{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "fourier transforms\n",
      "========"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f = np.ones(101)\n",
      "g = np.ones(101)/10\n",
      "#y = np.linspace(1001)\n",
      "for i in xrange(len(f)):\n",
      "    if i > 11:\n",
      "        f[i] = 0\n",
      "        g[i] = 0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.subplot(131)\n",
      "plt.plot(f)\n",
      "plt.subplot(132)\n",
      "plt.plot(g)\n",
      "plt.subplot(133)\n",
      "plt.plot(f+g)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "[<matplotlib.lines.Line2D at 0xb14f9d8c>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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PzOQWtsBruRuhy+VCbm4usrKygr7bbThY4NXEQqAm7q9yC3kd/PU709XX18NsNiM/Px8O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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb1437eac>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.subplot(131)\n",
      "plt.plot(np.fft.fft(f))\n",
      "plt.subplot(132)\n",
      "plt.plot(np.fft.fft(g))\n",
      "plt.subplot(133)\n",
      "plt.plot(np.fft.fft(f+g))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/usr/lib/python2.7/dist-packages/numpy/core/numeric.py:460: ComplexWarning: Casting complex values to real discards the imaginary part\n",
        "  return array(a, dtype, copy=False, order=order)\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "[<matplotlib.lines.Line2D at 0xb14a39ec>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Vq1xs1q9fP2zduhX79+/Hc889h0ceecTtsfiBbSxGhWLUYuyXLgHNzUCHDu49\n9vffB/7zP4Ht24N/nqFAYyPw5ZfAgw8CH37our22lpJHOnRwL+wh4bF7Mz0ZYM/OSKTuus3m/H5R\nUREGDBiAhIQEREVFYcqUKVi7dq3TPiNHjkSXn2ZPjBgxAhUVFW6PxQ9sYzEqFNOunWsoRvLWbTb3\nHntxMfDQQ5SvrTVWu307efRqvYJQ4+RJ4J13gGPH1Ld//TUQFweMHKmeKXT6ND0IAXVhl9Y0CJRd\nAxZj9zQ9GXAv7AcPco67L3z9tfr7Wt31yspKxMfHt7yOi4tDZWWlZvtvvvkmJkyY4PYc3Nn1+HHg\n4kW3H2dUcHc/GBWKUfPYJWEHHMKuPM8ff6T3r70W6NED0OrE33sv8NRTwPr12uewdasxwn/qFOAu\n4rh4MfDMM8Dzz6tv376dRD05WV3Yv/+erhegLuyB9NaBAKU7upueDDhmstXUANu2ZSMpKdtpe1MT\ncP31wMaN9GNg9HHyJJCRAVRXu05P/vRTO5qa7Pjp0rdgU7rwbvj000+xfPlyfPHFF6rbJbuWlAB7\n92bjjjuyXfa57z6KtT7wgO7DMgBuuAEoLASGD3d+3263o7rajldfBTp3Du45uPPYARKi9u0pfS86\n2rHP0aNA//4UBhw2jGLOgwY5t/PttyRmc+dSiYK77nI9flUVcMstwNChNNtVTfjKyoDx44GPPgIS\nEtS/x4cfAgsWUBvK0CRAQnzTTUDXrsChQ669XACw24H//m9AazLo7t1AVhblqR85Qg87eTtSfB0g\nu1265Jy3XlcXuPg6AED4SX19vRg7dqx4+eWXVbfLDzF4sBD79rnu8+WXQgBCvP++v2fTuvj8c7pu\n69a5bjt9Wohu3RyvJTts375djBs3ruX9/Px8UVBQ4PL5ffv2if79+4uSkhLVY8vtes89Qqxa5brP\n+fNCtGkjRF6ezi/ECCGEqK4mu6qYRQghRK9eQpw8SX8H4BZ2Qt7e0aNC9OvnvP3994WYNMnxul8/\nIY4ccd5nzRohJk6kv3//e3X7v/MO7bN9uxBDh6qfy6uvCnHffUIMGybE5s3q+8yeLURqqhA33KC+\n/cwZIWJihEhKEuK999T3mT9fiLlzhejbV4i9e123nzsnRKdOQtTV0bX/9lvXfW65RYhPPqG/e/YU\n4sQJ5+1vvCHEf/yH47XchkIIUVkpxFVXOX/GH9v6FYoRXkxPBrS77Js30//Hj/tzNq0P6XpJ10+O\nVnc9KyugpPaPAAAgAElEQVQLJSUlKCsrQ319PdasWYPc3Fynfb777jtMnDgR7777LgYMGODxPLTs\n+tln1Btju3qHO7sCxmbFuPPYAYobK+PsxcUUkgCAfv3U7f/559QrufZailtXV7vus3o1MHUqMGYM\n8OmnrtsvXKAYvd1OnrZaRHHDBuC664AlS4BXXlH/np9+SnVbpkyhYyr57DNqo107iix89pnrPseP\nU4kFQD0cI/fYAddwTKA9dr+E3ZvpyYBj4WMlmzeT8VgAvOP4cbpuagKglTkRGRmJpUuXYty4cUhL\nS8O9996L1NRULFu2DMuWLQMAvPDCCzh37hzmzJmDzMxMDFfGAxRoZcWwXX2jtBTIzga2bVMvm2tm\nVszZs0C3bo7XPXu6ZsYcPQokJdHfWsK+axeJZVQUiftXXzlvr6uj98aMAW6+WV3Yd+4E0tPp4XLD\nDRSPV7J1K4VZbrmFxi1+/NH1OLt20edvvZXCQkqKiuhcAYqjFxU5b29ooMqNV19Nr9Vm5Mpj7ICr\nsIdUjN2b6cmAtmd35AjF2rTqFDPqlJYCd9wBPP206zZ3mRPjx4/H+PHjnd6bPXt2y99vvPEG3njj\nDd3noZUVc+QInZ9KqjzjhuPHSeyOHycvVPIEJczMirlwwVnY1Tz2igoqEgaoC7tUlzw1lV4PGkSi\nK692+PXX9HBo3x4YPRrYs4cG4Tt0cOwjDVgCJN5bt5KHL2fLFmDmTPou6ekk4tnZju07dgCDB1MZ\n4qFDaQBVmSZ88CB58wAV8dq40fkY331Hhb2keHlcnGvv4fRpGg+T6NKFrqVESHns3qIl7DU1jh8y\no5/jx+lH2dTkegMa1V0H3Nt1yBDgzBn1GYyMOlK3vmtX9WXUzJygdOECiaCEmsdeWQnExtLfffqQ\nZ3rpkvP2Tp0cA/6SsMvZswe45hr6u2NH8oKVWStyYb/xRldv+/RpeshIgjpypGte/a5dgJTIFx1N\nDyqlt33woGPwV63w2fHj9ACTiI11FXalx37llc7CHsjJSUAICHtzM42qZ2RQ7Wee6KIf6QelJgCh\nIOznzlGXMz6eshcYfZSWOux67pzztuZmepAb4bFHRdGx5BVZf/jBORsnJoayVySEIDGNi6PXbdoA\nffs62//wYRJIicGDXdN29+wBMjMdr6+5ht6TaG6mUIwk7JJ+yO+DnTspq0i6VmrCLn+AAHRM+XHq\n6sgjl0JLiYmUjSZ/UCmFPS6OroGc77+nayXRuTNdS/lxAhmKMVTY27VzjRnW1lKh/o4d6YnmJqWa\nkXH5MnkkcXHkaSiFvb4+wOlTblCzK0DnFB1NN0NpqTHnYgVKS+maqdlVWhfTi6xVn7HZXL12pceu\nLAR24QJ9Ti7+/fo5T+yR6pJLSB67PB9eTdjlU/WPHqVj9O5Nr9u0oVCKPFa/axdaFq0AyDMvKnI+\nzu7d7oX98GFK3ZTCLJGR9H3kdejlA6eAusdeVeUs7Jby2Nu2dRUA6eYH6ItrzWRjnJEGsdq00Rb2\nQNV29oSaXQGHbdmu3nH6NF0zs+0KuBYCu3DBWbR79XL22OVhGIkBA5yFUKpLLtGtGzl20mpNjY3A\ngQMk1BKZmc7CXlTkmuM/bBiJucSuXc77SHF/6Ti1teSNyx8yygeIPAwjoQzHlJQ4PHrAVdibm12z\nYizlsasV7j93ziHs3bqppz1JtLaZqe6+b3W1YxArOtq1y375srHCrrRrQwP9WDt1Yrsqcfd9m5ro\nhu/SxXy7Aq4eu1ooRu6xqwl7UpJz3Fop7ACJuOQpf/MNtSE/Tno6vS+di1K0ARJ2KWNFCFeP3Waj\nz0j77N1Loi0PWV57LQm7ZKM9e5wHPQE6d3nVSqWw9+hB2TdSuObcOboP5B55584W8tjVuuw1NRRL\nBNwLwN69NLOstjaopxgyCEFZA8oReAm5sKvF2M0OxUjeus3m3q6nTtHA2KFDwT/PUOH226mkrRrn\nzpGoR0QEx66eKnsqUfPY5aEYpccuj69LJCdThpTE11+7esFZWVREC6BwinIGeseO9JmdO+m1msc+\nfDhluQhB4ZG2bV0fMnJh37KF0hzlxMRQ5o0UOvzyS+eHA+A82Nvc7JzeCdBvvk8fh9deVeWoEyOh\nDMVYzmOXh2K0qp4JAdx9Nw2yeqggaxm+/ZZukvvvV6+1Ip8ootZlN9tj12NXAJg9m7qp27YF9xxD\nhaYmEpT/9/+cxU6iujp4dtVT2VOJWoxd7kl37073pTR47sljr64mr79vX+d9PAk7QLnomzeTN3zg\ngHNsHKDYd6dO5HF/8AHlpSsZPhyQKmRs2kRtKpHy6pubqS3luQwZ4hjsraigB7Cykoo8HKMcOAVc\nQzFh7bF7irFreXbV1ZQyd/fd5Lm3Bvbupdzc7t3VK8opQzGhFmPXY1eAPKxHHmk9dj12jLrq2dnO\ng3QSeuzqqwDoqeypRDlJ6YcfnD32Nm3oN3rmDL1WE/a+falnVlfniFkrB38lYReCRFUp2oBjMt4/\n/0npjUoxtdmo5sw//0n/1OrP3HQThYIOHybP/cYbXfe59lo6lyNHKC4uz9sHKCZ/9CjZ4sgRxyxb\nOfLMGOXAKaA+eBq2Hrtal/3cOc+hGClLQB6HU+PQIcfASKhz6hSwb592SdM9e+j7amWUKEMxylis\n2aEYPXb98Uf6cd96q3u7HjsWPmtr1tTQd9GqSOjJrvKZnVp29fWB7W1lT8B5klJDA30v+SQhwDkc\nU1rqWowrMpLeO3aMPO0hQ1yPExtLse6PPybhVZvsPHo09dj/+7+B6dPVz3fiRApz7dtH64uqfZ97\n7wXuuYcGZNUKqY0bB/zf/1Gpgqws1+3t29P3KS52ja9L9O1LvW7AsXKSHLXB00Der4YuK62ny67m\nuR0/ThcyMxNYuVK97SNHyAgdO9KF1EoHU1ZdCxbS4IvWscaOpaf+v/9NU6aV7N1LFRHPn9cWAHmX\nXenVh0MopqyMboDMTLphm5sptiynvp4Gr5qa6DpI6W1KjLKrp2P9538C69ZRmddf/MJ1+9699H17\n9FD/rQczFKO3smeerCRoXV02Ll/OBuAYOFU2I89ll5wwJWlp9FD7+mvKW1fjV78iL3vOHLqPlXTs\nCHzyCc1kVpQ3amHECCoDHB2t7QHPmUPX+aWX1LcPH04P1aeeogeNGlLu/d699N2UJCY6MnTUPHa1\nwdOqKjvy8uzqB/QS0z12PV126ceSnk4XUz5hQmLnTuC228ibkKdWybHbSUjcdfuLiz2XNti61bVe\nhPJ8Bw1SLygEkEGPHwdmzNBuZ98+EjQ9Hnso5rF7Y9euXWkftZDTgQP0UM/OdgycKSkvpxvHXV3v\nM2eAFSvcf4/Dh93bvqaGwgHPPae9z/btJOihaNfY2FiUy7q05eXliFOOdIKEXfoXE5Pd4rErwzAS\nUmZMczN5qWrlc++4A1izhpIBlIOREk8+SYL9+OPa32H4cPKmr7hCe58RI1yzbuQMHkzFw/r0Ud9u\nswF5eXQ+11+vvs+wYfR7++c/6bsp6dfPYV+1GLva4GlycrbTtfcH0wdP9aQ7SgIgTUM+dcp1H2n0\nWj7qreT//o9yWd2t9Pb731NdCKkbpeTcOYr1P/GEdhtPPEHf6e9/V9/+1Vd0c48c6RgwktPYSEWF\nEhL0C0CopTt6Y1eAJoGozU7VY9cPP6TPT52q/tAHgFdfpQepWqEogD53//3Aww9rh1EWL6YbUMuu\np06R+E2dqm5XgL5z//76QjGBtqueyp5K5DF25cCpRJ8+FE8+cYIe0spQDUDi98knFLOWCmopiYoi\n8Vfz+I3m5z8H/uu/tLc//DCwdi05ivJZpxKJiY4SKRUVVEtGjtrgadjG2LUG2aRYbPfungUgPl49\njv7llxSKGTFC3bMTggTglVdoAEc+JViispJGymfPBvLz1b/DH/8ITJhA56AWFxaCMjyWLqW21Cbu\n7NxJ5ynPBJBz4gTdAFFR7oVd6rJrpcWZPXgq2bVLF0pTVZaLCIRdAQpnPfEEhWmUNUcAOre//IUy\nUX73O/U2/vlP+h6DB5MDoMa2bfTgP39evVdYVEQPocGD6bspU3OFoO8YH08P7fJy1weRHrv66rFr\nVfZ0hzzGruWxp6XRdZdKIagRHQ089hhQUGBcyCyYdOtGi3f88pfq26++mu7jxkb19M4rr6TrKYVs\nw7oImJ4uu1os1pMANDZSF/eaa8izUxOAw4epq5iVRT9EtZXE//Uv8izuv187/e6LL4BJkyj+/be/\nuW4vKyNBzsykPHS12s1SDm5SkiPjR4508wMOYVdOalF6dqEciomIUPc+vRF2aVahcrC5ro688LFj\nyRNUs/0XX9CNNm8e2V3tYfvFF2T7GTNoIWYlTU10LtddRw92tbBPURE9gNq2pQFC5YO/poauRZcu\n5J117+469Vxu144dyZOTn6+/D+zx48ejuLgYR48exW9+8xuP+8vTHbU89iFDKGSmnFqv5KWXXPPG\nw5nHH9deGaxtW3I0Dhyge1x5XSIjaR/JwQz7dEe1QTapypuUBSC/eYWgab9S3quaAJSWkofbpQvF\n4Q8dchXCPXvoprTZtL2/3btJcIcMoR+pmsclDw2oeew7dlD7NhsdT22fr7+m84yIIO9O6WXKhT06\nmlLKlKLoKRZrdihGbldAPRzjya7NzTTbcMgQsm+nTq7FlQ4fpjaio+m679jhen6SXTt1Io/ywAHX\nfaRZilp2PXiQMje6diW7qo3TSHYFHONBcuR2BchrV4b85Ha12eh7nT/v2B5oAfCEfIKSlrCnpVHy\nwpEjoRFGCRUSE2nMZtAg16QAwHkANawnKGkVAZO6d1FR5KXIY0/nz5NwSKPkWsIudQGl0XBlHP7Q\nIcfo9XXXqQuAlLEQFUViovTqjx0jcYiJof3Ubm4pzALQ8ZQzKhsbSdCk85UPskgoBaB3b+fZfYBz\nl71TJ9eHkNkeu9yugHqY7dQpR+xRza7KmK1yajrgale1B7ZkV8C1nghANtm7l/KX+/enh6jyXKUH\nNqBuV8A59S0QdgVcbWt0rRi5x64VirniCvpeK1ZoD4y2RoYPB/73f7WzgOQDqJbz2GtrnScaKMMx\nylQhNQFQls30JABSQX05DQ0O7xAgoygFQD6NOT6evovyAbJ/v0NE1ASgrIxuaOnprLYQgVIAlKVR\n6+pIjCTBu+IKuuHl8VqzPXZPdpUKI0n5vYGw66BB9PBVnouUOw6oD8IePEjHl6byp6e7PrTldk1N\nde0VNjfT+UorCfpiV8B1hSKlsBtdK0aPxw7QfXP11VQugSHmzaO5Gmp5+4DzAGpYe+xqg2w//uic\ns6rMeT51ylXYld1x5aCNJwFITnaski7f3rev41yyslyX65JPL7bZXEt8Su1IAyVqAqCc0KDm2clX\noAHo+8sfIFIOuzQIZbORyMuX/TJ78NSTXaurSbSkc/THrtL4X7t2FN6Q73PpEom9ZBM1uyqnsHuy\nq1SNUB4fLy93vA/4ZlfAdU3Rjh1d7WpkKEbusZ8/ry3sv/0t8M471hgYDRQ9e9KgvHJVJ4kuXRwh\n1LD22JVd9uZm1+Wu5NOTAfJo5JNStDw7eWxPKQCXL5OQS4Lati0JgLxWx969zmVCpQEhOQcOOGKo\ngGs45uxZevJK+bFqAqAUdnlalISnLvuZM843P6DeZTc7FCP32D3ZtUsXegDK48me7Ao4P7ABR4aG\nxNdf04NcuhZSPFi+MIgnuwLUpvI48t5YIOxaX0/3g3xswuxQjNxjl2c6Kbn2WvUZmK2dW25xzWGX\nkI+fhL3HLveSL12iLyNfX7BHD/ehmKuuIoGQC4knz66khLxx+Q0xaJDzjbl/v3N5ztRURz0I+T5y\nAUhPdw7pSCIj91qUQqPHY//uO88ee48ezp/p1MnZszM7FKP02JV2VfbEbDbqyssHEz3Z9fJlCm3J\nr6cnu3boQMeRP9Q92fXMGTqWfEKLJ7t2706hMfmgt5pd5cIuDZzKfz9qdjXLY5dnOjH+I096sJTH\nrvTqANcuu1LYIyPpBpN77UrPTq1MqHIAQ3ljKm/u9u2pTanu8unT9FSVT9RTCoDSqwNc13NUCkCf\nPnRDS2lPFy9SLFPuzSoFQNldB0hEQ91jd2dXwDVLRGlXaRKTlA9fXEzb5d/Tk10B6o1JdhPCdR/J\nq5e+k9oD25NdbTbXOQhlZc7fx1e7muWxyyedMf4jTwEO6zx2ZSxWS9jlXfZTp1zrgyQkOGYpSiVD\n5R7swIHkbUvd7YMHXYV90CDndDRPAnDgALUhv7lTU0l8pB++2morynRG5T4REdSbkATg22/Jo5Sn\nR/kaijEzxu5tKAZwtivgWnfkiivoQSiVHvDHrlKYraqKQoLymYEdOpBNpFVyfLEr4DyAKs0mVoZi\n5D2xULOr8vjuQjGM98gnoGllHPmKqaEYZXcd8ByKAZwFQPKU5ILboQN51lK3XW3m17XXOhfpaWhw\nLTeank4TnwD6Xzm63a4deZFSSeuiItfazXKhOXeODKmsRZ2U5JjJWFbmWmtDTyhGOchmZiimoYGE\nTO6BeArFAM52ra2l66UsZSIXZbWeWEoKjWmcP6/ujQPOWS+SXZWDfvLemJZd5et0qp2L3K6VlZQB\nJLeJ5LFLbei1q5GhGHmFSQ7FBBZ5KCbQD02/hd2bFVkCEYoBnAWguFi9HrJcANQ8u/79ydOuqKCb\nOz3d9ea+/noqHAbQ/2qz5iTxr6ujm1tZ5lOK+TY3Ox4wyskKyckO71BL2D112fUOnuqx1y9/+Usk\nJSUhIyMDe9zV0/0JpV1//JHOR349vbVrSQmlDiqv1eDB7u0aFUUzkHfuJDFt08b1OKNH08zihgbP\ndgWosNfIkc7bu3YlD6u8nEJptbXU05Ljya4dO9L5SSlveu1qpMcuDxewsAcWSdiFCPy19UvYvV2R\nRenZBSIUo1XoXlrl5NIluvmk/GIJm41u1u3bgQ0b1AvujxxJN+apU7TqzZgxrvvceCN9/quvKDSj\nLIAUHU1ZDt99R+ejltMqHxPQEnapeh6gr8uu5rHrsdf69etx9OhRlJSU4C9/+QvmzJnjesIK2rSh\nc5Py6I2wK6DeEwNc7ap8YPfqRccqKqJ9cnJc25DsWl1NIRS1SSZSb0wtTAd4tivgHI7Ra1ezPHaO\nsQcW6aFZW0v3aiAf2H4Ju7crsihjsWqhGLln19zs2bPTEgDJs9uzh2Lu8gVrJUaOJM9Na7WVtm3J\nm3vhBYr1KovlA1Rf5KOPSPiVXp1EejqVIpAEQIknAWjXjrxD6bpoDbJ5ymPXY69169Zh+k+rGIwY\nMQI1NTWoUs6iUWCzOdvWnV2lsMPJk74Ju2TX6moSROUDG/BsV4DE/N13qWegVm1w9Gjy+FevptmU\n8swtCcmuWjXG9Qj7VVfRtQB8t2swkYS9sZHOQyuPnfEeKcYuX5QmUPgl7N6uyKInFCOPxZ4+TT8k\nZe1lPQKQlUU39+uv06oqatxxB02qaGx0zmGXc++9VO1vyhT17VddRXHdhQupnK8aEyfScbRqUesR\nAPlSW1rpjp5CMXrspbZPhXLmkApy26rZtX17EiTpHJWTdQD6TnV1lBWkZdfkZPJsFyyg+vuRKkvF\nSMufbdxI5VfVuOsuKvo2ebK6ULZpQ7XB586lonBqTJxIdb0LC9XtGhNDHnZ1dWDtarSw19Q4Zp2q\n1TxhfEMKxQRD2P1aQcnbFVl+/BGorc0GkA3Ac5ddOaFDIjaW4pJVVSQAahMjEhNpaayVK9UXcAAo\nhW3rVjqO1ld58EH6547Fi6lHoLacF0CC//jjVGtEzavv04dunNOnKb1SbZEAaWJWZqa+LvvZs3a8\n+aYd//634z299hKKCmpan3NeDMCx0o6aXQGHbdu0obROpYjZbI6Vdo4coZVulERF0QIIzz0Hp+8m\nJzqaart8+ql26GDUKIenrMW8eSTeEyaobx85kuL0+/apV/q02ehBVFJCs5bV1gGQT7jTY9fvvrPj\ngw/sqrXrg0HnznT8s2c5DBNoQlbYvVmRBSDxWrbM8b5al71DB+quX7xIP3iV5hAZSfHu/Hyatqt1\nURYsIIHXqhENkJCoLW3lDaNHu9/epQuFc3Jy1B8gEREk2P/1X3QuysVzAboO0qXW6rLLne+2bbMx\nd242UlLo9fz583XZS7lPRUUFYpXpQj8hF/Y33nAfigEc4Zj6eno4q12LW28F3nuPPG4tu8ydS3Hv\nsWPVtwMU5tGayq2XgQPdr8Rjs5FdpTK8alxzDX2figr1B39cnGOAVU8opmvXbEyblo1Jk+j1/Pnz\n9X8hH4iIIHEvK2NhDzRSjD3kQjHersiiZ/DUZnMsjqvWXZeYMIEWvXC3GlJiIol7KDBvnna4B6Dv\n8eqr2t6hVEulro4eesqbTM/gqR575ebm4u233wYA7NixA9HR0YjRmhMtQ25bLY9dr11ff53CIFpC\n0qkT8Npr6mEYo5k2TTvcAzjsOnasepxeXiOnqoocFTlmD54CJDrHj3MOe6Dp2JGcnO+/DzFh93ZF\nFmmATerpa3l2AwZQ/q+Wxw4A48fTTfDww/58g9DhnnvcV8eTPPZjx6gHoox1Kqeeq8Vitey1bNky\nLPupKzVhwgT069cPAwYMwOzZs/Haa6/pOn9Pg6eAPrsOH055/lor04QbWVk0AK81iCvZtb6eelzK\neuZ67KqXefPmITU1FRkZGZg4cSLOywvzuKFrV/bYg4FUb7+sLMRCMQCtyDJ+/Hhd+0ZEkJfV2Eix\n0tpa9cL80mBiRYXr5BKJPn3oRlDLdglH2rcn0dP6PpJnpzWoqLekgJq9Zs+e7fR66dKl3p6+x8FT\nwJHXfdVV2h57mzYUk7aKXQFaItGTXUtLSeSVoh3IkgJjx47FokWLEBERgWeffRYLFy5EQUGBx891\n7Urnx8IeeKKj6dr6Gw5WYvgYt54uuyQAWoOnEla6+QH330caZNOakGV23W62qzbuvk+vXjRLdt8+\n/Xb1NRSTk5ODiJ+6eiNGjNCV7QSQsH/zjWv8n/GfHj3o2gb6oWm4sMs9O60u+8CB5Jl+9512l721\nERtLPZRvvlEf0AuFut1sV++JiKDe56ZN+u0aiAf28uXLMUFrQEdBdDSVV1CbxMf4xw030LUNuVCM\nt+j17LZsoS67Wu5va6RDB8qweP99WnBZidyzE4KusZGer9Kuat7d1VdTSufOncBP47MMKMPr7beB\nP/zBdZsk7EJQTNaTx56Tk4NTytU7AOTn5+P2nwZwFixYgLZt22LatGmqbciznbKzs9G1azbataPa\n4kxg+fnPKV26a1fAbrfDLtUw8RNThN1TLDYhgeLwTz+tnknQWnn2WZpU5anL3thI183Ia6fHrm3a\n0MDvmDGu2R+tmXnzgOXL1e0qX82+QwfPHvuGDRvcHmvlypVYv349Nm3apLmP8/wEKs9w883qvTDG\nP0aNonTZrl2B0aOzkZ2d3bLNn1RWw4VdOcim9mOJiqLp3nfcYey5hTq33UaenXIqPkBCKhWTMjoM\nA+izKwD8z/+4Vkps7QwcSKULtEpSSLaVhN1X2xYWFmLx4sXYsmUL2nuxXM+0abyWabCIigL+8Y/A\n3xOmhmIuXHBeBkzOvfcad07hQkQE8MAD6tukhXGlMIyRA6eAfrvqTKBqddxzj/Y2ybZSiQJfbfv4\n44+jvr4eOT9VPRs5cqSudFZlmWkmsAQjxGVqKMbdqueMd7Rr54jBGl1PBGC7BpPOnemaAv7ZtkS5\nYCxjWUzLihGCfqyBXDWktSMJgNmhGBb2wKIUdqNty4QfpnjsdXU0GBQVZbxnaWUkARDCHI9dWiKQ\nhT2wyIXdjDAbE34YLuxXXkmDaz/8wDd/oJHH2Y3uCUl2Bdi2gUay6+XLjtr3DOMOw4W9SxfyPtir\nCzxyj11r8DJYSHblEFvgkex6/rzxdmXCE8OFvXNn+oGysAceSQCam42/tp07U3XCujpH7jUTGCS7\n8j3D6MUUYecfaXAwW9jZrsGBry3jLaaGYri7HliuvNIh7GaFYtiugadzZ1rflUMxjF5M8dhPnmTv\nIxhInl1TkzkeO4fYggN77Iy3cCjGQsiF3WjPju0aPOSDp3xtGT0YPkGJs2KCh1xczQzFsF0Di5l2\nZcITzoqxEJIANDZyKMZKcG+I8Rb22C0Ee+zWhPPYGW8xXNilHynPTgw80gxFM8S1fXvqKZw9y3YN\nNGbalQlPTBF27rIHBzMH2Ww2OmZFBds10PDgKeMtHIqxEGYPsnXpwsIeDDp0oBm9585xKIbRh8/C\nPm/ePKSmpiIjIwMTJ07E+fPndX2uXTuaQFNSQmuaMoGjd2/gxAmgulpdXKurq5GTk4Pk5GSMHTsW\nNTU1LvuUl5fj5ptvxqBBgzB48GD88Y9/1H38zp2BAwfYroHGZiPbHjjg/0PzpZdeQkREBKqrqwNz\nckxI4rOwjx07FgcPHsS+ffuQnJyMhQsX6vqczUZeR10dkJLi/XEDtdhroNsKhfaio4HERO0ue0FB\nAXJycnDkyBGMGTMGBQUFLvtERUXh5ZdfxsGDB7Fjxw786U9/wjfffKPr+JLHfsMNXp02ALarJ264\nAais9M9jLy8vx4YNG9DXwCWRQuHaGdFWMNrzB5+FPScnBxER9PERI0agoqJC92c7dways0nkvaU1\nGdaX9rKzaSBTrQjXunXrMH36dADA9OnT8a9//ctln969e2Po0KEAgE6dOiE1NRUnTpzQdezOnYG0\nNKBXL69Pm+3qAWmNY3889ieffBIvvvii7w34QChcOyPaCkZ7/hCQGPvy5csxYcIE3ft37kyrnjOB\n5+abtW/+qqoqxMTEAABiYmJQVVXltq2ysjLs2bMHI0aM0HVstmvwkK6rr8K+du1axMXFIT09PXAn\nxYQsbico5eTk4NSpUy7v5+fn4/afli1fsGAB2rZti2nTpuk+6MyZwB13eHmmjC6WLMmBzXYKQ4a4\n367cxu4AAAaBSURBVM9ms8HmpstUW1uLyZMnY8mSJejUqZOuY0+aBFx9tTdny+glKQn4/e8p3KaF\n1v26YMECLFy4EJ988knLe0KIYJwmEyoIP1ixYoUYNWqUuHTpkuY+APhfiPwbOHCgOHnypBBCiBMn\nToiBAweq2qy+vl6MHTtWvPzyy2zXMPjniQMHDohevXqJhIQEkZCQICIjI0Xfvn1FVVUV2zXE//mK\n7Sdjek1hYSGeeuopbNmyBT169PClCcZgnn76aXTv3h3PPPMMCgoKUFNT4zKAKoTA9OnT0b17d7z8\n8ssmnSkTTBITE/HVV1+hW7duZp8KEyR8FvakpCTU19e3/DhGjhyJ1157LaAnxwSW6upq3HPPPfju\nu++QkJCA999/H9HR0Thx4gRmzZqFf//73/j8889x4403Ij09vSVUs3DhQtx6660mnz0TKPr164cv\nv/yShd3C+CzsDMMwTGgStJmnhYWFSElJQVJSEhYtWuT157UmyuiZZKNFU1MTMjMzWwZ+/WmrpqYG\nkydPRmpqKtLS0rBz506/2lu4cCEGDRqEIUOGYNq0abh8+bJX7c2YMQMxMTEYIhs1dff5hQsXIikp\nCSkpKU6Dap4IRbsCgbNta7Ur4J9tQ92uQGBtG/J29Tk674bGxkbRv39/UVpaKurr60VGRoY4dOiQ\nV22cPHlS7NmzRwghxA8//CCSk5PFoUOHxLx588SiRYuEEEIUFBSIZ555RnebL730kpg2bZq4/fbb\nhRDCr7YefPBB8eabbwohhGhoaBA1NTU+t1daWioSExNFXV2dEEKIe+65R6xcudKr9rZu3Sp2794t\nBg8e3PKe1ucPHjwoMjIyRH19vSgtLRX9+/cXTU1NHs8zVO0qROBs2xrtKoT/tg11uwoRONuGg12D\nIuzbtm0T48aNa3m9cOFCsXDhQr/avOOOO8SGDRvEwIEDxalTp4QQ9GPSyuxQUl5eLsaMGSM2b94s\nbrvtNiGE8LmtmpoakZiY6PK+r+2dPXtWJCcni+rqatHQ0CBuu+028cknn3jdXmlpqdMPRevz+fn5\noqCgoGW/cePGie3bt3s8z1C0qxCBs21rtasQgbdtKNlViMDaNhzsGpRQTGVlJeLj41tex8XFobKy\n0uf25BNlvJ1kI/HEE09g8eLFLbNlAe8n7EiUlpaiZ8+eeOihh3DNNddg1qxZ+PHHH31ur1u3bnjq\nqadw9dVXo0+fPoiOjkZOTo7P7Xn6fidOnEBcXFzLfnrtE4p2BQJn29ZqVyCwtg01uwKBtW042DUo\nwu5u4ou31NbWYtKkSViyZAmuvPJKl+PoOdaHH36IXr16ITMzU3Niht62AKCxsRG7d+/Go48+it27\nd6Njx44uaYPetHfs2DG88sorKCsrw4kTJ1BbW4t3333X5/bU8PR5PW2Hml2BwNq2tdrVm/08EYp2\nBQJr23Cwa1CEPTY2FuXl5S2vy8vLnZ44emloaMCkSZPwwAMP4M477wRATzJpdt3JkyfRS0dhkm3b\ntmHdunVITEzE1KlTsXnzZjzwwAM+tQXQEzMuLg7Dhg0DAEyePBm7d+9G7969fWrvyy+/xKhRo9C9\ne3dERkZi4sSJ2L59u8/tSWh9P6V9KioqEBsb67G9ULMrEFjbtla7qn3WF9uGql2BwNo2HOwaFGHP\nyspCSUkJysrKUF9fjzVr1iA3N9erNoQQmDlzJtLS0jB37tyW93Nzc/HWW28BAN56662WH5A78vPz\nUV5ejtLSUqxevRq33HIL3nnnHZ/aAqhQVnx8PI4cOQIA2LhxIwYNGoTbb7/dp/ZSUlKwY8cOXLp0\nCUIIbNy4EWlpaT63J6H1/XJzc7F69WrU19ejtLQUJSUlGD58uMf2Qs2uQGBt21rtCvhv21C2KxBY\n24aFXT2OFPjI+vXrRXJysujfv7/Iz8/3+vOfffaZsNlsIiMjQwwdOlQMHTpUfPTRR+Ls2bNizJgx\nIikpSeTk5Ihz58551a7dbm8ZYfenrb1794qsrCyRnp4u7rrrLlFTU+NXe4sWLRJpaWli8ODB4sEH\nHxT19fVetTdlyhRx1VVXiaioKBEXFyeWL1/u9vMLFiwQ/fv3FwMHDhSFhYW6zzNU7SpEYGzbWu0q\nhH+2DXW7ChFY24a6XXmCEsMwjMUwfGk8hmEYJriwsDMMw1gMFnaGYRiLwcLOMAxjMVjYGYZhLAYL\nO8MwjMVgYWcYhrEYLOwMwzAW4/8Dq7Qmhki8Y/AAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb13b3e0c>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we see how changing the width of a square wave or a top-hat function will change it's fourier spectrum.\n",
      "\n",
      "the function g has double the width of the function f and the fourier spectrum of the function g is thinner than that of the function f"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f = np.ones(101)\n",
      "g = np.ones(101)\n",
      "#y = np.linspace(1001)\n",
      "for i in xrange(len(f)):\n",
      "    if i > 11:\n",
      "        f[i] = 0\n",
      "    if i > 21:\n",
      "        g[i] = 0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.subplot(141)\n",
      "plt.plot(f)\n",
      "plt.subplot(142)\n",
      "plt.plot(g)\n",
      "plt.subplot(143)\n",
      "plt.plot(np.fft.fftshift(np.fft.fft(f)))\n",
      "plt.subplot(144)\n",
