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Verified Commit 5b9eb24d authored by Christian Rohlfing's avatar Christian Rohlfing
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Bugfix in PAM

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IUE Pulsamplitudenmodulation.ipynb
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%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
# Copyright 2020 Institut für Nachrichtentechnik, RWTH Aachen University # Copyright 2020 Institut für Nachrichtentechnik, RWTH Aachen University
%matplotlib widget %matplotlib widget
from ipywidgets import interact, interactive, fixed, interact_manual from ipywidgets import interact, interactive, fixed, interact_manual
import ipywidgets as widgets import ipywidgets as widgets
from IPython.display import Markdown, Latex from IPython.display import Markdown, Latex
import matplotlib.pyplot as plt import matplotlib.pyplot as plt
from scipy import signal # convolution, from scipy import signal # convolution,
from scipy.io import wavfile # wavfile from scipy.io import wavfile # wavfile
import rwth_nb.plots.mpl_decorations as rwth_plots import rwth_nb.plots.mpl_decorations as rwth_plots
import rwth_nb.misc.transforms as rwth_transforms import rwth_nb.misc.transforms as rwth_transforms
import rwth_nb.misc.media as rwth_media import rwth_nb.misc.media as rwth_media
import rwth_nb.misc.filters as rwth_filters import rwth_nb.misc.filters as rwth_filters
from rwth_nb.misc.signals import * from rwth_nb.misc.signals import *
def convolution(s, h): def convolution(s, h):
# Convolve s and h numerically # Convolve s and h numerically
g = signal.convolve(s, h, mode='same')*deltat; #g = g[0:len(s)]; g = signal.convolve(s, h, mode='same')*deltat; #g = g[0:len(s)];
return g return g
def ient_ideal_lowpass(s, fg): def ient_ideal_lowpass(s, fg):
# Convolve with impulse response of ideal lowpass # Convolve with impulse response of ideal lowpass
return convolution(s, 2*fg*si(2*np.pi*fg*t)) return convolution(s, 2*fg*si(2*np.pi*fg*t))
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
<div> <div>
<img src="figures/rwth_ient_logo@2x.png" style="float: right;height: 5em;"> <img src="figures/rwth_ient_logo@2x.png" style="float: right;height: 5em;">
</div> </div>
# Pulsamplitudenmodulation # Pulsamplitudenmodulation
Zum Starten: Im Menü: Run <span class="fa-chevron-right fa"></span> Run All Cells auswählen. Zum Starten: Im Menü: Run <span class="fa-chevron-right fa"></span> Run All Cells auswählen.
## Übersicht ## Übersicht
![Blockdiagramm](figures/pam_block_diagram.png) ![Blockdiagramm](figures/pam_block_diagram.png)
Hier Rauschprozess $n(t)$ (Kanal) vernachlässigt (ansonsten $g(t)\rightarrow y(t)=g(t)+n_e(t)$ mit $n_e(t)=n(t)\ast s(-t)$) Hier Rauschprozess $n(t)$ (Kanal) vernachlässigt (ansonsten $g(t)\rightarrow y(t)=g(t)+n_e(t)$ mit $n_e(t)=n(t)\ast s(-t)$)
## Nutzsignal ## Nutzsignal
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
fs = 400000 # interne Abtastrate fs = 400000 # interne Abtastrate
