{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "42d10222-774f-4175-bda3-95e82945b802",
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://www.astroml.org/astroML-notebooks/chapter10/astroml_chapter10_Modeling_Toolkit_for_Time_Series_Analysis.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0de4c2f1-b7d0-4885-a0e1-5e075be72fb9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from astroML.datasets import fetch_rrlyrae_templates\n",
    "from scipy.signal import fftconvolve\n",
    "from scipy import fftpack\n",
    "from matplotlib import mlab\n",
    "from astroML.datasets import fetch_LIGO_large\n",
    "from scipy.fftpack import fft\n",
    "from scipy.stats import norm\n",
    "from astroML.fourier import PSD_continuous\n",
    "from astroML.plotting import setup_text_plots\n",
    "setup_text_plots(usetex=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "464586c1-74de-44b7-af05-382e1bc2b00c",
   "metadata": {},
   "source": [
    "<h2>Main concepts for time series analysis</h2>\n",
    "<p>The time series discussed here will be limited to two-dimensional scalar data sets: pairs of random variables, (<span class=\"math notranslate nohighlight\">\\(t_1\\)</span>, <span class=\"math notranslate nohighlight\">\\(y_1\\)</span>),…,(<span class=\"math notranslate nohighlight\">\\(t_N\\)</span>; <span class=\"math notranslate nohighlight\">\\(y_N\\)</span>), with no assumptions about the sampling of the time coordinate t. In many ways, analysis methods discussed here are closely related to the parameter estimation and model selection problems discussed in the context of regression. However, unlike regression problems where different y measurements are typically treated as independent random\n",
    "variables, in such models the value of <span class=\"math notranslate nohighlight\">\\(y_{i+1}\\)</span> directly depends on the preceding value <span class=\"math notranslate nohighlight\">\\(y_i\\)</span>.</p>\n",
    "<p>The main tasks of time series analysis are:</p>\n",
    "<ol class=\"arabic simple\">\n",
    "<li><p>To characterize the presumed temporal correlation between different values of y, including its significance.</p></li>\n",
    "<li><p>To forecast (predict) future values of y.</p></li>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a146f64-7ae7-4431-b9fc-93b7ec7d1813",
   "metadata": {},
   "source": [
    "<h2>Fourier analysis</h2>\n",
    "<p>Fourier analysis plays a major role in the analysis of time series data. In Fourier analysis, general\n",
    "functions are represented or approximated by integrals or sums of simpler trigonometric functions.</p>\n",
    "<p>For periodic functions, such as periodic light curves\n",
    "in astronomy, it is often true that a relatively small number of terms (less than 10) suffices to reach\n",
    "an approximation precision level similar to the measurement precision.</p>\n",
    "</section>\n",
    "<section id=\"some-useful-concepts\">\n",
    "<h2>Some useful concepts</h2>\n",
    "<p>The <strong>Fourier transform</strong> of function h(t) is defined as</p>\n",
    "<div class=\"math notranslate nohighlight\">\n",
    "\\[H(f)=\\int_{-\\infty}^{\\infty} h(t) exp(-i2\\pi ft)dt\\]</div>\n",
