init mods for distance learning summer 2020

.gitignore

@@ -1,9 +1,24 @@
-*-checkpoint.ipynb
-*.cut 
-solving_2nd_order_ode.pdf
-frequency_response_2nd_order_ode.pdf
 clearlogs.sh
 
+## tmp folder
+tmp
+
+## rendered pdf files
+laplace_transform/*.pdf
+laplace_system_analysis/*.pdf
+
+## for tutorial_latex_deu
+sig_sys_ex.pdf
+D1483A84E2_*.pdf
+1CFE5FE3A1.pdf
+8C3958BE4F_*.pdf
+A8A2DEE53A.pdf
+D410BDAAE0.pdf
+
+## ipynb stuff
+*-checkpoint.ipynb
+*.cut
+
 ## Core latex/pdflatex auxiliary files:
 *.aux
 *.lof

README.md

@@ -1,2 +1,47 @@
 # signals-and-systems-exercises
-Exercises for the bachelors course Signals and Systems
+
+## Tutorial
+
+**Continuous- and Discrete-Time Signals and Systems - A Tutorial with Computational Examples**
+
+- https://github.com/spatialaudio/signals-and-systems-exercises
+
+## Lecture
+
+This Jupyter notebook based tutorial using Python is accompanying the lecture
+
+**Continuous-Time and Discrete-Time Signals and Systems - Theory and Computational Examples**
+
+- https://github.com/spatialaudio/signals-and-systems-lecture
+
+Lecture and tutorial are designed for International Standard Classification of Education (ISCED) level 6.
+
+## License
+
+- Creative Commons Attribution 4.0 International License (CC BY 4.0) for text/graphics
+- MIT License for software
+
+## Referencing
+
+Please cite as
+
+Frank Schultz,
+*Continuous- and Discrete-Time Signals and Systems - A Tutorial with Computational Examples*,
+University of Rostock,
+https://github.com/spatialaudio/signals-and-systems-exercises,
+Either: SHA of the master branch commit to be cited. Year of commit.
+Or: zenodo.org DOI. release year of DOI.
+
+## DOI Versions
+
+- summer term 2020: TBD
+
+## Authorship
+
+University of Rostock:
+
+- Frank Schultz (concept, design, main author)
+- Till Rettberg (concept, design)
+- Sascha Spors (proof reading, concept)
+- Matthias Geier (proof reading, technical advisor)
+- Vera Erbes (proof reading)

ci/requirements.txt

@@ -0,0 +1,5 @@
+Sphinx>=1.3.6
+Sphinx-RTD-Theme
+nbsphinx
+ipykernel
+sphinx_bootstrap_theme

convolution_dt/ipython_kernel_config.py

@@ -0,0 +1,3 @@
+c.InlineBackend.figure_formats = {'svg', 'pdf'}
+c.InlineBackend.rc = {'font.size': 10, 'figure.dpi': 96}
+

dft/ipython_kernel_config.py

@@ -0,0 +1,3 @@
+c.InlineBackend.figure_formats = {'svg', 'pdf'}
+c.InlineBackend.rc = {'font.size': 10, 'figure.dpi': 96}
+

