{ "metadata": { "name": "", "signature": "sha256:34482166f6ab7fedee41d7d32fdd334177e42045a9dc0fa0c23df92b77dc7bd8" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "%pylab inline" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] }, { "output_type": "stream", "stream": "stderr", "text": [ "WARNING: pylab import has clobbered these variables: ['f', 'mod']\n", "`%matplotlib` prevents importing * from pylab and numpy\n" ] } ], "prompt_number": 36 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Amplitude modulation" ] }, { "cell_type": "code", "collapsed": false, "input": [ "f = 10 # Hz\n", "time = 1 #seconds\n", "sr = 44100\n", "\n", "phs = linspace(0, 2* pi* f* time, time*sr)\n", "plot(sin(phs))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 37, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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CHlQmOGivOYC+CAYG5CePMVpwSFaCtDYHl3rUdox59VC1IK09D3lQmeBQZhG4\nKqGLcLDSytAO0lWqXiwE6rx60LZJsKGFuJXVASxki3lFMDsLIyOy20mLg8v9/doOyUKmZkWPRZKV\n0dHiHPLqwZUex8bkrEKeVmuVtJAHlQkOFnYEaGftFjiMjeVfhLSQqWknCqAfqF31+0G/clizRm6v\nMzurx8GCHvOgMsHBQnQukrW7EkBeDq6NcW4uHwftTK1KO1SKOGZXfW7tNQfQt0sL6095UJngkFcA\nVer3F+HgUoTa2WLRTE173UN7zcG1Y7YQoMqsx1g5FEReASS9Vc1+v0tD0K4coFifWTtT0173cJms\n5HXMLitZbS2Avl0WXfeIwaEgtEtH0M9QrHDQrhzGxsTBLi9n/13t08kzM+6SlbJXDlWxif5+WcPJ\ns+4R20oOoC0AsBGgtLMkKOaUXHAoYowW+v0WHLMFLWjbRNUSx6yoTHCw0k6xYIzarQQrjlEzQFlw\nihY4FGltadtE1dq9WVGZ4GBlIVZbABY4WOgz59HD8rLssnKxv9+CUyzzmkMVbUI7QGVFZYJDmQWg\n7RTBRraonanNzLg7jDg2JoEm67qHhSDteh609WjBLvPo0eVhxDyoTHDIuwhpJUPRrl5cl/FlDNQu\nr9/XJ4FmZkaPgxXHrK3HsiaOLjcn5EFlgkNfnwxkVmO00tvUzpKq5pTyOATXJXwex2hhMbhq608W\nWjp59ai13gAVCg6gny1ayFAscMjjlFz2+xMOWbXg+iZneRxjFR2zth6t2EQeLWitN0DFgoN2dLbQ\n27SyMK9dQmtrAfJXDq44jI7K7duXlrJzsLDmoFnRu+73W9BjVlQqOOStHFyJ0IoxWsiStA1BWwuQ\nzzG6XvdIboSYBRZ2K2kvBrtOVrS7GnlQqeCQRwQuRVirrRyVzwIL1Yv2moOPlo6mFiCfY3TdStAO\n1FZaWxYSBW0tZEWlgoOF6KxdPua5/tKS+36/hcVgC1pY7RzKuubgI1HQ1kJWVCo4aDtm0F94yrtl\nbmzMbb9f2xCsaKGsHFzpcWQELl+GxcX0v7O0JO1Zzc0JVdRjVlQqOGg7ZtAXwcgIzM9nM0YrDkk7\nSFtYc/ChR80WX60mfytLq9XK5gQLlWxsKzmCtmMG/SwlMcYs42ChlWEhSFtYc6hioM6qBws2WcU1\nsKyoVHDQdsyQXQSuS+g8HKq2CJpwsKCFsnLQ1IOFRKGKesyKSgUHCzsCsoog6ffXanocrDgk7UzN\nStau6Zhw+rwtAAAVjUlEQVSTZGVkxB0H7cpheFjarAsLehws6DErKhUcLERn7ZaOBQ4WjNHK+pOF\ndkbWZMX1/XyyBijXWsjbatVec4hbWR3CQnTWztrzcnApwjzGWNVWQtk4+EpWymYTFtYcYuXgEFkF\nsLQk2+y0+/3alcPUlJtnFjcjj1NyycFKFVk2Dj70mGfNQdsmtJNGHxyyolLBIa9j1uz3T03B+Li7\n61vhkMcpueSQd/3JJYesTnFx0X2ykscxV1GP2pXD4KDcr2l+PhuH2FZyBAsizOqULl6sJoesTsk1\nh6Gh7MZ48aLumkOiR5fJSlYOVdVjHg7r17u7fq2mbxNZUangkEcAriOzhQCVlYMvY9TkkGfdwzWH\nPM7Ahx7LVjn4Sla0OWjrMSsqFRzKKgDXDiFPe61qlUPCIa0e6nX9ysFKkK6iHi04Zgv+KQsqFRyi\nAPJz8OEQtMchix7m5mBgQHrDrmAlQFrgoK1HC3aZxSbq9bjm4BSJAOr1dN/XdkhV5qB9KjbhkNYY\nfYxBEmguX9bjULYgbYWDLz2m5TAzI+eF1qxxyyELKhUcBgel15x2EdJKllRFDmVzSr6ytCwOwUKQ\nrqoeLXDIYhM+WmtZUangANlEUNXepgUOWZxS8jwJH2ctNCsHyO4QVnt7r8ocsiYKmi0lqGBwyCIC\nC73Nqu4OyeMUXW7hTDhoZu2gXzkkY5C21VpVPWbhsLDg/rwJZLMJ7cVoKBYcNgF/C3wP+BtgQ4fv\nHQaeA54GHitwvVTQzhazGqOF3SEWsiRfjlnbGLU5DA5Cf7/cTC8tB209alf0Ps6bgA2byIIiweFT\nSHC4Ffi7xvt2qAMTwOuA1xe4XipoZ4sDA2KMmouQWbdwarczfLZ0tI3RAgdtp1S23UoWWoxlDw4P\nAA82Xj8I/Msu33Ucgztj3ToZ2DTwaYyaHLJc/9IlCWYut