*sig)\n", " s = filters.gaussian_filter(s,32.0)\n", " if nplot>0: plot(s[:nplot]/amax(s))\n", " l = find(((s>roll(s,-1))*(s>=roll(s,1))*(s>amax(s)*0.5)))\n", " signs = d[l]\n", " return signs\n", "\n", "def signal_decode(sig,subsample=1,nplot=0):\n", " signs = signal_bits(sig,subsample=subsample,nplot=nplot)\n", " bits = 1*(signs<0)\n", " return decode(bits)\n", "\n", "print signal_decode(signal,subsample=16,nplot=1000)" ] }, { "cell_type": "markdown", "id": "8b5fc3b9", "metadata": {}, "source": [ "# Frequency Modulation" ] }, { "cell_type": "markdown", "id": "38ee1cff", "metadata": {}, "source": [ "Now we're going to perform frequency modulation.\n", "\n", "Note that we change the instantaneous frequency, but accumulate the phase over time. If we just change the frequency discontinously, we'd get jumps in the output." ] }, { "cell_type": "code", "execution_count": 48, "id": "d9d641d3", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "def modulate(f,b,signal):\n", " \"Frequency modulation.\"\n", " fs = f+signal*b\n", " phis = add.accumulate(2*pi*fs)\n", " signal = sin(phis)\n", " return signal" ] }, { "cell_type": "markdown", "id": "5a0cda1d", "metadata": {}, "source": [ "Now let's create a modulated signal." ] }, { "cell_type": "code", "execution_count": 49, "id": "70cddbe4", "metadata": { "collapsed": false }, "outputs": [], "source": [ "freq = 0.1\n", "b = 0.02\n", "modulated = modulate(freq,b,signal)" ] }, { "cell_type": "markdown", "id": "67cb22a7", "metadata": {}, "source": [ "Let's add some amplitude modulation as well, mostly to show that frequency modulation is robust to such disturbances." ] }, { "cell_type": "code", "execution_count": 50, "id": "167b7773", "metadata": { "collapsed": false }, "outputs": [], "source": [ "am = filters.gaussian_filter(randn(len(modulated)),10.0)\n", "am /= amax(am)\n", "modulated *= 1.0+0.3*am" ] }, { "cell_type": "code", "execution_count": 51, "id": "2a2c9b9b", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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HZ2cn3n33XW2dIdJIiLHzjQJsMpGvdl5KI++6zVXiSmP4fSUzVT06710eU5eI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\nzAAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(modulated[:2000])" ] }, { "cell_type": "markdown", "id": "2571e145", "metadata": {}, "source": [ "# Decoding with Windowed Fourier Transform" ] }, { "cell_type": "code", "execution_count": 128, "id": "dc0dfcf3", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 128, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Xj780rO0lGo10qaO1u8X8/fLJl2PT4k3m79/+tvFnT1sX0NMDHDuG3ANvm/f/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\nAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(abs(fft(modulated[0:512])))\n", "plot(abs(fft(modulated[512:1024])))\n", "plot(abs(fft(modulated[1024:1536])))" ] }, { "cell_type": "code", "execution_count": 130, "id": "9036f66c", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 130, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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V2LBY/ud/4Pvf12bCeCtcF0/BASnTCN8hAS861dslGndr8Eop7E57j7fv6Wu+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\nYx1fDprOTwf9hQ9Lh5OQAJm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DDz/cuj5Q+nj69OnWWQhms5mtW7eSnZ0dEP17/PHHKSsr\no6SkhPXr13PDDTfwyiuvBETfAJqbm2loaACgqamJLVu2kJWVFTD9Gzp0KGlpaRQXFwOwbds2xo4d\ny+233+5e//rg+ECnPvjgAzVq1Ch15ZVXqscff/xy7rpP3HXXXSopKUkFBwer1NRUtWbNGnXmzBk1\nc+ZMNXLkSJWbm6vq6ur6u5ke++c//6l0Op2aMGGCmjhxopo4caLavHlzwPTxiy++UNnZ2WrChAkq\nKytL/eEPf1BKqYDpX4v8/Hx1++23K6UCp2/Hjx9XEyZMUBMmTFBjx45tzZNA6Z9SSu3bt09NmTJF\njR8/Xs2dO1fV19e73b9+ueGHEEKIvhe4tz4RQogBTgJeCCEClAS8EEIEKAl4IYQIUBLwQggRoCTg\nhRAiQP1/1oZ1XK95UxoAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(abs(fft(modulated[0:512]))[20:80])\n", "plot(abs(fft(modulated[512:1024]))[20:80])\n", "plot(abs(fft(modulated[1024:1536]))[20:80])" ] }, { "cell_type": "markdown", "id": "cf1ee9a4", "metadata": {}, "source": [ "First, compute spectra of length 512 (just like you did above) every 16 steps. This will give you `len(modulated)/16` vectors of length 512. You can actually put these together into an image and display them. This is called a _spectrogram_. If you plot `result[:200,1:80].T`, it should look something like