dirac_impulse_ct/dirac_impulse_CT_D410BDAAE0.ipynb

@@ -0,0 +1,113 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Prof. [Sascha Spors](https://orcid.org/0000-0001-7225-9992),\n",
+    "Professorship Signal Theory and Digital Signal Processing,\n",
+    "[Institute of Communications Engineering (INT)](https://www.int.uni-rostock.de/),\n",
+    "Faculty of Computer Science and Electrical Engineering (IEF),\n",
+    "[University of Rostock, Germany](https://www.uni-rostock.de/en/),\n",
+    "\n",
+    "Tutorial Signal- und Systemtheorie (Course #24015),\n",
+    "Summer Semester 2020\n",
+    "\n",
+    "**Introduction**\n",
+    "\n",
+    "Feel free to contact lecturer [frank.schultz@uni-rostock.de](https://orcid.org/0000-0002-3010-0294)\n",
+    "\n",
+    "- lecture: https://github.com/spatialaudio/signals-and-systems-lecture\n",
+    "- tutorial: https://github.com/spatialaudio/signals-and-systems-exercises\n",
+    "\n",
+    "WIP...\n",
+    "This [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/) project is currently under heavy development while adding new material for the summer term 2020.\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "plt.figure(figsize=(10, 8))\n",
+    "N = 2**12\n",
+    "x = np.arange(-N, N)/(N//3)\n",
+    "epsilon = [20, 10, 5, 2, 1]\n",
+    "\n",
+    "plt.subplot(2, 1, 1)\n",
+    "for e in epsilon:\n",
+    "    y = np.ones_like(x) * e\n",
+    "    y[x < -1/(2*e)] = 0\n",
+    "    y[x > +1/(2*e)] = 0\n",
+    "    plt.plot(x, y, label=r'$\\epsilon=$ %d' % e, lw=2)\n",
+    "plt.legend(loc='upper left')\n",
+    "# plt.xlabel('x')\n",
+    "plt.ylabel(r'$\\delta_\\epsilon(x) = \\epsilon \\cdot \\mathrm{rect}(x \\epsilon)$')\n",
+    "plt.title(r'$\\delta_\\epsilon(x) = \\epsilon \\cdot \\mathrm{rect}(x \\epsilon)$')\n",
+    "plt.xlim(-3, 3)\n",
+    "plt.yticks(np.arange(0, 25+5, 5))\n",
+    "plt.ylim(0, 21)\n",
+    "plt.grid(True)\n",
+    "\n",
+    "x[x == 0] = 1e-16  # avoid div by 0\n",
+    "plt.subplot(2, 1, 2)\n",
+    "for e in epsilon:\n",
+    "    y = np.sin(e*x) / (np.pi*x)\n",
+    "    y[x == 0] = e / np.pi  # correct result for x = 0, L'Hospital rule\n",
+    "    plt.plot(x, y, label=r'$\\epsilon=$ %d' % e, lw=2)\n",
+    "plt.legend(loc='upper left')\n",
+    "plt.xlabel('x')\n",
+    "plt.ylabel(r'$\\delta_\\epsilon(x) = \\sin(\\epsilon x) \\, / \\, (\\pi x)$')\n",
+    "plt.title(r'$\\delta_\\epsilon(x) = \\sin(\\epsilon x) \\, / \\, (\\pi x)$')\n",
+    "plt.xlim(-3, 3)\n",
+    "plt.yticks(np.arange(-2, 6+2, 2))\n",
+    "plt.ylim(-2, 7)\n",
+    "plt.grid(True)\n",
+    "\n",
+    "plt.savefig('D410BDAAE0.pdf')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Copyright\n",
+    "\n",
+    "The notebooks are provided as [Open Educational Resources](https://en.wikipedia.org/wiki/Open_educational_resources). Feel free to use the notebooks for your own purposes. The text is licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/), the code of the IPython examples under the [MIT license](https://opensource.org/licenses/MIT). Please attribute the work as follows: *Frank Schultz, Signals and Systems - A Tutorial Featuring Computational Examples* with the github URL and commit number and/or version tag."
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python [conda env:mypy] *",
+   "language": "python",
+   "name": "conda-env-mypy-py"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}

dirac_impulse_ct/ipython_kernel_config.py

@@ -0,0 +1,3 @@
+c.InlineBackend.figure_formats = {'svg', 'pdf'}
+c.InlineBackend.rc = {'font.size': 10, 'figure.dpi': 96}
+

dirac_impulse_dt/ipython_kernel_config.py

@@ -0,0 +1,3 @@
+c.InlineBackend.figure_formats = {'svg', 'pdf'}
+c.InlineBackend.rc = {'font.size': 10, 'figure.dpi': 96}
+

dtft/ipython_kernel_config.py

@@ -0,0 +1,3 @@
+c.InlineBackend.figure_formats = {'svg', 'pdf'}
+c.InlineBackend.rc = {'font.size': 10, 'figure.dpi': 96}
+

