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GDET3 Elementarsignale.ipynb

 %% Cell type:code id: tags:
 
 ``` python
 # Copyright 2019 Institut für Nachrichtentechnik, RWTH Aachen University
 %matplotlib notebook
 
 from ipywidgets import interact, interactive
 import ipywidgets as widgets
 
-import scipy as sp
-import scipy.special
-import scipy.signal
 
 from ient_nb.ient_plots import *
 from ient_nb.ient_signals import *
 ```
 
 %% Cell type:markdown id: tags:
 
 <div>
     <img src="ient_nb/figures/rwth_ient_logo@2x.png" style="float: right;height: 5em;">
 </div>
 
 # Elementarsignale
 
 Folgende Signale wurden bereits in `ient_signals` definiert:
 
 ``` python
 gauss     = lambda t: np.exp(-(t)**2)
 unitstep  = lambda t: np.where(t>=0, 1, 0)
 rect      = lambda t: unitstep(t+0.5) - unitstep(t-0.5)
 tri       = lambda t: rect(t/2)*(1-abs(t))
 si        = lambda t: np.sinc(t/np.pi) # English notation sinc(t) = sin(pi t)/(pi t)
 ```
 
 %% Cell type:markdown id: tags:
 
 ## Signale
 
 Jedes der oben definierten Elementarsignale wird im Folgenden geplottet.
 
 ### Gauß-Signal
 
 $\displaystyle s(t) = \mathrm{e}^{\pi t^2}$
 
 %% Cell type:code id: tags:
 
 ``` python
 fig,ax = plt.subplots(1,1); ax.plot(t, gauss(t));
 ax.set_xlabel(r'$\rightarrow t$'); ax.set_ylabel(r'$\uparrow s(t)=\mathrm{e}^{-\pi t^2}$', bbox=ient_wbbox)
 ax.axis('equal'); ax.set_xlim([-2.75, 2.75]); ient_grid(ax); ient_axis(ax);
 ```
 
 %% Cell type:markdown id: tags:
 
 ### Sprungfunktion
 $\epsilon(t)=\begin{cases}
     0\quad\text{für}\ t<0 \\
     1\quad\text{für}\ t\geq 0 \text{ .}
 \end{cases}$
 
 %% Cell type:code id: tags:
 
 ``` python
 fig,ax = plt.subplots(1,1); ax.plot(t, unitstep(t));
 ax.set_xlabel(r'$\rightarrow t$'); ax.set_ylabel(r'$\uparrow s(t)=\epsilon(t)$', bbox=ient_wbbox)
 ax.axis('equal'); ax.set_xlim([-2.25,2.25]); ient_grid(ax); ient_axis(ax);
 ```
 
 %% Cell type:markdown id: tags:
 
 ### Rechteckimpuls
 
 $\mathrm{rect}(t) = \begin{cases}
     1\quad\text{für}\ |t| \leq 1/2\\
     0\quad\text{für}\ |t| > 1/2\text{ .}
 \end{cases}$
 
 %% Cell type:code id: tags:
 
 ``` python
 fig,ax = plt.subplots(1,1); ax.plot(t, rect(t));
 ax.set_xlabel(r'$\rightarrow t$'); ax.set_ylabel(r'$\uparrow s(t)=\mathrm{rect}(t)$', bbox=ient_wbbox)
 ax.axis('equal'); ax.set_xlim([-2.25,2.25]); ient_grid(ax); ient_axis(ax);
 ```
 
 %% Cell type:markdown id: tags:
 
 ### Dreieckimpuls
 $\Lambda(t) = \begin{cases}
   1-|t|\quad\text{für}\ |t|\leq 1\\
   0\quad\text{für}\ |t| > 1\text{ .}
 \end{cases}$
 
 %% Cell type:code id: tags:
 
 ``` python
 fig,ax = plt.subplots(1,1); ax.plot(t, tri(t));
 ax.set_xlabel(r'$\rightarrow t$'); ax.set_ylabel(r'$\uparrow s(t)=\Lambda(t)$', bbox=ient_wbbox)
 ax.axis('equal'); ax.set_xlim([-2.25,2.25]); ient_grid(ax); ient_axis(ax);
 ```
 
