monochromatic_analytical_wdm_check.ipynb

monochromatic_analytical_wdm_check.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyNOuap2Cfx8csshGUg4rn4t",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/avivajpeyi/3bbf7271b33226f30aad57422fb5d2a4/monochromatic_analytical_wdm_check.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Monochromatic Signal WDM check\n",
        "\n",
        "\n",
        "We choose to analyse the monochromatic signal\n",
        "\n",
        "$y(t) = A\\sin(2\\pi f_{0} t)\\, ,$\n",
        "\n",
        "\n",
        "\n",
        "with constant amplitude and frequency $A, \\ f_{0} \\in \\mathbb{R}$, sampled at equally spaced time bins $\\Delta t$, for $N$ number of points, such that the observation time is given by\n",
        "\n",
        "$T_{\\text{obs}} = N\\,\\cdot \\Delta t\\, .$\n",
        "\n",
        "\n",
        "We write the DTFT of the signal as\n",
        "\n",
        "\n",
        "\\begin{align}\n",
        "\\tilde{y}[f_{p}] & =\\sum_{k = -N/2}^{N/2 - 1} y[k]\\exp(-2\\pi i p k / N) \\\\\n",
        "&= \\frac{A}{2i}\\sum_{k = -N/2}^{N/2 - 1} \\left( e^{i\\left[\\frac{2\\pi}{N}(m_{0} - p)\\right]k} - e^{-i\\left[\\frac{2\\pi}{N}(m_{0} + p)\\right]k}\\right)\\,.\n",
        "\\end{align}\n",
        "Here we define the integer $m_{0}$ such that the frequency\n",
        "\n",
        "$f_{0} = m_{0}/(N\\Delta t)$.\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "jaV8w-EDkUdQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from typing import Tuple\n",
        "\n",
        "def compute_bins(Nf:int, Nt:int, T:float) -> Tuple[np.ndarray, np.ndarray]:\n",
        "    \"\"\"Get the bins for the wavelet transform Eq 4-6 in Wavelets paper \"\"\"\n",
        "    delta_T = T / Nt\n",
        "    delta_F = 1 / (2 * delta_T)\n",
        "    t_bins = np.arange(0, Nt) * delta_T\n",
        "    f_bins = np.arange(0, Nf) * delta_F\n",
        "    return  t_bins, f_bins\n",
        "\n",
        "def monochromatic_wnm(f0:float, dt:float, A:float, T:float, Nt:int, Nf:int):\n",
        "    N = Nt * Nf\n",
        "    t_bins, f_bins = compute_bins(Nf, Nt, T)\n",
        "    wnm = np.zeros((Nt, Nf))\n",
        "    m0 = int(f0 * N * dt)\n",
        "    f0_bin_idx = int( 2 * m0 / Nt)\n",
        "    odd_t_indices = np.arange(Nt) % 2 != 0\n",
        "    wnm[odd_t_indices, f0_bin_idx] = A * np.sqrt(2 * Nf)\n",