this." ] }, { "cell_type": "code", "execution_count": 32, "id": "12ea208e", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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PW+a5UmUzzSfJVZREwN4q0MKHwmqfdoKCnQnyWL/cbHbWajW8/PLLeOONN1Cr1XDMMcfg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\neKhtDGrAQiqbJwETVRoS1/b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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "# YOUR CODE HERE; OUTPUT SHOULD LOOK LIKE THE IMAGE BELOW\n", "axis(\"off\"); imshow(imread(\"Figures/example-spectrogram.png\"))" ] }, { "cell_type": "markdown", "id": "3c1efdad", "metadata": {}, "source": [ "Next, try to recover the instantaneous value of the frequency from this. This gives the value of the modulating function. Plot it relative to the original signal; note that you need to subsample the original image, since the way you computed the spectrogram involved stepping along the original signal every 16 steps. This computation actually takes only one or two function calls to standard library functions. \n", "\n", "Note that the decoding works a lot better for arbitrary signals if you restrict the frequency bands where you are looking for spectral peaks to the range where the frequency modulation is actually occurring." ] }, { "cell_type": "code", "execution_count": 31, "id": "85658ec8", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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L4pG7EI7pZSLduFqT7WXcxMIz5AmgtZ6tDjik+EzLyU6LYPYknpX6qdMG9SWa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\nFIdnyD148OAhxeEZcg8ePHhIcfw/RhPIHsI6oAsAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# YOUR CODE HERE; OUTPUT SHOULD LOOK LIKE THE IMAGE BELOW\n", "axis(\"off\"); imshow(imread(\"Figures/example-recovered.png\"))" ] }, { "cell_type": "markdown", "id": "6f7aec7a", "metadata": {}, "source": [ "Finally, decode your signal." ] }, { "cell_type": "code", "execution_count": 30, "id": "48d5c00d", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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IX85UNHgfTn3/iPAY9J0otlS7fkN8xdR314lCXaH48/0HxeAX/xImIYS5NEXM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\nRK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# YOUR CODE HERE; OUTPUT SHOULD LOOK LIKE THE IMAGE BELOW\n", "axis(\"off\"); imshow(imread(\"Figures/example-decoded.png\"))" ] }, { "cell_type": "markdown", "id": "4516cc47", "metadata": {}, "source": [ "You have now gone through the steps of frequency demodulation using a FFT. This is actually something people do as part of software defined radio (e.g., GNU Radio).\n", "\n", "Wrap up your function so that you can apply it to any modulated signal:" ] }, { "cell_type": "code", "execution_count": 121, "id": "10572d6f", "metadata": { "collapsed": false }, "outputs": [], "source": [ "def fft_fm_demodulate(modulated,lo=1,hi=80):\n", " \"\"\"Perform FM demodulation. Search for the peak frequencies is\n", " restricted to the frequency bins in the interval [lo,hi).\"\"\"\n", " pass" ] }, { "cell_type": "code", "execution_count": 29, "id": "ecdb3b03", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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ZmnFTxlDqsZ3JHz+vTV2hCcV0GkThiigidpNoVeL3ylRKfzufIe+uhmIt+WbM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\n5ti7SZufkDse5xwpeA6KLNCZk988vPz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2f2lFRP6NgicirqHgiYhrKHgi4hoKnoi4hoIn\nIq6h4ImIayh4IuIaCp6IuIaCJyKuoeCJiGsoeCLiGgqeiLiGgicirqHgiYhrKHgi4hoKnoi4hoIn\nIq6h4ImIayh4IuIaCp6IuIaCJyKuoeCJiGsoeCLiGgqeiLjGXyHmeG0rfILLAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# YOUR CODE HERE; OUTPUT SHOULD LOOK LIKE THE IMAGE BELOW\n", "axis(\"off\"); imshow(imread(\"Figures/example-fmresult.png\"))" ] }, { "cell_type": "markdown", "id": "7ec42a02", "metadata": {}, "source": [ "# Decoding with Quadrature" ] }, { "cell_type": "markdown", "id": "134429f6", "metadata": {}, "source": [ "Try to write a quadrature demodulator for the above signal. Have a look at the section on quadrature detectors here: \n", "\n", "http://en.wikipedia.org/wiki/Detector_(radio)#Frequency_and_phase_modulation_detectors\n", "\n", "This is actually very simple (two lines of code) once you figure out how." ] }, { "cell_type": "code", "execution_count": 28, "id": "d05f7f43", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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PRrwwrDeelbwZEvwSfZ55yPXZCyLZdBJe7tmSJp0GEex2govXMnB0cmTDG4NY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\nnARBkKX/A5VaTI0E9sWQAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# YOUR CODE HERE; OUTPUT SHOULD LOOK LIKE THE IMAGE BELOW\n", "axis(\"off\"); imshow(imread(\"Figures/example-quadrature.png\"))" ] }, { "cell_type": "code", "execution_count": 20, "id": "e1c049b2", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The quick brown fox jumped over the lazy dogs.