franalbani/Lucas_y_su_osciloscopio.ipynb

## Lucas_y_su_osciloscopio.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lucas y su osciloscopio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Auxiliares (no hace falta leer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using matplotlib backend: Qt5Agg\n",
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Artilugio para tener una manera fácil de actualizar todo el código:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from IPython.display import display, Math, Latex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "IPython.notebook.execute_cells_below()"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.display import Javascript, display\n",
    "from ipywidgets import widgets\n",
    "\n",
    "def run_all(ev):\n",
    "    display(Javascript('IPython.notebook.execute_cells_below()'))\n",
    "\n",
    "button = widgets.Button(description=\"Run all below\")\n",
    "button.on_click(run_all)\n",
    "display(button)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Situación"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Frecuencia de muestreo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fs = 10e6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Frecuencia de la señal:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f0 = 1e6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cantidad de muestras:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m = 2500"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tiempos de muestreo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "t = arange(-m // 2, m // 2)/fs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Amplitud \"desconocida\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mV = 1e-3 # milivolt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "A = 0.8 * mV"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ruido:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sigma = A / 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "r = random.normal(0, sigma, t.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bias sacado a ojo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "bias = A * 0.52"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Señal:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = A * sin(2*pi*f0*t) # ideal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "v = x + r + bias # con ruido y bias"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ms = 1e-3 # milisegundo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "zoom = (-0.05 * ms < t) & (t < -0.03 * ms)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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6wG125GhfHzuWlSOXROfVVznPDeBG0VmwYMERH4Usmq4GB4EXXij0zwHcmK5a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3ueBhwjIh92xZZeG0TkGmPMVRllPwacPEC925VmaFPto4On3u0JgLGBxeuBp0VkE/CQiHzJGJNV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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8fc6fe3978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(t[zoom]/ms, v[zoom]/mV)\n",
    "grid()\n",
    "_ = xlabel('Tiempo [ms]')\n",
    "_ = ylabel('Tensión [mV]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "FFT normalizada para que las unidades sean en Volt:\n",
    "\n",
    "(ojo que en tu gráfico de FFT creo que la escala vertical quedó multiplicada por 2500, que es el tamaño de la FFT)\n",
    "\n",
    "(No uso ventanas para simplificar)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "V = fft.fftshift(fft.fft(v, n=m)) / m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "freqs = fft.fftshift(fft.fftfreq(m, 1 / fs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "MHz = 1e6 # mega hertz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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308SJE1m6dGm39ZYtW0alUum1/fTp01m0aFG3Ze3t7VQqFTo6un+L+Zw5c2hpaem2bNWq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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8fc714dd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(freqs / MHz, abs(V) / mV)\n",
    "grid()\n",
    "xlabel('Frecuencia [MHz]')\n",
    "ylabel('Tensión [mV]')\n",
    "_ = axis([-5, 5, 0, 0.5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df = diff(freqs)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Armo un índice booleano auxiliar para capturar los elementos asociados a 1 MHz:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "around_1MHz = (MHz - df < abs(freqs)) & (abs(freqs) < MHz + df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(Podrían ser más de dos si la frencuencia de muestreo no es muy amiga de la de la señal. Quizá esta no sea la mejor manera de capturarlos. Por las dudas divido por la mitad de la longitud del vector)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 243,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(around_1MHz)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Amplitud estimada:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0.799 mV'"
      ]
     },
     "execution_count": 244,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'%0.3f mV' % (sum(abs(V[around_1MHz]) / mV) / (sum(around_1MHz)/2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A partir de acá viene el \"librepensamiento\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "k = 1000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Construyo una matriz de $m \\times k$ en donde cada columna es una realización del proceso (x + bias + ruido):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y = (x + bias).reshape(m, 1) + random.normal(0, sigma, size=(m, 1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Y = fft.fftshift(fft.fft(y, n=m, axis=0), axes=0) / m"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculo los $k$ estimadores de amplitud:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "A_est = sum(abs(Y[around_1MHz, :] / mV), axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$0.800 \\,\\mbox{mV} \\pm 4.31 \\,\\mu\\mbox{V}$$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(Math('%0.3f \\,\\mbox{mV} \\pm %0.2f \\,\\mu\\mbox{V}' % (mean(A_est), std(A_est)*1000)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Me gustaría concluir que este método tiene un error de $4 \\, \\mu \\mbox{V}$, que misteriosamente se parece a:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{\\sigma}{\\sqrt m} \\approx 3.2 \\,\\mu\\mbox{V}$$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(Math('\\\\frac{\\sigma}{\\sqrt m} \\\\approx %0.1f \\,\\mu\\mbox{V}' % (1e6 * sigma / sqrt(m))))"
   ]
  }
 ],
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