 %% Cell type:markdown id: tags:
 
 ### Si-Funktion
 $\displaystyle \mathrm{si}(t) = \frac{\sin(t)}{t}$
 
 %% Cell type:code id: tags:
 
 ``` python
 fig,ax = plt.subplots(1,1); ax.plot(t, si(np.pi*t));
 ax.set_xlabel(r'$\rightarrow t$'); ax.set_ylabel(r'$\uparrow s(t)=\mathrm{si}(\pi t)$', bbox=ient_wbbox)
 ax.set_xlim([-5.5,5.5]); ient_grid(ax); ient_axis(ax);
 ```
 
 %% Cell type:markdown id: tags:
 
 ## Zeitverschiebung, -dehnung und -spiegelung
 
 %% Cell type:markdown id: tags:
 
 Verschobener Rechteckimpuls $s(t) = \mathrm{rect}\left(t-\frac{1}{2}\right)$
 
 %% Cell type:code id: tags:
 
 ``` python
 s = lambda t: rect(t-1/2)
 
 # Plot
 fig,ax = plt.subplots(1,1); ax.plot(t, s(t));
 ax.set_xlabel(r'$\rightarrow t$'); ax.set_ylabel(r'$\uparrow s(t)$', bbox=ient_wbbox)
 ax.axis('equal'); ax.set_xlim([-2.25,2.25]); ient_grid(ax); ient_axis(ax);
 ```
 
 %% Cell type:markdown id: tags:
 
 Gedehnter Rechteckimpuls $s(t) = \mathrm{rect}\left(\frac{t}{2}\right)$
 
 %% Cell type:code id: tags:
 
 ``` python
 s = lambda t: rect(t/2)
 
 # Plot
 fig,ax = plt.subplots(1,1); ax.plot(t, s(t));
 ax.set_xlabel(r'$\rightarrow t$'); ax.set_ylabel(r'$\uparrow s(t)$', bbox=ient_wbbox)
 ax.axis('equal'); ax.set_xlim([-2.25,2.25]); ient_grid(ax); ient_axis(ax);
 ```
 
 %% Cell type:markdown id: tags:
 
 Zur Verdeutlichung der Zeitspiegelung wird $s(t) = t \cdot \mathrm{rect}\left(t-\frac{1}{2}\right)$ betrachtet:
 
 %% Cell type:code id: tags:
 
 ``` python
 s = lambda t: rect(t-0.5)*t
 
 # Plot
 fig,ax = plt.subplots(1,1); ax.plot(t, s(t));
 ax.set_xlabel(r'$\rightarrow t$'); ax.set_ylabel(r'$\uparrow s(t)$', bbox=ient_wbbox)
 ax.axis('equal'); ax.set_xlim([-2.25,2.25]); ient_grid(ax); ient_axis(ax);
 ```
 
 %% Cell type:markdown id: tags:
 
 Betrachte nun $s(-t)$:
 
 %% Cell type:code id: tags:
 
 ``` python
 # Plot
 fig,ax = plt.subplots(1,1); ax.plot(t, s(-t));
 ax.set_xlabel(r'$\rightarrow t$'); ax.set_ylabel(r'$\uparrow s(-t)$', bbox=ient_wbbox)
 ax.axis('equal'); ax.set_xlim([-2.25,2.25]); ient_grid(ax); ient_axis(ax);
 ```
 
 %% Cell type:markdown id: tags:
 