      "plt.plot(np.fft.fftshift(np.fft.fft(g)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "[<matplotlib.lines.Line2D at 0xb1452e4c>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SHR3d/njx4sWYOXOm123VngZCQisGH86pIDRRomGTUQ/WXh/orURTW1vb/vgvf/mL0wgb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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb147abec>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Here we will see the fourier transforms of saw-tooth and traingular functions."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "st = np.zeros(101) # saw tooth function\n",
      "for i in xrange(len(st)):\n",
      "    st[i] = i%9"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tr = np.zeros(101) # triangular function\n",
      "for i in xrange(len(tr)):\n",
      "    if i%20 < 10:\n",
      "        tr[i] = i%10\n",
      "    if i%20 > 9:\n",
      "        tr[i] = 10-i%10"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.subplot(121)\n",
      "plt.plot(st)\n",
      "plt.subplot(122)\n",
      "plt.plot(tr)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "[<matplotlib.lines.Line2D at 0xaecf768c>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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yMl6qDisOzhXvqGF7nC9c+7p6XJxLHYxq8XahbbZzdAGqDzWV8tbBTVnIVBSw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\nGTJkyJBCZMU7Q4YMGVKI/w821pEsIbXEowAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xaecd32ec>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.subplot(121)\n",
      "plt.plot(np.fft.fftshift(np.fft.fft(st)))\n",
      "plt.subplot(122)\n",
      "plt.plot(np.fft.fftshift(np.fft.fft(tr)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "[<matplotlib.lines.Line2D at 0xaec02dac>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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JWk5hYWCEQb9+clTU2ir7yqBB5raHrk4dGbhcvheQOTLQl2UuRxEVJS9DGwhT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\niMAwICIiMAyIiAgMAyIiAsOAiIgA/D/DxEiDxQyDowAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xaec7810c>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.linspace(-5,5,501)\n",
      "a = 0\n",
      "b = 1\n",
      "plt.subplot(121)\n",
      "plt.plot(np.exp(-(x-a)**2/(2*b**2)))\n",
      "plt.subplot(122)\n",
      "plt.plot(np.fft.fftshift(np.fft.fft(np.exp(-(x-a)**2/(2*b**2)))))\n",
      "plt.xlim([240,260])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "(240, 260)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2lh9zwgTljhkovvzyS0RHR+PHH39ETk4OkpOT+zyv0WigcXK1WlFRkfX/2dnZyM7OlilS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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb154966c>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Above, we see the fourier spectrum of a gaussian function with sigma = 1. We will now look at the fourier spectrum of a gaussian wave when it is thinned i.e sigma is reduced such that the gaussian function will eventually resemble a delta function! Note that we have normalized the gaussian such that the area under the gaussian is always unity!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from ipywidgets import StaticInteract, RangeWidget, RadioWidget\n",
      "\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline\n",
      "\n",
      "#var = 1\n",
      "\n",
      "def plot(var):\n",
      "    fig, ax = plt.subplots(figsize=(4, 3),subplot_kw={'axisbg':'#EEEEEE','axisbelow':True})\n",