fs0, data = wavfile.read('data/krawehl.wav') fs0, data = wavfile.read('data/krawehl.wav')
f = 0.99*data/np.max(np.abs(data)) # Normalisieren #data = np.hstack((data,data))
f = signal.resample(f, int(len(f)/fs0*fs)) # Etwas hochtasten für schönere Plots f0 = 0.99*data/np.max(np.abs(data)) # Normalisieren
f = signal.resample(f0, int(len(f0)/fs0*fs)) # Etwas hochtasten für schönere Plots
(t, deltat) = np.linspace(-len(f)/fs/2, len(f)/fs/2, len(f), retstep=True) # Zeitachse in Sekunden (t, deltat) = np.linspace(-len(f)/fs/2, len(f)/fs/2, len(f), retstep=True) # Zeitachse in Sekunden
F, f_ax = rwth_transforms.dft(f, fs) # Fourier-Transformation F, f_ax = rwth_transforms.dft(f, fs) # Fourier-Transformation
# Plot # Plot
fig,axs=plt.subplots(2,1, figsize=(8,4)); fig,axs=plt.subplots(2,1, figsize=(8,4));
ax = axs[0]; ax.plot(1000*t, f, 'rwth:blue'); ax = axs[0]; ax.plot(1000*t, f, 'rwth:blue');
ax.set_xlabel(r'$\rightarrow t$ [ms]', bbox=rwth_plots.wbbox); ax.set_ylabel(r'$\uparrow f(t)$'); rwth_plots.axis(ax); ax.set_xlabel(r'$\rightarrow t$ [ms]', bbox=rwth_plots.wbbox); ax.set_ylabel(r'$\uparrow f(t)$'); rwth_plots.axis(ax);
ax = axs[1]; ax.plot(f_ax, np.abs(F), 'rwth:blue'); ax = axs[1]; ax.plot(f_ax, np.abs(F), 'rwth:blue');
ax.set_xlabel(r'$\rightarrow f$ [Hz]', bbox=rwth_plots.wbbox); ax.set_ylabel(r'$\uparrow |F(f)|$'); ax.set_xlabel(r'$\rightarrow f$ [Hz]', bbox=rwth_plots.wbbox); ax.set_ylabel(r'$\uparrow |F(f)|$');
ax.set_xlim([-10E3, 10E3]); rwth_plots.axis(ax); ax.set_xlim([-10E3, 10E3]); rwth_plots.axis(ax);
rwth_media.audio_play(f, fs, r'$f(t)$') rwth_media.audio_play(f0, fs0, r'$f(t)$')
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
## Sender ## Sender
Trägersignal $s(t)=\frac{1}{\sqrt{t_0}}\mathrm{rect}\left(\frac{t}{t_0}\right)$ mit Breite $t_0 = 0{,}5 T$ (oder $t_0 = 1{,}25 T$ für Aufgabe 11) und $T=125\mu\mathrm{s}$ Trägersignal $s(t)=\frac{1}{\sqrt{t_0}}\mathrm{rect}\left(\frac{t}{t_0}\right)$ mit Breite $t_0 = 0{,}5 T$ (oder $t_0 = 1{,}25 T$ für Aufgabe 11) und $T=125\mu\mathrm{s}$
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
T = 125E-6 T = 125E-6
t0 = 0.5*T t0 = 1.25*T
#t0 = 1.25*T # Aufgabe 11: '#' entfernen und alle Cells erneut laufen lassen #t0 = 1.25*T # Aufgabe 11: '#' entfernen und alle Cells erneut laufen lassen
# Trägersignal # Trägersignal
s = lambda t,t0: 1/np.sqrt(t0)*rect(t/t0) s = lambda t,t0: 1/np.sqrt(t0)*rect(t/t0)
phi_ss = convolution(s(-t,t0),s(t,t0)) phi_ss = convolution(s(-t,t0),s(t,t0))
# Plot # Plot
fig, axs = plt.subplots(1,2,figsize=(8,4)); fig, axs = plt.subplots(1,2,figsize=(8,4));
ax = axs[0]; ax.plot(t*1E6, s(t,t0), 'rwth:blue'); ax = axs[0]; ax.plot(t*1E6, s(t,t0), 'rwth:blue');
ax.set_xlabel(r'$\rightarrow t$ [$\mu$s]'); ax.set_ylabel(r'$\uparrow s(t)$'); ax.set_xlabel(r'$\rightarrow t$ [$\mu$s]'); ax.set_ylabel(r'$\uparrow s(t)$');
ax.set_xlim([-2E6*t0, 2E6*t0]); rwth_plots.axis(ax); ax.set_xlim([-2E6*t0, 2E6*t0]); rwth_plots.axis(ax);
rwth_plots.annotate_distance(ax, r'$t_0$', (-t0/2*1E6,10), (t0/2*1E6,10)); rwth_plots.annotate_distance(ax, r'$t_0$', (-t0/2*1E6,10), (t0/2*1E6,10));
