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   "source": [
    "\\tableofcontents % LaTeX rendered pdf will have a TOC with links\n",
    "% These TeX commands run at the start to remove section numbering\n",
    "%\\renewcommand{\\thesection}{\\hspace*{-1.0em}}\n",
    "%\\renewcommand{\\thesubsection}{\\hspace*{-1.0em}}\n",
    "%\\renewcommand{\\thesubsubsection}{\\hspace*{-1.0em}}"
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  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ce05783c-75b8-4284-8f4d-830f5fd0cff6",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sk_dsp_comm import sigsys as ss\n",
    "from sk_dsp_comm import synchronization as sync\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9410d6b2-9b30-447d-b9d3-7488b3bd1036",
   "metadata": {},
   "source": [
    "# Automatic Frequency Control"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d18c610-51f3-4609-954c-13d831554e81",
   "metadata": {},
   "source": [
    "The module `synchronization.py` has component classes for implementing AFC. The following example shows how to implement the AFC a quadricorrelator/frequency discriminator class for sample-by-sample processing, as is needed for tracking loop simulation/implementation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a16d4f86-dc74-472b-9636-b231e741ce02",
   "metadata": {},
   "source": [
    "## AFC Tracking Loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "14cb09f2-14dd-47a4-872f-4f68659c6e5b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define input signal for AFC\n",
    "f_clk_afc = 100e3\n",
    "n = np.arange(100000)\n",
    "fc = 1000\n",
    "fm = 100\n",
    "# Test with amplitude modulation\n",
    "x_in = (1 + 0.8*np.cos(2*np.pi*fm/f_clk_afc*n))*np.exp(1j*2*np.pi*fc/f_clk_afc*n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a8426f60-d643-41b8-ae5e-c18b437df980",
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   "outputs": [],
   "source": [
    "Bn_afc = 10\n",
    "y_d_afc, y_lf_afc, x_out_afc = sync.cbb_afc(x_in, Bn_afc, 1.0, fc_afc=0.0, f_clk_afc=f_clk_afc, afc_open=False)\n",
    "plt.plot(n/f_clk_afc*1e3,y_d_afc,label='Discrim Out')\n",
    "plt.plot(n/f_clk_afc*1e3,y_lf_afc,label='LF Out')\n",
    "# Plot RC lowpass step response theory\n",
    "# Analog\n",
    "plt.title(r'AFC Frequency Step Response')\n",
    "plt.ylabel(r'Frequency/Frequency Error')\n",
    "plt.xlabel(r'Time (ms)')\n",
    "plt.legend()\n",
    "plt.grid();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8eb6a05c-2a8d-4051-9be1-619c608e2321",
   "metadata": {},
   "outputs": [],
   "source": [
    "Px_in, fx_in = ss.psd(x_in,2**15,f_clk_afc)\n",
    "plt.plot(fx_in,10*np.log10(Px_in),label='Input Signal at 1kHz')\n",
    "Px_out, fx_out = ss.psd(x_out_afc[10000:],2**15,f_clk_afc)\n",
    "plt.plot(fx_out,10*np.log10(Px_out),label='AFC Output, less transient')\n",
    "plt.title(r'PSD at Input and Output of AFC')\n",
    "plt.xlabel(r'Frequency (Hz)')\n",
    "plt.ylabel(r'PSD (dB)')\n",
    "plt.ylim(-20,40)\n",
    "plt.xlim(-500,2000)\n",
    "plt.legend()\n",
    "plt.grid();"
   ]
  }
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