      "    ax.grid(color='w', linewidth=2, linestyle='solid')\n",
      "    #ax.legend(loc='upper right')\n",
      "    x = np.linspace(-2, 2, 201)\n",
      "    y = (1./(var*(2*np.pi)**(1./2)))*np.exp(-x**2/(2*var**2))\n",
      "    ax.plot(x, y, lw=5, alpha=0.4,label=var)\n",
      "    return fig\n",
      "\n",
      "StaticInteract(plot,var=RangeWidget(0.01, 0.1, 0.01))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "\n",
        "    <script type=\"text/javascript\">\n",
        "      var mergeNodes = function(a, b) {\n",
        "        return [].slice.call(a).concat([].slice.call(b));\n",
        "      }; // http://stackoverflow.com/questions/914783/javascript-nodelist/17262552#17262552\n",
        "      function interactUpdate(div){\n",
        "         var outputs = div.getElementsByTagName(\"div\");\n",
        "         //var controls = div.getElementsByTagName(\"input\");\n",
        "         var controls = mergeNodes(div.getElementsByTagName(\"input\"), div.getElementsByTagName(\"select\"));\n",
        "         function nameCompare(a,b) {\n",
        "            return a.getAttribute(\"name\").localeCompare(b.getAttribute(\"name\"));\n",
        "         }\n",
        "         controls.sort(nameCompare);\n",
        "\n",
        "         var value = \"\";\n",
        "         for(i=0; i<controls.length; i++){\n",
        "           if((controls[i].type == \"range\") || controls[i].checked){\n",
        "             value = value + controls[i].getAttribute(\"name\") + controls[i].value;\n",
        "           }\n",
        "           if(controls[i].type == \"select-one\"){\n",
        "             value = value + controls[i].getAttribute(\"name\") + controls[i][controls[i].selectedIndex].value;\n",
        "           }\n",
        "         }\n",
        "\n",
        "         for(i=0; i<outputs.length; i++){\n",
        "           var name = outputs[i].getAttribute(\"name\");\n",
        "           if(name == value){\n",
        "              outputs[i].style.display = 'block';\n",
        "           } else if(name != \"controls\"){\n",
        "              outputs[i].style.display = 'none';\n",
        "           }\n",
        "         }\n",
        "      }\n",
        "    </script>\n",
        "    \n",
        "    <div>\n",
        "      \n",
        "    <div name=\"var0.01\" style=\"display:block\">\n",
        "      <img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQQAAADICAYAAAAOVZ9xAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
        "AAALEgAACxIB0t1+/AAAFHhJREFUeJzt3X1sU+UeB/DvYYwgDJhLXEsY3PHWDAZ0hemigQtjdjDi\n",
        "eocQAir2ChoyNYJDwvwDMqJgCSEG0ASiEzu5F0UiY+qcbLKpgEgiW0Te5iUsGbNrhDEElbu35/6x\n",
        "y5HRdqc96zld2+8nMYH10N/zeDhfnqc9/VUSQggQEQEYEOoBEFH/wUAgIhkDgYhkDAQikjEQiEjG\n",
        "QCAimV+B0NnZCYvFgtzcXABAS0sLrFYrTCYTsrOz0draqukgiUgffgXCjh07MHnyZEiSBABwOByw\n",
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        "\">\n",
        "    </div>\n",
        "    \n",
        "      <b>var:</b> <input type=\"range\" name=\"var\" min=\"0.01\" max=\"0.1\" step=\"0.01\" value=\"0.01\" style=\"width:350px\" oninput=\"interactUpdate(this.parentNode);\" onchange=\"interactUpdate(this.parentNode);\">\n",
        "    </div>\n",
        "    "
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "<ipywidgets.interact.StaticInteract at 0xaeeb9f8c>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from ipywidgets import StaticInteract, RangeWidget, RadioWidget\n",