fs/FourierSeries_D1483A84E2.ipynb

@@ -0,0 +1,147 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Prof. [Sascha Spors](https://orcid.org/0000-0001-7225-9992),\n",
+    "Professorship Signal Theory and Digital Signal Processing,\n",
+    "[Institute of Communications Engineering (INT)](https://www.int.uni-rostock.de/),\n",
+    "Faculty of Computer Science and Electrical Engineering (IEF),\n",
+    "[University of Rostock, Germany](https://www.uni-rostock.de/en/),\n",
+    "\n",
+    "Tutorial Signal- und Systemtheorie (Course #24015),\n",
+    "Summer Semester 2020\n",
+    "\n",
+    "**Introduction**\n",
+    "\n",
+    "Feel free to contact lecturer [frank.schultz@uni-rostock.de](https://orcid.org/0000-0002-3010-0294)\n",
+    "\n",
+    "- lecture: https://github.com/spatialaudio/signals-and-systems-lecture\n",
+    "- tutorial: https://github.com/spatialaudio/signals-and-systems-exercises\n",
+    "\n",
+    "WIP...\n",
+    "This [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/) project is currently under heavy development while adding new material for the summer term 2020.\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "\n",
+    "def my_sinc(x):  # we rather use definition sinc(x) = sin(x)/x, thus:\n",
+    "    return np.sinc(x/np.pi)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "T = 1  # signal period in s\n",
+    "# max k in Fourier series\n",
+    "K_des = [40, 40, 40, 40, 40]  \n",
+    "# signal high duration per period, <=T\n",
+    "Th_des = [0.1*T, 0.2*T, 0.5*T, 0.8*T, T]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "for idx, (K, Th) in enumerate(zip(K_des, Th_des)):\n",
+    "    print(idx, K, Th)\n",
+    "\n",
+    "    A = 1/Th  # such that sinc amplitude is always 1 for ck*T\n",
+    "\n",
+    "    # Fourier series coefficients\n",
+    "    w0 = 2*np.pi/T\n",
+    "    k = np.arange(-K, K)\n",
+    "    tmp = w0 * k * Th/2\n",
+    "    ck = A*Th/T * my_sinc(tmp)\n",
+    "\n",
+    "    # Fourier transform for single rect pulse\n",
+    "    w = w0 * np.linspace(-K, K, K*2**4, endpoint=True)\n",
+    "    X = A*Th * my_sinc(w*Th/2)\n",
+    "\n",
+    "    # time vector\n",
+    "    fh = w0*K / (2*np.pi)  # highest frequency in the signal\n",
+    "    fs = 10*fh  # sampling frequency, >2*fh according to sampling theorem\n",
+    "    Ts = 1/fs  # sampling period\n",
+    "    tmin = -2*T\n",
+    "    tmax = +2*T\n",
+    "    trange = tmax - tmin\n",
+    "    t = np.arange(np.int(trange/Ts))*Ts + tmin\n",
+    "\n",
+    "    # Fourier series synthesis\n",
+    "    x = np.sum(ck[:, np.newaxis] *\n",
+    "               np.exp(+1j*w0*k[:, np.newaxis]*t[np.newaxis, :]), axis=0)\n",
+    "    print('imag of x must be around 1e-16 due to numerical precision errors',\n",
+    "          np.max(np.abs(np.imag(x))))  # very small, thus:\n",
+    "    x = np.real(x)\n",
+    "\n",
+    "    plt.figure(figsize=(10, 4))\n",
+    "    plt.subplot(1, 2, 1)\n",
+    "    plt.plot(k, ck*T, 'C0o', label='Fourier coefficients')\n",
+    "    plt.plot(w*T/(2*np.pi), X, 'C7',\n",
+    "             label='Fourier transform of single impulse with $T_h$, $A$')\n",
+    "    plt.xlim(-K, +K)\n",
+    "    plt.xlabel(r'$k$, $\\omega T \\, / \\, (2\\pi)$')\n",
+    "    plt.ylabel(r'$T \\cdot c_k$')\n",
+    "    plt.title(r'Fourier series coefficients, %d$\\leq k \\leq $%d' % (-K, +K))\n",
+    "    plt.legend()\n",
+    "    plt.text(K/10, 0.9, r'$T=$%3.1f s, $T_h=$ %3.1f s, $A=$%3.1f' % (T, Th, A))\n",
+    "    plt.grid(True)\n",
+    "    plt.subplot(1, 2, 2)\n",
+    "    plt.plot(t, x)\n",
+    "    plt.xticks(np.arange(tmin, tmax+T/2, T/2))\n",
+    "    plt.xlim(tmin, tmax)\n",
+    "    plt.ylim(-1/5*A, 6/5*A)\n",
+    "    plt.xlabel(r'$t \\, / \\, s$')\n",
+    "    plt.ylabel(r'$x(t)$')\n",
+    "    plt.title(r'Fourier series synthesis, %d$\\leq k \\leq $%d' % (-K, +K))\n",
+    "    plt.grid(True)\n",
+    "    plt.savefig('D1483A84E2_'+str(idx)+'.pdf')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Copyright\n",
+    "\n",
+    "The notebooks are provided as [Open Educational Resources](https://en.wikipedia.org/wiki/Open_educational_resources). Feel free to use the notebooks for your own purposes. The text is licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/), the code of the IPython examples under the [MIT license](https://opensource.org/licenses/MIT). Please attribute the work as follows: *Frank Schultz, Signals and Systems - A Tutorial Featuring Computational Examples* with the github URL and commit number and/or version tag."
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python [conda env:mypy] *",
+   "language": "python",
+   "name": "conda-env-mypy-py"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}

fs/ipython_kernel_config.py

@@ -0,0 +1,3 @@
+c.InlineBackend.figure_formats = {'svg', 'pdf'}
+c.InlineBackend.rc = {'font.size': 10, 'figure.dpi': 96}
+