ax = axs[1]; ax.plot(t*1E6, phi_ss, 'rwth:blue'); ax = axs[1]; ax.plot(t*1E6, phi_ss, 'rwth:blue');
ax.set_xlabel(r'$\rightarrow t$ [$\mu$s]', bbox=rwth_plots.wbbox); ax.set_ylabel(r'$\uparrow s(t)\ast s(-t)$'); ax.set_xlabel(r'$\rightarrow t$ [$\mu$s]', bbox=rwth_plots.wbbox); ax.set_ylabel(r'$\uparrow s(t)\ast s(-t)$');
ax.set_xlim([-2E6*t0, 2.5E6*t0]); rwth_plots.axis(ax); ax.set_xlim([-2E6*t0, 2.5E6*t0]); rwth_plots.axis(ax);
rwth_plots.annotate_distance(ax, r'$2t_0$', (-t0*1E6,.1), (t0*1E6,.1)); fig.tight_layout(); rwth_plots.annotate_distance(ax, r'$2t_0$', (-t0*1E6,.1), (t0*1E6,.1)); fig.tight_layout();
Markdown("$t_0 = {:.3f}\ \mu\\mathrm{{s}}$".format(t0*1E6)) Markdown("$t_0 = {:.3f}\ \mu\\mathrm{{s}}$".format(t0*1E6))
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Tiefpassfilterung (ideal, Grenzfrequenz $f_\mathrm{g} = \frac{1}{2T}$) und ideale Abtastung Tiefpassfilterung (ideal, Grenzfrequenz $f_\mathrm{g} = \frac{1}{2T}$) und ideale Abtastung
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
# Tiefpassfilterung # Tiefpassfilterung
fg = 1/(2*T) fg = 1/(2*T)
fTP = ient_ideal_lowpass(f, fg) fTP = ient_ideal_lowpass(f, fg)
# Abtastung # Abtastung
nT_idx = np.arange(0, len(t), int(fs*T)); nT = t[nT_idx]; nT_idx = np.arange(0, len(t), int(fs*T)); nT = t[nT_idx];
fa_nT = fTP[nT_idx]; fa_nT = fTP[nT_idx];
fa = np.zeros_like(t); fa[nT_idx] = fa_nT fa = np.zeros_like(t); fa[nT_idx] = fa_nT
# Plot # Plot
rwth_media.audio_play(f, fs, r'$f(t)$') rwth_media.audio_play(f0, fs0, r'$f(t)$')
rwth_media.audio_play(fTP, fs, r'$f(t)\ast h_\mathrm{LP}(t)$') rwth_media.audio_play(signal.resample(fTP, len(f0)), fs0, r'$f(t)\ast h_\mathrm{LP}(t)$')
display(Markdown("$f_g = {:.1f}\ \\mathrm{{Hz}}$".format(fg))) display(Markdown("$f_g = {:.1f}\ \\mathrm{{Hz}}$".format(fg)))
fig,ax=plt.subplots(); fig,ax=plt.subplots();
ax.plot(1000*t, fTP, 'rwth:blue', label=r'$f(t)$'); ax.plot(1000*t, fTP, 'rwth:blue', label=r'$f(t)$');
rwth_plots.plot_dirac(ax, 1000*nT, fa_nT, 'rwth:red', label=r'$f_\mathrm{a}(t)$') rwth_plots.plot_dirac(ax, 1000*nT, fa_nT, 'rwth:red', label=r'$f_\mathrm{a}(t)$')
ax.set_xlabel(r'$\rightarrow t$ [ms]', bbox=rwth_plots.wbbox); ax.legend(); ax.set_xlabel(r'$\rightarrow t$ [ms]', bbox=rwth_plots.wbbox); ax.legend();
ax.set_xlim([0, 10]); rwth_plots.axis(ax); ax.set_xlim([0, 10]); rwth_plots.axis(ax);
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Sendesignal Sendesignal
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
def sender_carrier(s, fa, t0): def sender_carrier(s, fa, t0):
m = convolution(s(t, t0), fa/deltat) m = convolution(s(t, t0), fa/deltat)
return m return m
m = sender_carrier(s, fa, t0) m = sender_carrier(s, fa, t0)
# Plot # Plot
fig,ax=plt.subplots(); fig,ax=plt.subplots();
ax.plot(1000*t, m, 'rwth:blue'); ax.plot(1000*t, m, 'rwth:blue');
ax.set_xlabel(r'$\rightarrow t$ [ms]', bbox=rwth_plots.wbbox); ax.set_ylabel(r'$\uparrow m(t)$'); ax.set_xlabel(r'$\rightarrow t$ [ms]', bbox=rwth_plots.wbbox); ax.set_ylabel(r'$\uparrow m(t)$');