 ### Demo: Zeitverschiebung, -dehnung und -spiegelung
 $\displaystyle s\left(\pm\frac{t-t_0}{T}\right)$
 
 %% Cell type:code id: tags:
 
 ``` python
 s = lambda t: rect(t-0.5)*t
 
 # Plot & demo
 fig, ax = plt.subplots(1, 1, figsize=(8, 4))
 @widgets.interact(T=widgets.FloatSlider(min=0.25, max=4, value=1, step=.1, description=r'Dehnung T', style=ient_wdgtl_style),
                   t0=widgets.FloatSlider(min=-2, max=2, value=0, step=.1, description=r'Verschiebung $t_0$', style=ient_wdgtl_style),
                   reflection=widgets.Checkbox(value=False, description='Spiegelung', style=ient_wdgtl_style))
 def update_signals(T, t0, reflection):
     if reflection:
         T = -T
     s_plot = s((t-t0)/T)
 
     if not ax.lines: # plot s(t) and g(t)
         ax.plot(t, s_plot, 'rwth');
         ax.set_xlabel(r'$\rightarrow t$'); ax.set_ylabel(r'$\uparrow s\left(\pm\frac{t-t_0}{T}\right)$')
         ax.axis('equal'); ax.set_xlim([-4.75, 4.75]); ient_axis(ax); ient_grid(ax); ax.minorticks_on()
 
     else: # update lines
         ax.lines[0].set_ydata(s_plot);
 ```
 
 %% Cell type:markdown id: tags:
 
 This notebook is provided as [Open Educational Resource](https://en.wikipedia.org/wiki/Open_educational_resources) (OER). Feel free to use the notebook for your own purposes. The code is licensed under the [MIT license](https://opensource.org/licenses/MIT).
 
 Please attribute the work as follows:
 *Christian Rohlfing, Übungsbeispiele zur Vorlesung "Grundgebiete der Elektrotechnik 3 - Signale und Systeme"*, gehalten von Jens-Rainer Ohm, 2019, Institut für Nachrichtentechnik, RWTH Aachen University.

index.ipynb

 %% Cell type:markdown id: tags:
 
 <div>
     <img src="ient_nb/figures/rwth_ient_logo@2x.png" style="float: right;height: 5em;">
 </div>
 
 # Übungsbeispiele zur Vorlesung Grundgebiete der Elektrotechnik 3 &ndash;  Signale und Systeme
 
 ## Inhaltsverzeichnis
 
 1. Determinierte Signale in linearen zeitinvarianten Systemen
   * [Elementarsignale](GDET3%20Elementarsignale.ipynb) (Elementarsignale sowie Zeitverschiebung, Spiegelung, Dehnung)
   * [Beispiel zur Berechnung des Faltungsintegrals](GDET3%20Faltungsbeispiel.ipynb)
   * [Demonstrator Faltungsintegral](GDET3%20Faltung%20GUI.ipynb)
 2. Laplace-Transformation
   * [Demonstrator Laplace-Transformation](GDET3%20Laplace-Transformation.ipynb)
 3. Fourier-Bechreibung von Signalen und Systemen
   * [RL-Hochpass](GDET3%20RL-Hochpass.ipynb)
 4. Diskrete Signale und Systeme
 5. Systemtheorie der Tiefpass- und Bandpasssysteme
 6. Korrelationsfunktionen determinierter Signale
 7. Statistische Signalbeschreibung
     * [Weißes Rauschen](GDET3%20Weißes%20Rauschen.ipynb)
     * [Verteilungs- und Verteilungsdichtefunktion](GDET3%20Verteilungsfunktion.ipynb)
 
+## Jupyter Quick Start
+
+* Zum Ausführen einer einzelnen Cell auf <span class="fa-step-forward fa"></span>-Button klicken
+* Zum Ausführen aller Cells eines Notebooks im Menü "Cell" -> "Run All"
+* Zum Neustart (und erneutem Ausführen) <span class="fa-forward fa"></span>-Button klicken
+
+
+## Mitwirkende
+
+* Christian Rohlfing
+* Emin Kosar
+
 %% Cell type:markdown id: tags:
 
 This notebook is provided as [Open Educational Resource](https://en.wikipedia.org/wiki/Open_educational_resources) (OER). Feel free to use the notebook for your own purposes. The code is licensed under the [MIT license](https://opensource.org/licenses/MIT).
 
 Please attribute the work as follows:
 *Christian Rohlfing, Übungsbeispiele zur Vorlesung "Grundgebiete der Elektrotechnik 3 - Signale und Systeme"*, gehalten von Jens-Rainer Ohm, 2019, Institut für Nachrichtentechnik, RWTH Aachen University.

postBuild

+jupyter contrib nbextension install --user
+jupyter nbextension enable hide_input/main
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requirements.txt

 numpy
 scipy
-matplotlib
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+matplotlib
+jupyter-contrib-nbextensions
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