Exponential Curves.ipynb

{
 "metadata": {
  "name": "Exponential Curves"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 75
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t =  np.linspace(0.0, 2, num=88001)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 80
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t60m = 6.90776;\n",
      "tau = 0.9/t60m;\n",
      "v = 1 - exp(-t/tau);\n",
      "vt = next(vt for vt in v if vt >= 1-0.001);\n",
      "index = nonzero(v == vt)[0][0]\n",
      "(v[index], t[index], index)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 99,
       "text": [
        "(0.99990000062946705, 1.3333333333333333, 35200)"
       ]
      }
     ],
     "prompt_number": 99
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(t,v)\n",
      "grid('on')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 96
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tau = 0.07;\n",
      "v = 1 - exp(-t/tau);\n",
      "(v[4999], t[4999])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 97,
       "text": [
        "(0.80270435674990726, 0.11361363636363636)"
       ]
      }
     ],
     "prompt_number": 97
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(v[0:4999])\n",
      "grid('on')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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hQ4eyadMm/0Trgg8/hDPOsPr0Dz6oRwiKSGjqtNg3NzeTkJDgG8fHx9Pc3HzA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\n"
      }
     ],
     "prompt_number": 98
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ti = -(4999.0/44100.0)/(np.log(1.0-0.791136)) #500\n",
      "ti/500"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 86,
       "text": [
        "0.00014476475183363877"
       ]
      }
     ],
     "prompt_number": 86
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ti = -(4999.0/44100.0)/(np.log(1.0-0.926475)) #300\n",
      "ti/300"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 87,
       "text": [
        "0.0001447642045839103"
       ]
      }
     ],
     "prompt_number": 87
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ti = -(4999.0/44100.0)/(np.log(1.0-0.980063)) #200\n",
      "ti/200"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 88,
       "text": [
        "0.00014476482261176465"
       ]
      }
     ],
     "prompt_number": 88
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "1/0.00014476475183363877"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 89,
       "text": [
        "6907.758880070359"
       ]
      }
     ],
     "prompt_number": 89
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "s = 600;\n",
      "t4 = (4999.0/44100.0)\n",
      "tau1 = s/6907.0;\n",
      "vti = 1 - exp(-t4/tau1);\n",
      "vti"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 64,
       "text": [
        "0.72880484580304972"
       ]
      }
     ],
     "prompt_number": 64
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tau1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 65,
       "text": [
        "0.0868683943825105"
       ]
      }
     ],
     "prompt_number": 65
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "0.6/6.907"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 66,
       "text": [
        "0.0868683943825105"
       ]
      }
     ],
     "prompt_number": 66
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}