        "    return wnm, t_bins, f_bins\n",
        "\n",
        "\n",
        "\n",
        "def plot_wnm(analytical_wnm, t_bins, f_bins):\n",
        "  fig, axs = plt.subplots(1, 1, figsize=(5, 5))\n",
        "  # x is time, y is freq\n",
        "  im = axs.imshow(analytical_wnm.T, aspect='auto', extent=[t_bins[0], t_bins[-1], f_bins[0], f_bins[-1]], origin='lower', cmap='Reds', interpolation='none')\n",
        "  cbar = fig.colorbar(im, ax=axs)\n",
        "  cbar.set_label(r'$w_{nm}$')\n",
        "  axs.set_ylabel('Frequency [Hz]')\n",
        "  axs.set_xlabel('Time (s)')\n",
        "  return fig, axs\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "f0 = 20\n",
        "dt = 0.0125\n",
        "A = 2\n",
        "Nt = 128\n",
        "Nf = 512\n",
        "N = Nt * Nf\n",
        "T = N * dt\n",
        "analytical_wnm, t_bins, f_bins = monochromatic_wnm(f0, dt, A, T, Nt, Nf)\n",
        "fig, axs = plot_wnm(analytical_wnm, t_bins, f_bins)\n",
        "axs.axhline(f0, color='k', lw=4, alpha=0.1)\n",
        "axs.set_ylim(f0-2.5, f0+2.5)\n",
        "axs.set_xlim(0, 100)\n",
        "plt.show()\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 482
        },
        "id": "AGdgtNcckg4G",
        "outputId": "fc160035-6de3-4f3e-a215-30777e530c8a"
      },
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "N=65536\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 2 Axes>"
            ],
            "image/png": 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Sr1szzhUrViggIEB2u92t9v7776ukpKS+YwcAWMTqUq3D4XBp5eXll33vlJQUjRgxQklJSS7Hd+/ercrKSpfjHTp0UFxcnLZu3Vo/H4Qb3F5V++KLL7o9g3z33XdrHRAAoOHZ/C40K/qRpNjYWJfjc+bM0dy5c2tcn52drT179mjnzp01zhUUFCggIEDh4eEux6OiolRQUFD3YGvJrcS5ceNGRUREuN3phx9+qJ/85Ce1DgoAcGU7ceKEwsLCnK8DAwMvec2MGTO0bt06BQUFNWR4deJW4vz5z39uqtP+/fvXKhgAgGdYvQFCWFiYS+K8lN27d+v06dO6/vrrnceqqqq0efNmvfTSS1q7dq0qKipUVFTkMussLCxUdHR0nWOtLdMT80GDBumPf/xjjeNfffWV8+YtAOAK42ezrrlp8ODBOnjwoPbt2+dsvXr10vjx453/7u/vr/Xr1zt/5tChQ8rPz1diYmJ9fApuMb1z0KZNm3Tw4EHt3btXb731lpo3by5JqqioUE5OjuUBAgB8U2hoqLp06eJyrHnz5mrRooXz+OTJk5WWlqaIiAiFhYVp2rRpSkxM9NiKWqmW3+P86KOPVFBQoL59++o///mPxSEBABqcFV/itOoRK9/x3HPP6Ze//KXGjh2rAQMGKDo6WsuWLbP0Pcyq1V61MTExysnJ0aRJk9S7d28tXbpUHTt2tDo2AEAD8ZZN3jdt2uTyOigoSAsWLNCCBQvq1K+VTM84L34ogYGBWrJkiWbMmKFhw4bp5Zdftjw4AAC8jekZp2EYLq8fffRRdezYURMmTLAsKABAAzO5sOcH+/FxphNnXl6eWrZs