{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Miscellaneous\n",
    "\n",
    "1. [Feedback](#Feedback)\n",
    "2. [Transforms](#Transforms)\n",
    "    1. [Fourier Transform](#Fourier-Transform)\n",
    "    2. [Laplace Transform](#Laplace-Transform)\n",
    "    3. [$z$-Transform](#$z$-Transform)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feedback"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import rwth_nb.misc.feedback as rwth_feedback\n",
    "\n",
    "mail_to = \"example@rwth-aachen.de\" # send feedback via mail\n",
    "feedback_name = rwth_feedback.get_notebook_name() # get name of notebook automatically\n",
    "rwth_feedback.rwth_feedback(feedback_name, [\n",
    "    {'id': 'likes', 'type': 'free-text', 'label': 'Das war gut:'}, \n",
    "    {'id': 'dislikes', 'type': 'free-text', 'label': 'Das könnte verbessert werden:'}, \n",
    "    {'id': 'misc', 'type': 'free-text', 'label': 'Was ich sonst noch sagen möchte:'}, \n",
    "    {'id': 'learning', 'type': 'scale', 'label' : 'Ich habe das Gefühl etwas gelernt zu haben.'},\n",
    "    {'id': 'supervision', 'type': 'scale', 'label' : 'Die Betreuung des Versuchs war gut.'},\n",
    "    {'id': 'script', 'type': 'scale', 'label' : 'Die Versuchsunterlagen sind verständlich.'},\n",
    "], \"feedback.json\", mail_to)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Transforms\n",
    "\n",
    "Following transforms are defined in `rwth_nb.misc.transforms`:\n",
    "\n",
    "- [Fourier Transform](#Fourier-Transform)\n",
    "- [Laplace Transform](#Laplace-Transform)\n",
    "- [$z$-Transform](#$z$-Transform)\n",
    "\n",
    "*Note that plotting basics are described in [RWTH Plots](RWTH%20Plots.ipynb).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fourier Transform\n",
    "\n",
    "```dft(s, fs, NFFT)```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import rwth_nb.plots.mpl_decorations as rwth_plots\n",
    "import rwth_nb.misc.transforms as rwth_transforms\n",
    "\n",
    "\n",
    "# Time Domain\n",
    "fs = 44100 # very high sampling rate assumed, to simulate quasi-continuous time and frequency axis\n",
    "t = np.linspace(-2.5, 2.5, 5*fs)\n",
    "s = np.sin(2*np.pi*500*t)\n",
    "\n",
    "# Fourier Transform\n",
    "S,f = rwth_transforms.dft(s, fs)\n",
    "\n",
    "# plots\n",
    "fig,axs = plt.subplots(2,1, **rwth_plots.landscape);\n",
    "\n",
    "ax = axs[0]; ax.plot(t*1000, s);\n",
    "ax.set_xlabel(r'$\\rightarrow t$ [ms]'); ax.set_ylabel(r'$\\uparrow s(t)$')\n",
    "ax.set_xlim([-11, 11]); ax.set_ylim([-1.1, 1.19]); rwth_plots.axis(ax);\n",
    "\n",
    "ax = axs[1]; ax.plot(f, np.abs(S));\n",
    "ax.set_xlabel(r'$\\rightarrow f$ [Hz]'); ax.set_ylabel(r'$\\uparrow |S(f)|$')\n",
    "ax.set_xlim([-1100, 1100]); ax.set_ylim([0, 0.65]); rwth_plots.axis(ax);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inverse Fourier transform\n",
    "\n",
    "```idft(S, Ntime, NFF)```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "s2 = rwth_transforms.idft(S, len(s));\n",
    "\n",
    "fig,ax = plt.subplots(**rwth_plots.landscape); \n",
    "ax.plot(t*1000, np.real(s2));\n",
    "ax.set_xlabel(r'$\\rightarrow t$ [ms]'); ax.set_ylabel(r'$\\uparrow \\mathcal{F}^{-1}\\{S(f)\\}$')\n",