    "<p>with <strong>inverse transformation</strong></p>\n",
    "<div class=\"math notranslate nohighlight\">\n",
    "\\[h(t)=\\int_{-\\infty}^{\\infty} H(t) exp(-i2\\pi ft)df\\]</div>\n",
    "<p>where t is time and f is frequency (for time in seconds, the unit for frequency is hertz, or Hz; the\n",
    "units for H(f) are the product of the units for h(t) and inverse hertz.<br />\n",
    "For a real function h(t), H(f) is in general a complex function.<br />\n",
    "In the special case when h(t) is an even function such that h(-t) = h(t), H(f) is real and even as well. For example, the\n",
    "Fourier transform of a pdf of a zero-mean Gaussian <span class=\"math notranslate nohighlight\">\\(N(0, \\sigma)\\)</span> in the time domain is a Gaussian\n",
    "<span class=\"math notranslate nohighlight\">\\(H(f) = exp(-2\\pi^2 \\sigma^2 f^2)\\)</span> in the frequency domain.<br />\n",
    "When the time axis of an arbitrary function\n",
    "h(t) is shifted by <span class=\"math notranslate nohighlight\">\\(\\Delta t\\)</span>, then the Fourier transform of <span class=\"math notranslate nohighlight\">\\(h(t + \\Delta t)\\)</span> is</p>\n",
    "<div class=\"math notranslate nohighlight\">\n",
    "\\[\\int_{-\\infty}^{\\infty}h(t+\\Delta t)exp(-i2\\pi ft)dt = H(f)exp(i2\\pi f\\Delta t)\\]</div>\n",
    "<p>Therefore, the <strong>Fourier transform of a Gaussian <span class=\"math notranslate nohighlight\">\\(N(\\mu, \\sigma)\\)</span></strong> is</p>\n",
    "<div class=\"math notranslate nohighlight\">\n",
    "\\[H_{Gauss}(f)=exp(-2\\pi^2\\sigma^2f^2)[cos(2\\pi f\\mu)+isin(2\\pi f \\mu)]\\]</div>\n",
    "<p>This is known as <strong>“white noise”</strong> since there is no frequency\n",
    "dependence (also known as “thermal noise” or Johnson’s noise).<br />\n",
    "An important quantity in time series analysis is the one-sided <strong>power spectral density (PSD)</strong> function\n",
    "(or power spectrum) defined for <span class=\"math notranslate nohighlight\">\\(0 \\leq f &lt; \\infty\\)</span> as</p>\n",
    "<div class=\"math notranslate nohighlight\">\n",
    "\\[PSD(f) \\equiv |H(f)|^2+|H(-f)|^2\\]</div>\n",
    "<p>The PSD gives the amount of power contained in the frequency interval between f and f + df.<br />\n",
    "The total power is the same whether computed in the frequency or the time domain:</p>\n",
    "<div class=\"math notranslate nohighlight\">\n",
    "\\[P_{tot} \\equiv \\int_0^{\\infty}PSD(f)df=\\int_{-\\infty}^{\\infty}|h(t)|^2dt\\]</div>\n",
    "<p>This result is known as <strong>Parseval’s theorem</strong>.</p>\n",
    "<section id=\"fourier-reconstruction-of-rr-lyrae-templates\">\n",
    "<h3>Fourier Reconstruction of RR-Lyrae Templates</h3>\n",
    "<p>Below is an example of a truncated Fourier representation of an RR Lyrae light curve. As we can see, the more terms that are included in the sum, the better is the resulting approximation.</p>\n",
    "<section id=\"import-a-rr-lyrae-template\">\n",
    "\n",
    "<p>From astroML.datasets, we take the RR Lyrae (variable star) light curve as an example. RR Lyrae has a periodical pulsation.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "3e7256e5-cca2-4951-a3a8-ae2f1e79d2ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x800 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "templates = fetch_rrlyrae_templates()\n",
