{
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  {
   "cell_type": "markdown",
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    "collapsed": false
   },
   "source": [
    "# Simulate noise\n",
    "\n",
    "Objects from `thztools`: `NoiseModel`, `NoiseModel.noise_amp`, `NoiseModel.noise_sim`, `timebase`, `wave`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import thztools as thz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## Set the simulation parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 256  # Number of samples\n",
    "dt = 0.05  # Sampling time [ps]\n",
    "\n",
    "sigma_alpha = 1e-4  # Additive noise amplitude [signal units]\n",
    "sigma_beta = 1e-2  # Multiplicative noise amplitude [dimensionless]\n",
    "sigma_tau = 1e-3  # Time base noise amplitude [ps]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulate a waveform\n",
    "\n",
    "Use `wave` to simulate a terahertz time-domain waveform `mu` with a timebase given by `timebase`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = thz.timebase(n, dt=dt)\n",
    "mu = thz.wave(n, dt=dt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulate noise\n",
    "\n",
    "Create an instance `noise_model` of the `NoiseModel` class and use the `noise_sim` method to use the model to generate time-domain noise `delta` for the waveform `mu`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "noise_model = thz.NoiseModel(sigma_alpha, sigma_beta, sigma_tau, dt=dt)\n",
    "\n",
    "delta = noise_model.noise_sim(mu, seed=0)\n",
    "sigma_mu = noise_model.noise_amp(mu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Show the noise\n",
    "\n",
    "Show the simulated noise `delta` together with statistical bounds given by the noise amplitude `sigma_mu`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "_, ax = plt.subplots()\n",
    "\n",
    "ax.plot(t, delta)\n",
    "ax.plot(t, sigma_mu, 'k:')\n",
    "ax.plot(t, -sigma_mu, 'k:')\n",
    "\n",
    "ax.set_xlabel('Time (ps)')\n",
    "ax.set_ylabel(r'Amplitude (units of $\\mu_{p})$')\n",
    "\n",
    "ax.set_xticks(np.arange(0, 11, 5))\n",
    "ax.set_xlim(0, 10)\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
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