6XJs7Nixat++vXbv3m1ZYACABmTV/Umex1lT27ZtL3m8S5cuNVZHAQDga9xOnO5u9O7p1U4AAPNsfjbZLCizWtGHt3M7cdrtdpfXS5Ys0ciRIxUaGmp5UACABkap1m1uJ87MzEyX1++++66effZZtWvXzvKgAADwVrX6HicAwLfYbBaVaplxAgAaBUq1brPg6WsAADQebs84V61a5fK6urpa69evV25ursvxUaNGWRMZAKDh+MmiDRDq3oW3cztxJicn1zj2+9//3uW1zWZTVVVVnYMCADQsb9mr9krgduKsrq6uzzgAALgisDgIAMBetSa4VY1etWqVKisr3e70gw8+0Ndff13roAAADcxLn8fpjdxKnLfccouKiorc7nTcuHE6depUbWMCAMBruVWqNQxDEydOVGBgoFudlpWV1SkoAEDDsvldaFb04+vcSpxmn7U5fvx4hYWF1SogAIAHsAGC29xKnN/fpxYAgMaKVbUAAB4rZgKJEwBAqdaERnAbFwAA6zDjBACwAYIJpmecx44dq484AAAedHGvWiuarzOdOK+55hrddNNNevPNN/m+JgCg0TGdOPfs2aNu3bopLS1N0dHR+v3vf68dO3bUR2wAgIZysVRrRfNxphPnddddpxdeeEEnT57U66+/rlOnTql///7q0qWL5s+frzNnztRHnACAemXVPrUkzstq2rSpxowZo6VLl+qZZ57R0aNH9cADDyg2NlZ33XUXe9UCAHxSrRPnrl27dN999ykmJkbz58/XAw88oM8++0zr1q3TyZMnNXr0aCvjBADUIxYHuc/011Hmz5+vzMxMHTp0SDfffLMWL16sm2++WX5+F3JwfHy8srKydPXVV1sdKwCgvvB1FLeZTpwLFy7Ub3/7W02cOFExMTGXvCYyMlKLFi2qc3AAAFghIyNDr7/+uux2u7p27epsvXr1Mt2X6cR55MiRH70mICDA9BNVAACeY1WZ1VtLtc8884w2bNggwzCUm5urgwcP6u9//7vefvtt032ZTpyZmZkKCQnRrbfe6nJ86dKlOn/+PAkTAK5EPl6q7d69u6KiotSsWTO1a9dOo0aNqnVfphcHpaenq2XLljWOR0ZG6qmnnqp1IAAA1JdHHnlEI0aM0PLly3Xy5Mk69WU6cebn5ys+Pr7G8bZt2yo/P79OwQAAPMSK73Ba9YSVenDXXXepU6dO+uijjzRu3Di1a9dOAwcOrFVfpku1kZGROnDgQI1Vs/v371eLFi1qFQQAwLN8/Xmc4eHhWrBggcuxzz//vFZ9mZ5x3n777Zo+fbo2btyoqqoqVVVVacOGDZoxY4bGjRtXqyAAAKhPffr0UVZWlsuxNm3a1Kov04nzT3/6k/r06aPBgwcrODhYwcHBGjJkiAYNGmT6Hmd6erp69+6t0NBQRUZGKjk5WYcOHXK5pqysTCkpKWrRooVCQkI0duxYFRYWmg0bAPBDfLxUm5eXp8cff1zt2rXTbbfdpieffFLvvfderfqyGYZh1OYHDx8+rP379ys4OFhdu3ZV27ZtTfcxbNgwjRs3Tr1799Y333yjhx9+WLm5ufrkk0/UvHlzSdK9996r999/X1lZWbLb7Zo6dar8/Pz0z3/+0633cDgcstvtOpa7T6GhoaZjBABvc+7cObXrcp2Ki4sVFhZWp74u/o7872+TFBbgX+fYHBWVavn6R5bEVh9KSkr08ccf6+DBgzp48KBeeOEF033UOnHWhzNnzigyMlI5OTkaMGCAiouL1apVKy1ZskS/+tWvJEmffvqpOnbsqK1bt6pv374/2ufF/yg+3btToaEhlsT5f9f0tKQfSXrm6G7L+pKsjU3y7vi8OTbJu+Pz5tgk747PG2KrkKG/6WsSpwmffPKJVq5cqfDwcHXu3Fldu3bVVVddVau+TC8OqqqqUlZWltavX6/Tp0+rurra5fyGDRtqFYgkFRcXS5IiIiIkSbt371ZlZaWSkpKc13To0EFxcXGXTZzl5eUqLy93vnY4HLWOBwAaC1/fAGHUqFGaNm2aSktLtWjRIh08eFDFxcX67LPPTPdlOnHOmDFDWVlZGjFihLp06WLZh1RdXa3U1FT169dPXbp0kSQVFBQoICBA4eHhLtdGRUWpoKDgkv2kp6frj3/8oyUxAUCj4eMbIERHR2vGjBkux6qqqmrVl+nEmZ2drb/97W+6+eaba/WGl5OSkqLc3Fxt2bKlTv3MmjVLaWlpztcOh0OxsbF1DQ8AcAUbPHiwMjMzNWnSJOexJk2a1Kov04kzICBA11xzTa3e7HKmTp2q1atXa/PmzS7Lg6Ojo1VRUaGioiKXWWdhYaGio6Mv2VdgYKACAwNrxu3vrwD/AEvi9bPwQa1WxXSRlbFJ3h2fN8cmeXd83hyb5N3xeUNstX4e5A+xakWsl5Zqd+3apaysLD3++OPq3bu3unfvrm7dumnkyJGm+zKdOO+//3698MILeumll+pcpjUMQ9OmTdPy5cu1adOmGjsS9ezZU/7+/lq/fr3Gjh0rSTp06JDy8/OVmJho6r1atIiw7EZ1sIX/E7Zsae2mEVbGJnl3fN4cm+Td8XlzbJJ3x+cNsdVunvQjfCxxHj161GWS9/7770u6sCI5NzdXubm5Wr9+fa0Sp+lVtbfccos2btyoiIgIde7cWf7+rquwli1b5nZf9913n5YsWaKVK1eqffv2zuN2u13BwcGSLnwd5YMPPlBWVpbCwsI0bdo0SdK//vUvt97j4oqx4lP5XrXCCwBqy+FwyB4TZ+mq2i9/P8yyVbUtXlnj8VW1gYGBGjJkiFJTUzV48GBL+zY94wwPD9ctt9xiyZsvXLhQkmrsF5iZmamJEydKkp577jn5+flp7NixKi8v19ChQ/Xyyy9b8v4AgIus2rzAe2acr7zyisaPH6+WLVtqxowZuvPOOxUUFFTnvr3qe5z1gRknAF9TLzPOe0coLNCCGWd5pVosfN/jM86LKisrtXTpUr388sv69NNPNWXKFN133311WjRaq3vM33zzjT766CO98sorOnfunCTp5MmTKikpqXUgAABYpaKiQqdPn9axY8fUrl07Pfzww5o0aZJeeumlOi9wNV2qPX78uIYNG6b8/HyVl5frF7/4hUJDQ/XMM8+ovLxcGRkZdQoIAOABHlgctHDhQi1cuFD/+c9/JEmdO3fW7NmzNXz4cEkX9iq///77lZ2d7XKrLioq6kf7DgoKUkhIiFq2bKmwsDCFhYXJbrdr1KhRstvttRraRbXaAKFXr141HiN2yy23aMqUKXUKBgDgIR5InG3atNHTTz+thIQEGYahN954Q6NHj9bevXvVuXNnzZw5U++//76WLl3q3Kt8zJgxbu1V/utf/1rr1q3TqFGjNH36dLVr164uo3JhulT7j3/8Q48++qgCAly/y3T11Vfriy++sCwwAIBvGzlypG6++WYlJCTo2muv1ZNPPqmQkBBt27ZNxcXFWrRokebPn69BgwapZ8+eyszM1L/+9S9t27btR/vOzs7W/v37FRQUpD59+ig5OVmbNm2yJG7TibO6uvqS2xR9/vnnPH0EAK5UFj9WzOFwuLTv7iF+KVVVVcrOzlZpaakSExN/dK9yd1yc0R4/flxDhw7VPffco+uuu67GcznNMl2qHTJkiJ5//nm9+uqrki5s6FtSUqI5c+ZYvg0fAKCB+PldaFb0I9VYtTpnzhzNnTu3xuUHDx5UYmKiysrKFBISouXLl6tTp07at2+f6b3Kv+ull17SuXPnXFqHDh20YcMGTZ482fmVx9ownTjnzZunoUOHqlOnTiorK9NvfvMbHTlyRC1bttTbb79d60AAAL7jxIkTLl9HudRWqJLUvn177du3T8XFxXr33Xc1YcIE5eTk1Pn933rrLYWHhztbTEyMOnbsqOHDh9dIxmaZTpxt2rTR/v37lZ2drQMHDqikpESTJ0/W+PHjnbv9AACuMBYvDrq4kvXHfHf/8549e2rnzp164YUXdNttt5neq/y73C3n1obpxClJTZs21R133GF1LAAAT/GSvWqrq6tVXl5u6V7lVjOdOBcvXvyD5++6665aBwMAaDxmzZql4cOHKy4uTufOndOSJUu0adMmrV27Vna7XZMnT1ZaWpoiIiKce5UnJiaqb9++Ho27Vt/j/K7KykqdP39eAQEBatasGYkTAK5EHphxnj59WnfddZdOnTolu92ubt26ae3atfrFL34hyXv3KjedOL/66qsax44cOaJ7771XDz74oCVBAQAamMWrat2xaNGiHzwfFBSkBQsWaMGCBXWNylKWPA81ISFBTz/9dI3ZKAAAvqZWi4Mu2VHTpjp58qRV3QEAGpKXLA66EphOnKtWrXJ5bRiGTp06pZdeekn9+vWzLDAAQAOyyaLEWfcuvJ3pxJmcnOzy2mazqVWrVho0aJDmzZtnVVwAAHgl04mzurq6PuIAAHgSpVq3WXaPEwBw5bL5+clmwapaK/rwdqYTZ1pamtvXzp8/32z3AAB4NdOJc+/evdq7d68qKyvVvn17SdLhw4fVpEkTXX/99c7rbI1gug4AvsOiUm0jWB1kOnGOHDlSoaGheuONN3TVVVdJurApwqRJk/Szn/1M999/v+VBAgDqGfc43Wa6GD1v3jylp6c7k6YkXXXVVXriiSdYVQsA8HmmZ5wOh0NnzpypcfzMmTM6d+6cJUEBABoYM063mU6ct9xyiyZNmqR58+bphhtukCRt375dDz74oMaMGWN5gACABuCBvWqvVKYTZ0ZGhh