    "x, y = templates['115r'].T\n",
    "\n",
    "fig = plt.figure(figsize=(10, 10))\n",
    "fig.subplots_adjust(hspace=0)\n",
    "\n",
    "kvals = [1, 3, 8]\n",
    "subplots = [311, 312, 313]\n",
    "\n",
    "for (k, subplot) in zip(kvals, subplots):\n",
    "    ax = fig.add_subplot(subplot)\n",
    "\n",
    "    # Use FFT to fit a truncated Fourier series\n",
    "    y_fft = np.fft.fft(y)\n",
    "    y_fft[k + 1:-k] = 0\n",
    "    y_fit = np.fft.ifft(y_fft).real\n",
    "\n",
    "    # plot the true value and the k-term reconstruction\n",
    "    ax.plot(np.concatenate([x, 1 + x]),\n",
    "            np.concatenate([y, y]), '--k', lw=2)\n",
    "    ax.plot(np.concatenate([x, 1 + x]),\n",
    "            np.concatenate([y_fit, y_fit]), color='gray')\n",
    "\n",
    "    label = \"%i mode\" % k\n",
    "    if k > 1:\n",
    "        label += 's'\n",
    "\n",
    "    ax.text(0.02, 0.1, label, ha='left', va='bottom',\n",
    "            transform=ax.transAxes)\n",
    "\n",
    "    if subplot == subplots[-1]:\n",
    "        ax.set_xlabel('phase')\n",
    "    else:\n",
    "        ax.xaxis.set_major_formatter(plt.NullFormatter())\n",
    "\n",
    "    if subplot == subplots[1]:\n",
    "        ax.set_ylabel('amplitude')\n",
    "    ax.yaxis.set_major_formatter(plt.NullFormatter())\n",
    "\n",
    "    ax.set_xlim(0, 2)\n",
    "    ax.set_ylim(1.1, -0.1)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0d5c8d7-4068-4786-8f91-7ef432d8205c",
   "metadata": {},
   "source": [
    "<h3> The Fast Fourier Transform (FFT)</h3>\n",
    "<p>The <strong>Fast Fourier transform (FFT)</strong> is an algorithm for computing discrete Fourier transforms in\n",
    "O(N logN) time, rather than O(N2) using a naive implementation. The algorithmic details for\n",
    "the FFT can be found in NumRec. The speed of FFT makes it a widespread tool in the analysis\n",
    "of evenly sampled, high signal-to-noise ratio, time series data.<br />\n",
    "An example below shows such analysis for a function with a single dominant frequency: a sine wave whose amplitude is modulated by a Gaussian.</p>\n",
    "<section id=\"id1\">\n",
    "\n",
    "</section>\n",
    "<section id=\"show-result-with-data-and-calculated-psd\">\n",
    "<h4>Show result with data and calculated PSD</h4>\n",
    "<p>The discrete Fourier transform (bottom panel) for two noisy data sets shown in the top panel. For 512 evenly sampled times t (dt = 0.977), points are drawn from h(t) = a + sin(t)G(t), where G(t) is a Gaussian N(mu = 0,sigma = 10). Gaussian noise with sigma = 0.05 (top data set) and 0.005 (bottom data set) is added to signal h(t). The value of the offset a is 0.15 and 0, respectively. The discrete Fourier transform is computed as described in this section. For both noise realizations, the correct frequency f = (2pi)-1 ~ 0.159 is easily discernible in the bottom panel. Note that the height of peaks is the same for both noise realizations. The large value of abs(H(f = 0)) for data with larger noise is due to the vertical offset.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3da42d0d-74d8-4d30-a8c9-7fb7e06280ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(1)\n",