3CC/D9p9tpBfx4ih+zX93HeJOGgvRhs\nIUBlQZHgsA040Xh9ovG+HerAN4AngF8ucL1UWL8eLlxI911fE7B+va4xal8f5G9amIe0HHwFqKjH\nlceELi/3/u7srNz6ZGDALYesetTWgoXdSr120f4tsL3N5/+55X298dMOPwocA7Y2/t6LwP9p98V9\n+/b90+uJiQkmJiZ60LsaFiZA2yGMjcnun8XF3vukLTjmyEFQ1QDV3y+anJrqfb8iC/NghUMnLUxO\nTjI5OemMVyf0Cg5v7/JvJ5DAcRzYAZzs8L1jjf+eAv4MWXfoGRzyImuWpGmMvrZw9vWtlPKbNnX/\nrhVDsMBhxw59Dtrj4DthisEhPYdOY9WaOO/fv784uTYo0lZ6GPhA4/UHgIfafGcUSNzvGPAO4PkC\n1+yJMokguV+7610RWThoj4FvDtrtNQsc0rZUFhfdP888QVo9+AxOFy+m20VYZZvIgiLB4XNIZfE9\n4N7Ge4Brgb9svN6OVAnPAI8Cf4Fse/UGCxOQ1hh9CiCLMfqonpIF6TR95iobY5nWXnydN8nCwVc1\nn9w3a2YmHYeq6jELity54yxwf5vPXwX+eeP1QeCuAtfIjLQT4GtXRBYOFoKDLw79/ZKBTk/3/vtT\nU7C93cpWQVgwxjJxqLIeEw4XL/Z+iI+v6mV8XL+KzILKnZBOm6klWziHhtxzsGIIq51DmRaDfd6F\nU3seysihihsDsqJywaFsIvSdJWly0G6vJfNQhj5zcstw11s4s3BYDTahyWF4WNqsaQ7Iat+uG1Zx\ncPA5+NoijBwEg4OylXduTo+D9hhk4RBtwi+HWk2fQxas2uBgQYSrwRhj9RLnAdLPw2qwCW0OaRGD\nwyrnEI1xZQun6/Mmaa8P+mOwGjhoJwpgYxzSorLBoVefueoCKBMH7QDlcwvnyIgEn14PoLIwD5GD\nDQ7z83Lb8JERPxzSonLBYXhYjLzXLYp97UiA8ogQ5DtV59CrpeJTC2n7zFGPAgt61J4Ln8lKFlQu\nOEC6CTh/HjZu1Ls+wLlzsKHTUzACcdAeh+Xl7rcKCMHB5xhAunaG9jyAfz2mWffwPQ7aHLS1kAWr\nNjhU3TGn7a+eP687DtPTcljO14PU0wYHX2OQloNPPa5dK3c7XVrq/j0LAUpbj4uLcopas3Lwrce0\nWLXBwachjI5Kz3BhoTcHCwFKk4NPp5iFg89MTVuPzTdi7MVhtesxaWv1efKMFvSYFqs6OPgSYa2W\n7qi8dhnvu6VjoYTW1kKZOFiopn06Ru0gnYVDrBw8IY1j9B2d0zpGTWOcmtJv6VioHKw4ZgtOyWeb\ns9ddURcXpf3V695HeVEWLcTg4BEWJkDbISTPDe52V1QLY2AhU7PimH3ORZpkxWegXrNGdhJ2e5b1\nhQsyVlVu6VjgkBaVDA7aWTv0FkHS0vG1ba/56VudYMEQtOchFAfNfn8WDpp6iHoMwyEtKhkcLETn\nXhympsR5+2rppOFgwRBiW0mgrUffLZ00HELNQ7fW1moI0mmxaoODtkMIUTpaMMZefWbtbBX0HTPo\n6/H8eb8tnbQcfI7B0JD8/3U7IGtBC74TprSoZHDYsEGE1gm+d+mk4RCidOzFwbchDAyIQXbrM4dw\nit3GYLVwSKNH38mKth7TcFgNWkiLSgaHTZvg7NnO/548Daq/X49DiOygF4cQIty0Sf5fO8H3OPS6\nPvh3jL3mYWFBbivu8/79VrRggUM3PfjmkIyBZjWdFpUMDps364swDQffAkhjjCE4nDmjx2HjRinj\nu50O9h2gemkh2aXj8146ZUlWtPXou3oZHpaKuls1HdtKHqHtkNJyCBGgehmCdpD0zaG/XzJyzV63\nBT320oIFDqH0aMEutZPXNKhkcNB2SGAjU7MgQuuOcXHRf0vHih61HbOVtpL16iW2lTyiV1/PQta+\nWkRoPUAlu3R8tnTWrpV79Hd6dvBqyVYt2ISV6qXTXFy6JBtmhof9ckiDSgaHoSF5fnCnvp6FDOXc\nOb+7pSCdIfjmYCFj7WaMIbRQq/UOUNqVg4UAFUqP2kEyjRa0n+UAFQ0O0N0xnjkj/651fRCBbtni\nl0MvQwjBoVeWND/v9+AVdDfGEFqA7uNw5kw4LXSqpkNxsGATnTjU68Jh0ya/HHppIYQe06CywaGb\nYzx9GrZu9Xv99evlFHSnXTKnT4dxzN2M8dQpXQ6JQ/KdJXUzxhDzAN2dUggOQ0Py0+l2KqH02C1Z\nCaXHThympqTj4Lulo62FtKhscOjmlEJMQH+/BIhOe6pDcOgWIJeXw2RJvYL0anDMYCNAaXPoVTlo\nc1gt85AWlQ0OVpySJoduAfL8edmhMzCgx8GKMfquIsGGU9LmsGGDrAMuLl79b5cvS5vR140oE1jQ\no/Y8pEVlg4MFEWhzGB2VttbcnM71QT9AJhwsaEF7HLT12NfXuZpOeu2+W4wW9GghWUmDygaHbiII\n0dvsxiF5nu/YmN/r12qdhbhaHJIVDt0ClLYekxaj5sK8FS2slioyDSobHCw4hE4cQi3EQmchhhqD\njRslU2y3SyakMVrPFjX1eOGCJCq+W4zdOIQag9FRCYaa1XQ3LYRKFNKgssGhk0NYXBRjCHECsROH\nkNmBdqY2OAgjI+3vYa/tFCF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"text": [ "" ] } ], "prompt_number": 37 }, { "cell_type": "code", "collapsed": false, "input": [ "f2 = 2\n", "phs2 = linspace(0, 2* pi* f2* time, time*sr)\n", "plot(sin(phs2))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 38, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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VKD+Ux++/h3XrvLNkRlmaHNQPxo6Vi9HLQ1rnzpUhrF4aMqiiGz1aOnK9PKR1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\nYII=\n", "text": [ "" ] } ], "prompt_number": 38 }, { "cell_type": "code", "collapsed": false, "input": [ "out = sin(phs) * sin(phs2) # Ring modulation\n", "plot(out) " ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 39, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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jz34GBw4k/0w/XLLjt78Nb36zjMEVK2RiT8oXviBC84lPwC9/CT09yT/TD5fKnN/5Drzu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\n/EHl8R8AD/q8ZwTgLc2MBF4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"text": [ "" ] } ], "prompt_number": 39 }, { "cell_type": "code", "collapsed": false, "input": [ "out = sin(phs) * (1 + sin(phs2)) # Amplitude modulation\n", "plot(out) " ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 40, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 40 }, { "cell_type": "code", "collapsed": false, "input": [ "phs = linspace(0, 2* pi* 30* time, 300, endpoint=False)\n", "plot(sin(phs))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 41, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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T129dBnoslsUOBjbktX37ReoxEnNuCSH6ADBE+tfF6shdXbEwpKwMLIsdDCyL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\n5a4g9y91ACj1RbHXQXXE2wD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"text": [ "" ] } ], "prompt_number": 41 }, { "cell_type": "code", "collapsed": false, "input": [ "phs2 = linspace(0, 2* pi* 3* time, 300, endpoint=False)\n", "plot(sin(phs2))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 42, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 42 }, { "cell_type": "code", "collapsed": false, "input": [ "out = sin(phs) * sin(phs2)\n", "plot(out)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 43, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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WTaPE/Lyym4HICpOW7UlE4LL0GwjH9vbsgYsugg0b4jO4PAjKAezcqQaX9oDm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\nh6Fl33lsD9yWnctCEfM/BXh24etnF76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"text": [ "" ] } ], "prompt_number": 43 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(abs(fft.rfft(out)))\n", "xlim((0, 40))\n", "grid()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 44 }, { "cell_type": "code", "collapsed": false, "input": [ "out = sin(phs) * (0.5 + sin(phs2))\n", "plot(out)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 45, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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v59pr4WUvg7PPhltvnfv/x8fl+whzEsVf1IEiUO11AFHcua4m9RVCmJ6Ww2mC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\ngMeAVyOJ4EgEDUAWGC+kXk+fGHp6YM8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"text": [ "" ] } ], "prompt_number": 45 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(abs(fft.rfft(out)))\n", "xlim((0, 40))\n", "grid()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 46 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Phase modulation" ] }, { "cell_type": "code", "collapsed": false, "input": [ "f = 10 # Hz\n", "time = 1 #seconds\n", "sr = 44100\n", "\n", "phs = linspace(0, 2* pi* f* time, time*sr)\n", "plot(sin(phs))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 47, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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CHlQmOGivOYC+CAYG5CePMVpwSFaCtDYHl3rUdox59VC1IK09D3lQmeBQZhG4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\nkNmBdqY2OAgjI+3vYa/tFCF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"text": [ "" ] } ], "prompt_number": 47 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Linear phase means constant frequency (frequency is the first derivative of phase)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It's simpler to do phase modulation (in ipython...):" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fm = 2\n", "mod = sin(linspace(0, 2 * pi * fm * time, time*sr))\n", "\n", "mod_phs = phs + mod\n", "plot(mod_phs)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 48, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 48 }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "mod_phs = phs + (2*pi*mod)\n", "plot(mod_phs)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 49, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 49 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(sin(mod_phs))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 50, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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wDrt32zmXr7W+RnNB+nXAZuAZ4MNNPvO5xt/XA6tUTl61msP06SJUWZ6ECw4f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\nzpyBu+6qnnEoOq1k4qyEyCG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"text": [ "" ] } ], "prompt_number": 50 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(abs(rfft(sin(mod_phs))))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 51, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 51 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(abs(rfft(sin(mod_phs))))\n", "xlim((0, 30))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 52, "text": [ "(0, 30)" ] }, { "metadata": {}, "output_type": "display_data", "png": 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fcNgs4D6GxD4zgZ8h0Y+ftHdxxrp1616/3dbWRltbm8vmE8HYWGaK3SAEmdK5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\nKv4W2Ob9hnI5/6iRD+SPfaJ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"text": [ "" ] } ], "prompt_number": 52 }, { "cell_type": "code", "collapsed": false, "input": [ "f = 4410 # Hz\n", "time = 1 #seconds\n", "sr = 44100\n", "phs = linspace(0, 2* pi* f * time, time*sr)\n", "\n", "fm = 2205\n", "mod = sin(linspace(0, 2 * pi * fm * time, time*sr))\n", "\n", "mod_phs = phs + mod\n", "\n", "plot(abs(rfft(sin(mod_phs))))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 53, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 53 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(abs(rfft(sin(mod_phs))))\n", "xlim((2000, 8000))\n", "grid()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 54 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Cool idea found in: http://nbviewer.ipython.org/github/jakevdp/JSAnimation/blob/master/animation_example.ipynb" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from JSAnimation import IPython_display\n", "from matplotlib import animation\n", "\n", "fig = plt.figure()\n", "ax = plt.axes(xlim=(0, 22050), ylim=(0,17000))\n", "ax.grid()\n", "line, = ax.plot([], [])\n", "amp_text = ax.text(10000, 15000, \"\")\n", "\n", "x = np.linspace(0, 22050, 22051)\n", "\n", "phs = linspace(0, 2* pi* f, time*sr)\n", "mod_amp = linspace(0, 4*pi, 100)\n", "\n", "def init():\n", " line.set_data([], [])\n", " return line,\n", "\n", "def animate(i):\n", " mod_phs = phs + (mod_amp[i] * mod)\n", " line.set_data(x, abs(rfft(sin(mod_phs))))\n", " amp_text.set_text(\"mod_amp = %f\"%mod_amp[i])\n", " return line,\n", "\n", "animation.FuncAnimation(fig, animate, init_func=init,\n", " frames=len(mod_amp), interval=300, blit=True)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "\n", "
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\n", "\n", "\n", "\n" ], "metadata": {}, "output_type": "pyout", "prompt_number": 55, "text": [ "" ] } ], "prompt_number": 55 }, { "cell_type": "markdown", "metadata": {}, "source": [ "http://www.soundonsound.com/sos/may00/articles/synth.htm\n", "\n", "http://www.sfu.ca/~truax/fmtut.html" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "C:M Ratios" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The ratio of the carrier and modulator frequencies is called the C:M ratio" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* FOR THE CARRIER TO BE THE FUNDAMENTAL: M MUST BE GREATER THAN OR EQUAL TO TWICE C, OR ELSE BE THE 1:1 RATIO.\n", "* WHEN C IS THE LOWEST FREQUENCY IN THE SPECTRUM, THE SPACING OF SIDEBANDS ABOVE IT (EXCEPT FOR 1:1) WILL BE: M - 2.C & 2.C\n", "* Harmonic N.F. ratios are always of the form 1:N, and inharmonic ones aren't.\n", "\n", "http://www.sfu.ca/~truax/fmtut.html" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Frequency Modulation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To do frequency modulation, we need to work with phase increments per sample:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "f = 10\n", "phs_inc = ones((time*sr)) * 2*pi*f/(time*sr)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 57 }, { "cell_type": "code", "collapsed": false, "input": [ "phs = cumsum(phs_inc)\n", "plot(sin(phs))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 58, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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NgTNbzPOS3iz6gjLko7SUtqwUJVd7EcBWADMA7gXwBIC31/vgF7+4B+3twJe+BIyMjGBk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\nV5CuTpha1R8NQxDQc86E6Y0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"text": [ "" ] } ], "prompt_number": 58 }, { "cell_type": "markdown", "metadata": {}, "source": [ "... Left as an exercise to the reader ...\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By: Andr\u00e9s Cabrera mantaraya36@gmail.com\n", "\n", "For Course MAT 240B at UCSB\n", "\n", "This ipython notebook is licensed under the CC-BY-NC-SA license: http://creativecommons.org/licenses/by-nc-sa/4.0/\n", "\n", "![http://i.creativecommons.org/l/by-nc-sa/3.0/88x31.png](http://i.creativecommons.org/l/by-nc-sa/3.0/88x31.png)" ] } ], "metadata": {} } ] }