544AH95je/UWVl5YVOmjbV5MmT9ec//9nyAAEA8CamE2ezZs308ssv689//rM+++wzSdJPf/pTNW/e3PLgAAANhFKt22o9pz516pROnTqlhIQENW/eXIZhWBkXAKAhXUycVjQfZzpxfvnllxo8eLCuvfZa3XzzzTp16pQkafLkyXwVBQDg80wnzpkzZ8rf31/5+flq1qyZ8/htt92mNWvWWBocAKCBMON0m+l7nH//+9+1du1atWnTxuV4QkKCjh8/bllgAIAGxKpat5keYWlpqctM86KzZ88qMDDQkqAAAPBWphPnz372My1evNj52mazqbq6Ws8++6xuuukmS4MDADQQSrVuM12qffbZZzV48GDt2rVLFRUVeuihh/Txxx/r7Nmz+uc//1kfMQIA6htfR3Gb6Rlnly5ddPjwYfXv31+jR49WaWmpxowZo7179+qnP/1pfcQIAIDXMDXjrKys1LBhw5SRkaFHHnmkvmICADQ0Fge5zVTi9Pf314EDB+orFgCAp9hkUam27l14O9N/Gtxxxx1atGhRfcQCAIDXM7046JtvvtHrr7+ujz76SD179qyxR+38+fMtCw4A0EBYHOQ204kzNzdX119/vSTp8OHDLudsjeADAwCfROJ0m9uJ89ixY4qPj9fGjRvrMx4AALya2/c4ExISdObMGefr2267TYWFhfUSFACggdn8/reyti7N5vurat0e4fcfG/bBBx+otLTU8oAAAB7AzkFu8/0/DQAAsJDb9zhtNluNxT8sBgIAH8HiILe5nTgNw9DEiROdT0ApKyvTPffcU+PrKMuWLbM2QgBA/bNZdH+yEdzjdDtxTpgwweX1HXfcYXkwAAB4O7cTZ2ZmZn3GAQDwJD/bhWZFPz7O9AYIAAAfRKnWbb4/QgAALMSMEwDAqloTSJwAAJ7HaYLvjxAAAAsx4wQAUKo1gcQJAGBVrQm+P0IAACzEjBMAINlkUam27l14OxInAIBVtSb4/ggBALAQM04AAKtqTSBxAgBYVWuC748QAAALkTgBABdKrH4WNBOl2vT0dPXu3VuhoaGKjIxUcnKyDh065HJNWVmZUlJS1KJFC4WEhGjs2LEqLCy0evSmkDgBAP8r1VrR3JSTk6OUlBRt27ZN69atU2VlpYYMGaLS0lLnNTNnztR7772npUuXKicnRydPntSYMWPq4xNwG/c4AQAesWbNGpfXWVlZioyM1O7duzVgwAAVFxdr0aJFWrJkiQYNGiRJyszMVMeOHbVt2zb17dvXE2Ez4wQA6H+raq1okhwOh0srLy//0RCKi4slSREREZKk3bt3q7KyUklJSc5rOnTooLi4OG3durUePgT3kDgBAJaXamNjY2W3250tPT39B9++urpaqamp6tevn7p06SJJKigoUEBAgMLDw12ujYqKUkFBQb18DO7waOLcvHmzRo4cqdatW8tms2nFihUu5wsLCzVx4kS1bt1azZo107Bhw3TkyBHPBAsAcNuJEydUXFzsbLNmzfrB61NSUpSbm6vs7OwGirD2PJo4S0tL1b17dy1YsKDGOcMwlJycrGPHjmnlypXau3ev2rZtq6SkJJcbxwAAC1ixovZikxQWFubSAgMDL/vWU6dO1erVq7Vx40a1adPGeTw6OloVFRUqKipyub6wsFDR0dH18jG4w6OLg4YPH67hw4df8tyRI0e0bds25ebmqnPnzpKkhQsXKjo6Wm+//bZ+97vfNWSoAODbPLBzkGEYmjZtmpYvX65NmzYpPj7e5XzPnj3l7++v9evXa+zYsZKkQ4cOKT8/X4mJiXWPtZa8dlXtxRvJQUFBzmN+fn4KDAzUli1bLps4y8vLXW5COxyO+g0UAFArKSkpWrJkiVauXKnQ0FDnfUu73a7g4GDZ7XZNnjxZaWlpioiIUFhYmKZNm6bExESPraiVvHhx0MWVU7NmzdJXX32liooKPfPMM/r888916tSpy/5cenq6yw3p2NjYBowaAK5QHvge58KFC1VcXKyBAwcqJibG2d555x3nNc8995x++ctfauzYsRowYICio6O1bNmy+vgE3Oa1M05/f38tW7ZMkydPVkREhJo0aaKkpCQNHz5chmFc9udmzZqltLQ052uHw0HyBIAf8537k3Xux00/9Lv8oqCgIC1YsOCSa2E8xWsTp3Shvr1v3z4VFxeroqJCrVq1Up8+fdSrV6/L/kxgYOAP3oQGAKAuvLZU+112u12tWrXSkSNHtGvXLo0ePdrTIQGAb7HZLCrV8lixelVSUqKjR486X+fl5Wnfvn2KiIhQXFycli5dqlatWikuLk4HDx7UjBkzlJycrCFDhngwagDwQTyP020eTZy7du3STTfd5Hx98d7khAkTlJWVpVOnTiktLU