      "\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline\n",
      "\n",
      "#var = 1\n",
      "\n",
      "def plot(var):\n",
      "    fig, ax = plt.subplots(figsize=(4, 3),subplot_kw={'axisbg':'#EEEEEE','axisbelow':True})\n",
      "    ax.grid(color='w', linewidth=2, linestyle='solid')\n",
      "    #ax.legend(loc='upper right')\n",
      "    x = np.linspace(-2, 2, 201)\n",
      "    y = np.fft.fftshift(np.fft.fft((1./(var*(2*np.pi)**(1./2)))*np.exp(-x**2/(2*var**2))))\n",
      "    ax.plot(y, lw=5, alpha=0.4,label=var)\n",
      "    #ax.set_xlim(150,200)\n",
      "    return fig\n",
      "\n",
      "StaticInteract(plot,var=RangeWidget(0.01, 0.1, 0.01))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "\n",
        "    <script type=\"text/javascript\">\n",
        "      var mergeNodes = function(a, b) {\n",
        "        return [].slice.call(a).concat([].slice.call(b));\n",
        "      }; // http://stackoverflow.com/questions/914783/javascript-nodelist/17262552#17262552\n",
        "      function interactUpdate(div){\n",
        "         var outputs = div.getElementsByTagName(\"div\");\n",
        "         //var controls = div.getElementsByTagName(\"input\");\n",
        "         var controls = mergeNodes(div.getElementsByTagName(\"input\"), div.getElementsByTagName(\"select\"));\n",
        "         function nameCompare(a,b) {\n",
        "            return a.getAttribute(\"name\").localeCompare(b.getAttribute(\"name\"));\n",
        "         }\n",
        "         controls.sort(nameCompare);\n",
        "\n",
        "         var value = \"\";\n",
        "         for(i=0; i<controls.length; i++){\n",
        "           if((controls[i].type == \"range\") || controls[i].checked){\n",
        "             value = value + controls[i].getAttribute(\"name\") + controls[i].value;\n",
        "           }\n",
        "           if(controls[i].type == \"select-one\"){\n",
        "             value = value + controls[i].getAttribute(\"name\") + controls[i][controls[i].selectedIndex].value;\n",
        "           }\n",
        "         }\n",
        "\n",
        "         for(i=0; i<outputs.length; i++){\n",
        "           var name = outputs[i].getAttribute(\"name\");\n",
        "           if(name == value){\n",
        "              outputs[i].style.display = 'block';\n",
        "           } else if(name != \"controls\"){\n",
        "              outputs[i].style.display = 'none';\n",
        "           }\n",
        "         }\n",
        "      }\n",
        "    </script>\n",
        "    \n",
        "    <div>\n",
        "      \n",
        "    <div name=\"var0.01\" style=\"display:block\">\n",
        "      <img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQ0AAADICAYAAADyQLS7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
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        "\">\n",
        "    </div>\n",
        "    \n",
        "      <b>var:</b> <input type=\"range\" name=\"var\" min=\"0.01\" max=\"0.1\" step=\"0.01\" value=\"0.01\" style=\"width:350px\" oninput=\"interactUpdate(this.parentNode);\" onchange=\"interactUpdate(this.parentNode);\">\n",
        "    </div>\n",
        "    "
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "<ipywidgets.interact.StaticInteract at 0xaec3762c>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}