    "\n",
    "tj = np.linspace(-25, 25, 512)\n",
    "hj = np.sin(tj)\n",
    "hj *= norm(0, 10).pdf(tj)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "7c49a4fa-2a0c-4a5f-b0a0-629828bb4aa2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x620 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the results\n",
    "fig = plt.figure(figsize=(10, 7.75))\n",
    "fig.subplots_adjust(hspace=0.35)\n",
    "ax1 = fig.add_subplot(211)\n",
    "ax2 = fig.add_subplot(212)\n",
    "\n",
    "offsets = (0, 0.15)\n",
    "colors = ('black', 'gray')\n",
    "linewidths = (1, 2)\n",
    "errors = (0.005, 0.05)\n",
    "\n",
    "for (offset, color, error, linewidth) in zip(offsets, colors,\n",
    "                                             errors, linewidths):\n",
    "    # compute the PSD\n",
    "    err = np.random.normal(0, error, size=hj.shape)\n",
    "    hj_N = hj + err + offset\n",
    "    fk, PSD = PSD_continuous(tj, hj_N)\n",
    "\n",
    "    # plot the data and PSD\n",
    "    ax1.scatter(tj, hj_N, s=4, c=color, lw=0)\n",
    "    ax1.plot(tj, 0 * tj + offset, '-', c=color, lw=1)\n",
    "    ax2.plot(fk, PSD, '-', c=color, lw=linewidth)\n",
    "\n",
    "# vertical line marking the expected peak location\n",
    "ax2.plot([0.5 / np.pi, 0.5 / np.pi], [-0.1, 1], ':k', lw=1)\n",
    "\n",
    "ax1.set_xlim(-25, 25)\n",
    "ax1.set_ylim(-0.1, 0.3001)\n",
    "\n",
    "ax1.set_xlabel('$t$')\n",
    "ax1.set_ylabel('$h(t)$')\n",
    "\n",
    "ax1.yaxis.set_major_locator(plt.MultipleLocator(0.1))\n",
    "\n",
    "ax2.set_xlim(0, 0.8)\n",
    "ax2.set_ylim(-0.101, 0.801)\n",
    "\n",
    "ax2.set_xlabel('$f$')\n",
    "ax2.set_ylabel('$PSD(f)$')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33736392-8082-4711-8f01-a546d36df4b4",
   "metadata": {},
   "source": [
    "<h3>The window function</h3>\n",
    "<p>The sampling window\n",
    "function in the time domain can be expressed as the sum of delta functions placed at sampled\n",
    "observation times. The Fourier transform of a set of delta functions with spacing <span class=\"math notranslate nohighlight\">\\(\\Delta t\\)</span> is another set of delta functions with spacing <span class=\"math notranslate nohighlight\">\\(1/\\Delta t\\)</span>; this result is at the core of the Nyquist sampling theorem. By the convolution theorem, pointwise multiplication of this sampling window with the data is equivalent to the convolution of their Fourier\n",
    "representations, as seen in the right-hand panels. When data are nonuniformly sampled, the impact of sampling can be understood using the same framework.<br />\n",
    "The sampling window is the sum of delta functions, but because the delta functions\n",
    "are not regularly spaced, the Fourier transform is a more complicated, and in general complex,\n",
    "function of f. The PSD can be computed using the discrete Fourier transform by constructing a\n",
    "fine grid of times and setting the window function to one at the sampled times and zero otherwise.\n",
    "The resulting PSD is called the <strong>spectral window function</strong>, and models how the Fourier-space signal\n",