2FhYWKiYnRXXfdpccee8xT4QIA4NnEOXDgwB+8OTx9+nRNnz69ASMCgEaKB1m7zasXBwEAGogHVtVeqXz/TwMAACzEjBMAQKnWBBInAIBVtSb4/p8GAABYiBknAEDy87vQrOjHx5E4AQCSLCrVilItAAD4DmacAABW1ZpA4gQAsKrWBN//0wAAAAsx4wQAsKrWBBInAIBSrQm+/6cBAAAWYsYJAPh2xmnFqlrfn3GSOAEAlGpNoFQLAIAJzDgBAGyAYAKJEwAg+dkuNCv68XG+/6cBAAAWYsYJAKBUawKJEwDAqloTfP9PAwAALMSMEwBAqdYE3x8hAAAWYsYJAJDNZpPNgvuTVvTh7UicAABKtSb4/ggBALAQM04AADNOE0icAIAL37+0Yru8RnCP0/f/NAAAwELMOAEAlGpNIHECANhyzwTf/9MAAAALMeMEAHw747SiVOv7M04SJwCAUq0JlGoBADCBGScAgFW1JpA4AQAXNj+wYgMEK/rwcr7/pwEAABZixgkAoFRrAokTAMCqWhN8/08DAAAsxIwTAECp1gTfHyEA4MddLNVa0UzYvHmzRo4cqdatW8tms2nFihUu5w3D0OzZsxUTE6Pg4GAlJSXpyJEjFg7cPBInAMBjSktL1b17dy1YsOCS55999lm9+OKLysjI0Pbt29W8eXMNHTpUZWVlDRzp/1CqBQB4rFQ7fPhwDR8+/JLnDMPQ888/r0cffVSjR4+WJC1evFhRUVFasWKFxo0bV+dwa4MZJwBA8vOzrlkkLy9PBQUFSkpKch6z2+3q06ePtm7datn7mMWMEwBgOYfD4fI6MDBQgYGBpvooKCiQJEVFRbkcj4qKcp7zBGacAADZbDbLmiTFxsbKbrc7W3p6uodHaB1mnAAAy5/HeeLECYWFhTkPm51tSlJ0dLQkqbCwUDExMc7jhYWFuu666+oWZx0w4wQAWC4sLMyl1SZxxsfHKzo6WuvXr3ceczgc2r59uxITE60M1xRmnAAAj225V1JSoqNHjzpf5+Xlad++fYqIiFBcXJxSU1P1xBNPKCEhQfHx8XrsscfUunVrJScn1z3WWiJxAgAkWfR1FJOFzF27dummm25yvk5LS5MkTZgwQVlZWXrooYdUWlqqu+++W0VFRerfv7/WrFmjoKAgC2KtHZthGIbH3r0BOBwO2e12FZ/Kd6m3A8CVyuFwyB4Tp+Li4jr/Xrv4O7JozyaFhYbUPbZzJQq/fqAlsXkrZpwAAJ6OYgKJEwBg3eYFFm6A4K18f4QAAFiIGScAgFKtCSROAADP4zTB90cIAICFmHECACjVmkDiBABIsn3brOjHt1GqBQDABGacAABKtSaQOAEAJE4TPFqq3bx5s0aOHKnWrVvLZrNpxYoVLudLSko0depUtWnTRsHBwerUqZMyMjI8EywAAPJw4iwtLVX37t21YMGCS55PS0vTmjVr9Oabb+rf//63UlNTNXXqVK1ataqBIwUAX2ezsPk2j5Zqhw8fruHDh1/2/L/+9S9NmDBBAwcOlCTdfffdeuWVV7Rjxw6NGjWqgaIEgEaAUq3bvHpV7Y033qhVq1bpiy++kGEY2rhxow4fPqwhQ4Zc9mfKy8vlcDhcGgAAVvHqxPnXv/5VnTp1Ups2bRQQEKBhw4ZpwYIFGjBgwGV/Jj09XXa73dliY2MbMGIAuEJRqXWb1yfObdu2adWqVdq9e7fmzZunlJQUffTRR5f9mVmzZqm4uNjZTpw40YARA8CViszpLq/9OsrXX3+thx9+WMuXL9eIESMkSd26ddO+ffv0l7/8RUlJSZf8ucDAQAUGBjZkqACARsRrE2dlZaUqKyvl972HojZp0kTV1dUeigoAfBSLg9zm0cRZUlKio0ePOl/n5eVp3759ioiIUFxcnH7+85/rwQcfVHBwsNq2baucnBwtXrxY8+fP92DUAOCDbLIocda9C2/n0cS5a9cu3XTTTc7XaWlpkqQJEyYoKytL2dnZmjVrlsaPH6+zZ8+qbdu2evLJJ3XPPfd4KmQAQCPn0cQ5cOBAGYZx2fPR0dHKzMxswIgAoLHi6Sju8tp7nACABsQ9Trd59ddRAADwNsw4AQCiVOs+EicAgFKtCZRqAQAwgRknAIAZpwkkTgCAuMfpPkq1AACYwIwTACCbzSabBWVWK/rwdiROAAD3OE2gVAsAgAnMOAEAYnGQ+0icAABJFpVqG0HipFQLAIAJzDgBACwOMoHECQAQ9zjdR6kWAAATmHECACjVmkDiBABQqTWBUi0AACYw4wQAiCmn+0icAADucZpAqRYAABOYcQIAmHGaQOIEAIh7nO6jVAsAgAnMOAEA3044rSjV1r0Lb8eMEwDwv3ucVjSTFixYoKuvvlpBQUHq06