added use_line_collection to stem

8dc722c6 · Lukas Müller · 1caeedc8 · 8dc722c6
Commit 8dc722c6 authored 4 years ago by Lukas Müller
--- a/Übung 11.ipynb
+++ b/Übung 11.ipynb
@@ -79,7 +79,7 @@
    "    axis1.set_xlim((0, 1))\n",
    "    axis1.plot(t, x_result)\n",
    "    axis1.plot(t, x_continuous(t, omega_max*ft/(2*pi)))\n",
-    "    axis1.stem(n/ft, x_discrete(n, ft))\n",
+    "    axis1.stem(n/ft, x_discrete(n, ft), use_line_collection=True)\n",
    "    axis1.set_xlabel('$t$ in s', fontsize=22)\n",
    "    axis1.set_yticks([-1, 0, 1])\n",
    "    axis2.cla()\n",

 %% Cell type:markdown id: tags:

 # Übung 11 - Abtastung & Aliasing

 In dieser Übung betrachten wir ein Signal $x(t)=\cos(2\pi\cdot f\cdot t)$ mit der Frequenz $f=10\,\text{Hz}$ , welches mit einer Frequenz $f_T$ abgetastet werden soll.

 Um die bei diesem Unterfangen möglicherweise auftretenden Probleme zu visualisieren, setzen wir in diesem Notebook eine variierende Abtastfrequenz $f_T$ ein, die durch einen Slider variiert werden kann.
 ## Berechnung und Definition

 %% Cell type:code id: tags:

 ``` python
 from numpy import cos, pi, abs
 import numpy
 from scipy.fft import fft, fftshift


 f = 10 # Hz
 ft = 40 # Hz
 duration = 1 # s

 t = numpy.linspace(0, duration, 5000)
 n = numpy.arange(0, duration*ft)
 zeropadding = 2**10
 Omega = numpy.linspace(-pi, pi, zeropadding)

 def x_continuous(t, f):
    return cos(2*pi*f*t)

 def x_discrete(n, ft):
    return cos(2*pi*f/ft*n)
 ```

 %% Cell type:markdown id: tags:

 ## Visualisierung

 %% Cell type:code id: tags:

 ``` python
 from IPython.display import display
 from ipywidgets import IntSlider, FloatSlider
 from matplotlib import pyplot
 %matplotlib notebook

 ft_slider = IntSlider(min=1, max=f*5, layout={'width':'100%'}, value=2)

 figure, (axis1, axis2) = pyplot.subplots(2, 1)
 pyplot.tight_layout()
 figure.set_figwidth(9.5)
 figure.set_figheight(10)
 x_result = x_continuous(t, f)

 def slider_update_plot(changes):
    ft = ft_slider.value # get the sampling frequency from the slider
    n = numpy.arange(0, duration*ft)
    dft = abs(fftshift(fft(x_discrete(n, ft), zeropadding)))/ft/duration
    max_index = numpy.argmax(dft[0:int(zeropadding/2)])
    omega_max = abs(Omega[max_index])

    # visualize
    axis1.cla()
    axis1.set_xlim((0, 1))
    axis1.plot(t, x_result)
    axis1.plot(t, x_continuous(t, omega_max*ft/(2*pi)))
-    axis1.stem(n/ft, x_discrete(n, ft))
+    axis1.stem(n/ft, x_discrete(n, ft), use_line_collection=True)
    axis1.set_xlabel('$t$ in s', fontsize=22)
    axis1.set_yticks([-1, 0, 1])
    axis2.cla()
    axis2.set_xlim((-12, 12))
    axis2.set_ylim((0, 1.1))
    axis2.plot(Omega*ft/(2*pi), dft)
    axis2.set_xticks(numpy.arange(-12, 13, 1))
    axis2.set_ylabel('DFT{x[n]}', fontsize=22)
    axis2.set_xlabel('$f$ in Hz', fontsize=22)

 ft_slider.observe(slider_update_plot)
 slider_update_plot(None)
 display(ft_slider)
 ```