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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}}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "519d6456-e844-4bb7-a9be-8f19ece1ea90",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib import cm\n",
    "from matplotlib.ticker import LinearLocator\n",
    "from sk_dsp_comm import sigsys as ss\n",
    "from sk_dsp_comm import digitalcom as dc\n",
    "from sk_dsp_comm import synchronization as sync\n",
    "from scipy import signal\n",
    "\n",
    "%config InlineBackend.figure_formats=['svg'] # SVG inline viewing"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a33e77a-c4ee-4e59-b672-626aa5fabfde",
   "metadata": {},
   "source": [
    "# Phase Lock Loops\n",
    "\n",
    "The module `synchronization.py` has component classes for implementing NCO's (32-bit and 48-bit), DSP loop filters (two types), accumulator (used in the loop filters), $K_p$ and $K_i$ calculation functions, and several digital PLL analysis functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2aa5972f-017c-44e3-ba28-3ab666eedfe0",
   "metadata": {},
   "outputs": [],
   "source": [
    "NCO1 = sync.NCO(3.25e6,120e6, n_bits=32)\n",
    "NCO2 = sync.NCO(3.0e6,120e6, n_bits=48)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c77f6dbc-16ba-40ae-806e-fe606171fe08",
   "metadata": {},
   "outputs": [],
   "source": [
    "Nclks = 100000\n",
    "n = np.arange(Nclks)\n",
    "x_32 = np.zeros(len(n))\n",
    "data_bit = 1\n",
    "for k in range(Nclks):\n",
    "    NCO1.update(0.0)\n",
    "    x_32[k] = NCO1.out_sin()\n",
    "    # x[k] = data_bit\n",
    "    # if NCO1.NCO32_pos_edge():\n",
    "    #     data_bit = 2*random.randint(0,2) - 1\n",
    "y_32 = dc.farrow_resample(x_32,3.5,3.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "65ff2d1e-b797-4a25-b4a4-facb8d5ee928",
   "metadata": {},
   "outputs": [],
   "source": [
    "Nclks = 100000\n",
    "n = np.arange(Nclks)\n",
    "x_48 = np.zeros(len(n))\n",
    "data_bit = 1\n",
    "for k in range(Nclks):\n",
    "    NCO2.update(0.0)\n",
    "    x_48[k] = NCO2.out_sin()\n",
    "    # x[k] = data_bit\n",
    "    # if NCO2.NCO48_pos_edge():\n",
    "    #     data_bit = 2*random.randint(0,2) - 1\n",
    "y_48 = dc.farrow_resample(x_48,3.5,3.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "28ff24b5-8d8e-4078-b513-01fbe3e4ad79",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(y_32[1000:1300])\n",
    "plt.plot(y_48[1000:1300])\n",
    "\n",
    "plt.grid();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0cf28109-61e2-4d0b-a83d-2e8f19ddba65",
   "metadata": {},
   "outputs": [],
   "source": [
    "Py_32, fy_32 = ss.psd(y_32,2**16,120,scale_noise=False)\n",
    "Py_48, fy_48 = ss.psd(y_48,2**16,120,scale_noise=False)\n",
    "plt.plot(fy_32,10*np.log10(Py_32),120)\n",
    "plt.plot(fy_48,10*np.log10(Py_48),120)\n",
    "plt.ylim(-60,0)\n",
    "plt.xlim(0, 4)\n",
    "plt.title(r'Sinusoid Spectrum using the Sinusoid Scaling Option')\n",
    "plt.xlabel(r'Frequency (MHz)')\n",
    "plt.ylabel(r'PSD (dB)')\n",
    "plt.grid();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b9d5045-53c1-4efe-9e7a-1b827bc2d539",
   "metadata": {},
   "source": [
    "## Complex Baseband PLL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e9f30f97-c4ff-4419-ac2e-4440d07b6fda",
   "metadata": {},
   "outputs": [],
   "source": [
    "fs = 100e3\n",
    "fc = 0\n",
    "n = np.arange(10000)\n",
    "x_in = np.exp(1j*2*np.pi*fc/fs*n + 1j*np.pi/8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "008ba0ec-e156-49ee-a589-4b68ab6850d0",
   "metadata": {},
   "outputs": [],
   "source": [
    "phi_pstep = sync.phi_phase_step(n,100,0.707,fs)\n",
    "phi_fstep = sync.phi_freq_step(n,100,0.707,fs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ebcea9ae-d67a-474f-9975-fae69ec0fe9a",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_d_pll, y_lf_pll, x_NCO_pll = sync.cbb_pll(x_in, 100, 1.0, fc_pll=0.0, f_clk_pll=fs, pll_open=False)\n",
    "t_pll = np.arange(0,len(y_d_pll))/fs\n",
    "plt.plot(t_pll*1e3,phi_pstep/2/np.pi * np.pi/8,label='Linear Theory')\n",
    "plt.plot(t_pll*1e3,y_d_pll,label='Measured')\n",
    "plt.title(r'Type 2 PLL Phase Step (Freq. Step) Response')\n",
    "plt.ylabel(r'Phase Error')\n",
    "plt.xlabel(r'Time (ms)')\n",
    "plt.legend()\n",
    "plt.grid();"
   ]
  }
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