    "is affected by the sampling. As discussed in detail in <a class=\"reference external\" href=\"http://adsabs.harvard.edu/full/1975Ap%26SS..36..137D\">Fourier analysis with unequally-spaced data</a>, the observed <strong>power spectral density (PSD)</strong> is a convolution of\n",
    "the true underlying PSD and this spectral window function.<br />\n",
    "We will see an example of an irregular sampling window in the figure below.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "472c2177-2a8c-4842-afa9-f29101602cda",
   "metadata": {},
   "outputs": [],
   "source": [
    "Nbins = 2 ** 15\n",
    "Nobs = 40\n",
    "f = lambda t: np.sin(np.pi * t / 3)\n",
    "\n",
    "t = np.linspace(-100, 200, Nbins)\n",
    "dt = t[1] - t[0]\n",
    "y = f(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "28239b10-141d-4b79-8d69-13da54805e73",
   "metadata": {},
   "outputs": [],
   "source": [
    "# select observations\n",
    "np.random.seed(42)\n",
    "t_obs = 100 * np.random.random(40)\n",
    "\n",
    "D = abs(t_obs[:, np.newaxis] - t)\n",
    "i = np.argmin(D, 1)\n",
    "\n",
    "t_obs = t[i]\n",
    "y_obs = y[i]\n",
    "window = np.zeros(Nbins)\n",
    "window[i] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "7fa21534-e55f-4ab1-92b4-0f42be53bcc7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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araparQ5f5BfYPRJwj23hgWQ1m001m01Jku2UyokFikqlMtL3bW5uxsMcURQpn88PvF+v1xvrpMxp3s4UWBQEeyBZX34gP5+UOSonQx7GGIVhKGNMfFuj0ZD0TxDpdDoyxqhQKMTDHwDmH2P9wOxi2SgAAJjNZaMAAGC+ECgAAIA1AgUAALBGoAAAANYIFAAAwBqBAgAAWCNQAAAAawQKAABgjUABAACsESgAAIA1AgUAALBGoAAAANYIFAAAwBqBAgAAWCNQAAAAawQKAABgjUABAACsESgAAIA1AgUAALBGoAAAANYIFAAAwBqBAgAAWCNQAAAAawQKAABgjUABAACsESgwlGaz6bqEhUS7u0G7u0Pbzx4ngaLdbqtUKl15PJPJqFQqqd1uJ1gVboI3uRu0uxu0uzu0/ez51sUPLRaLevr06ZXHd3Z2lMvlEqwIAADYcBIortPpdHR8fKwwDFWpVC4c6/f7kqTT01MXpS28fr9P2ztAu7tBu7tD2yfvvL3Pz7PDmligCILg0m2+7yudTl/7vecholQqqVwuy/O8+NjZ2Zkk6d69e+MpFENbWVlxXcJCot3doN3doe3dODs7G6ntJxYo/tuzcFNBEMTBI4oiHR8fXwgUd+/e1fv373X79m0tLS2NqVoAABZbv9/X2dmZ7t69O9L3L/VH7duwYIzR48eP9fTpU/m+L0lqNBp68uSJoihSp9ORpIFDHgAAYPo4CRQAAGC+sA8FAACwNnOBIggCGWMGTvrEeEVRJGOM2u22Go1GfDvPQTL29vYutDHtnox2uy1jDK/5hBljeM0naNB+UIPae5jnYKYCRRAEyufz8n1fh4eHiqLIdUlzrdVqaXV1VcViUbu7uwrDkOcgQZ1OJ25f2j0ZxhgdHx/L9/14fhdtP3nGGEVRdGH/Idp9sorF4oU2HdTewz4HMxUout1uvOJjbW0tnryJyahUKvEbPAxDpdNpnoOEGGOUz+fjr2n3ZOzu7urw8FDGGBljJNH2SfB9X0+fPlWpVIq3FqDdkzWovYd9DmYqUHzp6OjIdQkLo9FoaGdn59LtPAeTsbe3J9/3LyyX/hLtPlkPHz6MP5Ht7e1dOEbbT8be3p5KpZK2tra0vb196ZMw7Z6sQe19k+dgKnfKvMrm5mb8Qoui6MInOEyGMebCviA8B8k4H0/+66+/FIYh7Z6QTCZz4WvP82j7BDx//ly//fZb/DWv+eQNau8wDId6DmZu2WgQBPHJrVgsui5nrp3vF5JOp3V8fKxutyuJ5yAp29vbCsNQz549k+d5tHtCGo2Gcrmc9vb29OTJE0m85ictDEMZYy61Me0+OYP2gxrU3sM8BzMXKAAAwPSZ2TkUAABgehAoAACANQIFAACwRqAAAADWCBQAAMAagQIAAFgjUAAAAGsECgAAYO1/v3sxn6KNtPEAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1280x640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16, 8))\n",
    "fig.subplots_adjust(bottom=0.15, hspace=0.2, wspace=0.25,\n",
    "                    left=0.12, right=0.95)\n",
    "\n",
    "# First panel: data vs time\n",
    "ax = fig.add_subplot(221)\n",
    "ax.plot(t_obs, y_obs, '.k', ms=4)\n",
    "ax.text(0.95, 0.93, \"Data\", ha='right', va='top', transform=ax.transAxes)\n",