ePduzYUQ8DtA6JEwDgMe+8847S0tI0Z84c7dmzR927d9fQoUN1+vRpT4d2WSROAID+tzjIiua++fPna8qUKZo0aZI6deqkjIwMNWvWTK+//rolo6oPJE4AgEdKtRUVFdq9e7eSkpKcx/z8/JSUlKStW7fWxygt4fOLgwzDkCQ5zp3zcCQAYI2Lv88u/n6zsk+r+nE4HC7HAwMDFRgY6HLsv//9r6qqqhQVFeVyPCoqSp9++qkl8dQHn0+cX375pSQp9trOHo4EAKz15Zdfym6316mPgIAARUdHW/o7MiQkRLGxsS7H5syZo7lz51r2Hp7k84kzIiJCkpSfn1/n/8CuJA6HQ7GxsTpx4oTCwsI8HU6DYdyMuzEoLi5WXFyc8/dbXQQFBSkvL08VFRUWRHaBYRiyfa9k+/3ZpiS1bNlSTZo0UWFhocvxwsJCRUdHWxaP1Xw+cfr5XbiNa7fbG9X/WBeFhYUx7kaEcTcuF3+/1VVQUJCCgoIs6cuMgIAA9ezZU+vXr1dycrIkqbq6WuvXr9fUqVMbPB53+XziBAB4r7S0NE2YMEG9evXSDTfcoOeff16lpaWaNGmSp0O7LBInAMBjbrvtNp05c0azZ89WQUGBrrvuOq1Zs6bGgiFv4vOJMzAwUHPmzLlkfd2XMW7G3Rgwbt8Y99SpU726NPt9NsPK9cwAAPg4NkAAAMAEEicAACaQOAEAMIHECQCACT6fOK+057yZkZ6ert69eys0NFSRkZFKTk7WoUOHXK4pKytTSkqKWrRooZCQEI0dO7bGLh1Xuqefflo2m02pqanOY7467i+++EJ33HGHWrRooeDgYHXt2lW7du1ynjcMQ7Nnz1ZMTIyCg4OVlJSkI0eOeDDiuquqqtJjjz2m+Ph4BQcH66c//an+9Kc/uezT6gvj3rx5s0aOHKnWrVvLZrNpxYoVLufdGePZs2c1fvx4hYWFKTw8XJMnT1ZJSUkDjqKRMHxYdna2ERAQYLz++uvGxx9/bEyZMsUIDw83CgsLPR2aJYYOHWpkZmYaubm5xr59+4ybb77ZiIuLM0pKSpzX3HPPPUZsbKyxfv16Y9euXUbfvn2NG2+80YNRW2vHjh3G1VdfbXTr1s2YMWOG87gvjvvs2bNG27ZtjYkTJxrbt283jh07Zqxdu9Y4evSo85qnn37asNvtxooVK4z9+/cbo0aNMuLj442vv/7ag5HXzZNPPmm0aNHCWL16tZGXl2csXbrUCAkJMV544QXnNb4w7g8++MB45JFHjGXLlhmSjOXLl7ucd2eMw4YNM7p3725s27bN+Mc//mFcc801xu23397AI/F9Pp04b7jhBiMlJcX5uqqqymjdurWRnp7uwajqz+nTpw1JRk5OjmEYhlFUVGT4+/sbS5cudV7z73//25BkbN261VNhWubcuXNGQkKCsW7dOuPnP/+5M3H66rj/7//+z+jfv/9lz1dXVxvR0dHGn//8Z+exoqIiIzAw0Hj77bcbIsR6MWLECOO3v/2ty7ExY8YY48ePNwzDN8f9/cTpzhg/+eQTQ5Kxc+dO5zUffvihYbPZjC+++KLBYm8MfLZUe6U+560uiouLJf1vY/vdu3ersrLS5TPo0KGD4uLifOIzSElJ0YgRI1zGJ/nuuFetWqVevXrp1ltvVWRkpHr06KHXXnvNeT4vL08FBQUu47bb7erTp88VPe4bb7xR69ev1+HDhyVJ+/fv15YtWzR8+HBJvjvu73JnjFu3blV4eLh69erlvCYpKUl+fn7avn17g8fsy3x256Ar9TlvtVVdXa3U1FT169dPXbp0kSQVFBQoICBA4eHhLtdGRUWpoKDAA1FaJzs7W3v27NHOnTtrnPPVcR87dkwLFy5UWlqaHn74Ye3cuVPTp09XQECAJkyY4Bzbpf6bv5LH/Yc//EEOh0MdOnRQkyZNVFVVpSeffFLjx4+XJJ8d93e5M8aCggJFRka6nG/atKkiIiJ85nPwFj6bOBublJQU5ebmasuWLZ4Opd6dOHFCM2bM0Lp16zzyRAdPqa6uVq9evfTUU09Jknr06KHc3FxlZGRowoQJHo6u/vztb3/TW2+9pSVLlqhz587at2+fUlNT1bp1a58eN7yXz5Zqr9TnvNXG1KlTtXr1am3cuFFt2rRxHo+OjlZFRYWKiopcrr/SP4Pdu3fr9OnTuv7669W0aVM1bdpUOTk5evHFF9W0aVNFRUX55LhjYmLUqVMnl2MdO3ZUfn6+JDnH5mv/zT/44IP6wx/+oHHjxqlr16668847NXPmTKWnp0vy3XF/lztjjI6O1unTp13Of/PNNzp79qzPfA7ewmcT53ef83bRxee8JSYmejAy6xiGoalTp2r58uXasGGD4uPjXc737NlT