\n" ] } ], "source": [ "print signal_decode(-decoded)" ] }, { "cell_type": "markdown", "id": "686341e4", "metadata": {}, "source": [ "# Image Steganography" ] }, { "cell_type": "markdown", "id": "9e29c5d4", "metadata": {}, "source": [ "Steganography is the addition of hidden information to images. Let's pick a simple image." ] }, { "cell_type": "code", "execution_count": 34, "id": "4b017822", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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3thU9b2SeBgf3iRvIY36MYSVlRUAim6XhM6fFPGreooFlmvdYxDy2TGCgPOOG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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "image = 1.0*mean(imread(\"geyser.jpg\"),axis=2)\n", "image /= amax(image)\n", "gray()\n", "imshow(image)" ] }, { "cell_type": "markdown", "id": "6b94aa27", "metadata": {}, "source": [ "When viewed as a 1D signal, this image is much larger than our modulated signal." ] }, { "cell_type": "code", "execution_count": 52, "id": "a40288a3", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "12000000 1177600\n" ] } ], "source": [ "print image.size,len(modulated)" ] }, { "cell_type": "markdown", "id": "c7aed4f8", "metadata": {}, "source": [ "Let's add our frequency-modulated signal to this image. Since this ends up in the sky region, it is actually quite visible." ] }, { "cell_type": "code", "execution_count": 53, "id": "424ebb83", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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69Qo3Nzdwu91CTBiETqVS2N7eRr/fRygUQiqVwsXFBdrtNpxOJ/7jP/4Dg8EAjx8/Rj6f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fkO9oBeIpEYeHUJ4a5vcCL1Wbr3gT/bsMnvfUU/8R3fD1bSwBtJHUwBL67p/cjYuDbsyUMOZ6jD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\n6U//Mpe64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RDkGfZN8Gs68/Dwzde5e+E6/ZjNZgdWqfA89D1tJ/rwsiHG1cHaQ0Qcd+yM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WVnQ6nToYTSYTq1evpqWlBVdXVyorKxkYGKClpYU1a9ZgY2ODTqejsrKSzMxM6uvr6e7uVtaX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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "stega = 0.0+image.ravel()\n", "stega[:len(modulated)] += 0.1*modulated[:len(stega)]\n", "stega.shape = image.shape\n", "imshow(stega)" ] }, { "cell_type": "markdown", "id": "101ad76f", "metadata": {}, "source": [ "You should be able to decode the signal using your `fft_fm_demodulate` function" ] }, { "cell_type": "code", "execution_count": 56, "id": "063cf826", "metadata": { "collapsed": false }, "outputs": [], "source": [ "#fsignal = fft_fm_demodulate(stega.ravel()[:len(modulated)],lo=20)\n", "#print signal_decode(fsignal,subsample=1)" ] }, { "cell_type": "markdown", "id": "1a061e0d", "metadata": {}, "source": [ "Have a look at the decoded signal to get some idea of the quality." ] }, { "cell_type": "code", "execution_count": 60, "id": "b7785f05", "metadata": { "collapsed": false }, "outputs": [], "source": [ "#plot(fsignal[:5000])" ] }, { "cell_type": "markdown", "id": "5bc908ac", "metadata": {}, "source": [ "Finally, try to see what level of modulation is minimally sufficient for recovering the encoded signal. Of course, this is highly image dependent." ] }, { "cell_type": "code", "execution_count": null, "id": "b1d1b071", "metadata": { "collapsed": false }, "outputs": [], "source": [ "def roundtrip(l=0.01):\n", " stega = 0.0+image.ravel()\n", " stega[:len(modulated)] += l*modulated\n", " fsignal = fft_fm_demodulate(stega[:len(modulated)])\n", " return signal_decode(fsignal,subsample=1)\n", "\n", "for l in exp(linspace(log(0.5),log(0.001),20)):\n", " print \"%.4f\"%l,roundtrip(l)" ] } ], "metadata": {}, "nbformat": 4, "nbformat_minor": 5 }