    "ax.set_ylabel('$y(t)$')\n",
    "ax.set_xlim(0, 100)\n",
    "ax.set_ylim(-1.5, 1.8);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7c033e94-030f-4b7b-9aac-5100ab963ede",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute PSDs\n",
    "Nfreq = int(Nbins / 2)\n",
    "\n",
    "dt = t[1] - t[0]\n",
    "df = 1. / (Nbins * dt)\n",
    "f = df * np.arange(Nfreq)\n",
    "\n",
    "PSD_window = abs(np.fft.fft(window)[:Nfreq]) ** 2\n",
    "PSD_y = abs(np.fft.fft(y)[:Nfreq]) ** 2\n",
    "PSD_obs = abs(np.fft.fft(y * window)[:Nfreq]) ** 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef5a9a3e-9c67-4a3a-8371-cfcaf29349ac",
   "metadata": {},
   "source": [
    "<h4>Scale PSDs for plotting</h4>\n",
    "<p>Normalize the true PSD so it can be shown in the plot: in theory it’s a delta function, so normalization is arbitrary.</p>\n",
    "<div class=\"cell docutils container\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "00410c45-59de-490f-a2a6-3b89bc3c2c3a",
   "metadata": {},
   "outputs": [],
   "source": [
    "PSD_window /= 500\n",
    "PSD_y /= PSD_y.max()\n",
    "PSD_obs /= 500"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d632e8aa-6693-4829-bdd1-d0fe07d261fb",
   "metadata": {},
   "source": [
    "<h4>Show figure</h4>\n",
    "<p>An illustration of the impact of a sampling window function of resulting PSD.</p>\n",
    "<ul class=\"simple\">\n",
    "<li><p>The left panel shows a simulated data set with 40 points drawn from the function <span class=\"math notranslate nohighlight\">\\(y(t|P) = sin(t)\\)</span> (i.e., <span class=\"math notranslate nohighlight\">\\(f = 1/(2\\pi) ~ 0.16\\)</span>).</p></li>\n",
    "<li><p>The right panel shows the PSD computed for the data set from the top-left panel; it is equal to a convolution of the single peak (shaded in gray) with the window PSD shown in the bottom-right panel (e.g., the peak at f ~ 0.42 in the top-right panel can be traced to a peak at f ~ 0.26 in the bottom-right panel).</p></li>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "452789ed-fb36-4366-85ed-20e8fd8005fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1280x640 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Prepare the figures\n",
    "fig = plt.figure(figsize=(16, 8))\n",
    "fig.subplots_adjust(bottom=0.15, hspace=0.2, wspace=0.25,\n",
    "                    left=0.12, right=0.95)\n",
    "\n",
    "# First panel: data vs time\n",
    "ax = fig.add_subplot(221)\n",
    "ax.plot(t, y, '-', c='gray')\n",
    "ax.plot(t_obs, y_obs, '.k', ms=4)\n",
    "ax.text(0.95, 0.93, \"Data\", ha='right', va='top', transform=ax.transAxes)\n",
    "ax.set_ylabel('$y(t)$')\n",
    "ax.set_xlim(0, 100)\n",
    "ax.set_ylim(-1.5, 1.8)\n",
    "\n",
    "# Second panel: PSD of data\n",
    "ax = fig.add_subplot(222)\n",
    "ax.fill(f, PSD_y, fc='gray', ec='gray')\n",
    "ax.plot(f, PSD_obs, '-', c='black')\n",
    "ax.text(0.95, 0.93, \"Data PSD\", ha='right', va='top', transform=ax.transAxes)\n",
    "ax.set_ylabel('$P(f)$')\n",
    "ax.set_xlim(0, 1.0)\n",
    "ax.set_ylim(-0.1, 1.1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d43058a7-3935-4dac-86a3-11c194301e17",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