    "ax.set_xlim([-11, 11]); ax.set_ylim([-1.1, 1.19]); rwth_plots.axis(ax);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Laplace Transform\n",
    "Pole-zero plot is explained in [RWTH Plots](RWTH%20Plots.ipynb).  \n",
    "\n",
    "Inverse Laplace Transform\n",
    "\n",
    "```ilaplace_ht(t, H0, pp, pz, ord_p, ord_z, roc)```\n",
    "\n",
    "```ilaplace_Hf(f, H0, pp, pz, ord_p, ord_z, dB)```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig,axs = plt.subplots(1, 2, figsize=(10, 4))\n",
    "\n",
    "t = np.linspace(-6, 6, 1024)\n",
    "f = np.linspace(-6, 6, 1024)\n",
    "\n",
    "pp = np.array([-2]); pz = np.array([]) # Poles and Zeros\n",
    "ord_p = np.array([1]); ord_z = np.array([]) # Poles' and Zeros' orders\n",
    "roc = np.array([-2, np.inf]) # region of convergence\n",
    "H0 = 1\n",
    "\n",
    "# Time Domain\n",
    "s1, t1d , s1d = rwth_transforms.ilaplace_ht(t, H0, pp, pz, ord_p, ord_z, roc)\n",
    "\n",
    "ax = axs[0]\n",
    "ax.set_xlabel(r'$\\rightarrow t$'); ax.set_ylabel(r'$\\uparrow s_1(t)$') \n",
    "rwth_plots.grid(ax); rwth_plots.axis(ax)\n",
    "ax.set_xlim([-5.5,5.5]); axs[0].set_ylim([-0.1,1.05]); \n",
    "ax.plot(t, np.real(s1))\n",
    "rwth_plots.plot_dirac(axs[0], t1d, s1d);\n",
    "\n",
    "# Frequency Domain\n",
    "S1f = rwth_transforms.ilaplace_Hf(f, H0, pp, pz, ord_p, ord_z, dB=False)\n",
    "\n",
    "ax = axs[1]\n",
    "ax.set_xlabel(r'$\\rightarrow f$'); ax.set_ylabel(r'$\\uparrow S_1(f)$') \n",
    "rwth_plots.grid(ax); rwth_plots.axis(ax)\n",
    "ax.set_xlim([-5.5,5.5]); ax.set_ylim([-0.1,0.55]); \n",
    "ax.plot(f, S1f); "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $z$ Transform\n",
    "Pole-zero plot is explained in [RWTH Plots](RWTH%20Plots.ipynb).  \n",
    "\n",
    "Inverse $z$ Transform\n",
    "\n",
    "```iz_hn(n, H0, pp, pz, ord_p, ord_z, roc)```\n",
    "\n",
    "```iz_Hf(f, H0, pp, pz, ord_p, ord_z, dB)```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig,axs = plt.subplots(1, 2, figsize=(10, 4))\n",
    "\n",
    "n = np.linspace(-6, 6, 13)\n",
    "f = np.linspace(-6, 6, 1024)\n",
    "\n",
    "zp = np.array([.5, 2]); zz = np.array([0]) # Poles and Zeros\n",
    "ord_p = np.array([1, 1]); ord_z = np.array([1]) # Poles' and Zeros' orders\n",
    "roc = np.array([.5, 2]) # region of convergence\n",
    "H0 = -3/2\n",
    "\n",
    "# Time Domain\n",
    "s1= rwth_transforms.iz_hn(n, H0, zp, zz, ord_p, ord_z, roc)\n",
    "\n",
    "ax = axs[0]\n",
    "ax.set_xlabel(r'$\\rightarrow n$'); ax.set_ylabel(r'$\\uparrow s_1(n)$') \n",
    "rwth_plots.grid(ax); rwth_plots.axis(ax)\n",
    "ax.set_xlim([-5.5,5.5]); axs[0].set_ylim([-0.1,1.05]);\n",
    "rwth_plots.stem(axs[0], n, s1);\n",
    "\n",
    "# Frequency Domain\n",
    "S1f = rwth_transforms.iz_Hf(f, H0, zp, zz, ord_p, ord_z, dB=False)\n",
    "\n",
    "ax = axs[1]\n",
    "ax.set_xlabel(r'$\\rightarrow f$'); ax.set_ylabel(r'$\\uparrow S_1(f)$') \n",
    "rwth_plots.grid(ax); rwth_plots.axis(ax)\n",
    "ax.set_xlim([-5.5,5.5]); ax.set_ylim([0.3, 3.1]); \n",
    "ax.plot(f, S1f); "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This code is licensed under the [MIT license](https://opensource.org/licenses/MIT)."
   ]
  }
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