/v7+Lp/BoUOHlJ+ff0V/BoMHD9bBgwe1b98+Z+vVq5fGjx/v/HdfHHe/fv1qfN3o8OHDatu2rSQpPj5e0dHRLuN2OBzavn37FT3u8+fP13juZJMmTVRdXS3Jd8f9Xe6MMTExUUVFRdq9e7fzmg0bNqi6ulp9+vRp8Jh9mqdXJ9Wn7OxsIzAw0MjKyjI++eQT4+677zbCw8ONgoICT4dmiXvvvdew2+3Gpk2bjFOnTjnb+fPnndfcc889RlxcnLFhwwZj165dRmJiopGYmOjBqOvHd1fVGoZvjnvHjh1G06ZNjSeffNI4cuSI8dZbbxnNmjUz3nzzTec1Tz/9tBEeHm6sXLnSOHDggDF69Ogr7msZ3zdhwgTjJz/5ifPrKMuWLTNatmxpPPTQQ85rfGHc586dM/bu3Wvs3bvXkGTMnz/f2Lt3r3H8+HHDMNwb47Bhw4wePXoY27dvN7Zs2WIkJCTwdZR64NOJ0zAM469//asRFxdnBAQEGDfccIOxbds2T4dkGUmXbJmZmc5rvv76a+O+++4zrrrqKqNZs2bGLbfcYpw6dcpzQdeT7ydOXx33e++9Z3Tp0sUIDAw0OnToYLz66qsu56urq43HHnvMiIqKMgIDA43Bgwcbhw4d8lC01nA4HMaMGTOMuLg4IygoyGjXrp3xyCOPGOXl5c5rfGHcGzduvOT/zxMmTDAMw70xfvnll8btt99uhISEGGFhYcakSZOMc+fOeWA0vo3HigEAYILP3uMEAKA+kDgBADCBxAkAgAkkTgAATCBxAgBgAokTAAATSJwAAJhA4gQAwAQSJxq9iRMnKjk52WPvf+eddzqfePJjxo0bp3nz5tVzRAB+CDsHwafZbLYfPD9nzhzNnDlThmHUeH5nQ9i/f78GDRqk48ePKyQk5Eevz83N1YABA5SXlye73d4AEQL4PhInfNp3H+D7zjvvaPbs2S5PGAkJCXErYdWX3/3ud2ratKkyMjLc/pnevXtr4sSJSklJqcfIAFwOpVr4tOjoaGez2+2y2Wwux0JCQmqUagcOHKhp06YpNTVVV111laKiovTaa6+ptLRUkyZNUmhoqK655hp9+OGHLu+Vm5ur4cOHKyQkRFFRUbrzzjv13//+97KxVVVV6d1339XIkSNdjr/88stKSEhQUFCQoqKi9Ktf/crl/MiRI5WdnV33DwdArZA4gUt444031LJlS+3YsUPTpk3Tvffeq1tvvVU33nij9uzZoyFDhujOO+/U+fPnJUlFRUUaNGiQevTooV27dmnNmjUqLCzUr3/968u+x4EDB1RcXKxevXo5j+3atUvTp0/X448/rkOHDmnNmjUaMGCAy8/dcMMN2rFjh8rLy+tn8AB+EIkTuITu3bvr0UcfVUJCgmbNmqWgoCC1bNlSU6ZMUUJCgmbPnq0vv/xSBw4ckCS99NJL6tGjh5566il16NBBPXr00Ouvv66NGzfq8OHDl3yP48ePq0mTJoqMjHQey8/PV/PmzfXLX/5Sbdu2VY8ePTR9+nSXn2vdurUqKipcytAAGg6JE7iEbt26Of+9SZMmatGihbp27eo8FhUVJUk6ffq0pAuLfDZu3Oi8ZxoSEqIOHTpIkj777LNLvsfXX3+twMBAlwVMv/jFL9S2bVu1a9dOd955p9566y3nrPai4OBgSapxHEDDIHECl+Dv7+/y2mazuRy7mOyqq6slSSUlJRo5cqT27dvn0o4cOVKj1HpRy5Ytdf78eVVUVDiPhYaGas+ePXr77bcVExOj2bNnq3v37ioqKnJec/bsWUlSq1atLBkrAHNInIAFrr/+en388ce6+uqrdc0117i05s2bX/JnrrvuOknSJ5984nK8adOmSkpK0rPPPqsDBw7oP//5jzZs2OA8n5ubqzZt2qhly5b1Nh4Al0fiBCyQkpKis2fP6vbbb9fOnTv12Wefae3atZo0aZKqqqou+TOtWrXS9ddfry1btjiPrV69Wi+++KL27dun48ePa/Hixaqurlb79u2d1/zjH//QkCFD6n1MAC6NxAlYoHXr1vrnP/+pqqoqDRkyRF27dlVqaqrCw8Pl53f5/81+97vf6a233nK+Dg8P17JlyzRo0CB17NhRGRkZevvtt9W5c2dJUllZmVasWKEpU6bU+5gAXBobIAAe9PXXX6t9+/Z65513lJiY+KPXL1y4UMuXL9ff//73BogOwKUw4wQ8KDg4WIsXL/7BjRK+y9/fX3/961/rOSoAP4QZJwAAJjDjBADABBInAAAmkDgBADCBxAkAgAkkTgAATCBxAgBgAokTAAATSJwAAJhA4gQAwIT/Dz6Un9XD7JGkAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}