ax.set_xlim([0, 10]); rwth_plots.axis(ax); ax.set_xlim([0, 10]); rwth_plots.axis(ax);
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
## Kanal ## Kanal
Hier wird $n(t)=0$ angenommen. Hier wird $n(t)=0$ angenommen.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
n = np.zeros_like(t) n = np.zeros_like(t)
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
## Empfänger ## Empfänger
### Korrelationsfilter ### Korrelationsfilter
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
# Schicke m(t) und n(t) getrennt durch Korrelationsfilter # Schicke m(t) und n(t) getrennt durch Korrelationsfilter
def receiver_filter(m, n, s, t0): def receiver_filter(m, n, s, t0):
h = s(-t, t0) h = s(-t, t0)
g = convolution(h, m) g = convolution(h, m)
ne = convolution(h, n) ne = convolution(h, n)
y = g+ne y = g+ne
return (y,g,ne,h) return (y,g,ne,h)
y,g,ne,h = receiver_filter(m, n, s, t0) y,g,ne,h = receiver_filter(m, n, s, t0)
# Plot # Plot
fig,ax = plt.subplots(); fig,ax = plt.subplots();
ax.plot(1000*t, y, 'rwth:blue'); ax.plot(1000*t, y, 'rwth:blue');
ax.set_xlabel(r'$\rightarrow t$ [ms]', bbox=rwth_plots.wbbox); ax.set_ylabel(r'$\uparrow y(t)$'); ax.set_xlabel(r'$\rightarrow t$ [ms]', bbox=rwth_plots.wbbox); ax.set_ylabel(r'$\uparrow y(t)$');
ax.set_xlim([0, 10]); rwth_plots.axis(ax); ax.set_xlim([0, 10]); rwth_plots.axis(ax);
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
### Abtastung und Rekonstruktion ### Abtastung und Rekonstruktion
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
def receiver_sampling_lp(y): def receiver_sampling_lp(y):
# Abastung # Abastung
ya_nT = y[nT_idx] ya_nT = y[nT_idx]
ya = np.zeros_like(t) ya = np.zeros_like(t)
ya[nT_idx] = ya_nT ya[nT_idx] = ya_nT
# Rekonstruktion: Tiefpass und Multiplikation mit T # Rekonstruktion: Tiefpass und Multiplikation mit T
fe = ient_ideal_lowpass(ya/deltat, fg)*T fe = ient_ideal_lowpass(ya/deltat, fg)*T
return (fe, ya, ya_nT) return (fe, ya, ya_nT)
fe, ya, ya_nT = receiver_sampling_lp(y) fe, ya, ya_nT = receiver_sampling_lp(y)
# Plot # Plot
fig,ax=plt.subplots(); fig,ax=plt.subplots();
rwth_plots.plot_dirac(ax, 1000*nT, fe[nT_idx], 'rwth:black-50') rwth_plots.plot_dirac(ax, 1000*nT, fe[nT_idx], 'rwth:black-50')
ax.plot(1000*t, fe, 'rwth:blue'); ax.plot(1000*t, fe, 'rwth:blue');
ax.set_xlabel(r'$\rightarrow t$ [ms]', bbox=rwth_plots.wbbox); ax.set_ylabel(r'$\uparrow f_\mathrm{e}(t)$'); ax.set_xlabel(r'$\rightarrow t$ [ms]', bbox=rwth_plots.wbbox); ax.set_ylabel(r'$\uparrow f_\mathrm{e}(t)$');
ax.set_xlim([0, 10]); rwth_plots.axis(ax); ax.set_xlim([0, 10]); rwth_plots.axis(ax);
rwth_media.audio_play(fTP, fs, r'Sender: $f(t)\ast h_\mathrm{LP}(t)$') rwth_media.audio_play(signal.resample(fTP, len(f0)), fs0, r'Sender: $f(t)\ast h_\mathrm{LP}(t)$')
rwth_media.audio_play(fe, fs, r'Empfänger: $f_\mathrm{e}(t)$') rwth_media.audio_play(signal.resample(fe, len(f0)), fs0, r'Empfänger: $f_\mathrm{e}(t)$')
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
### Kompensation am Empfänger ### Kompensation am Empfänger
In diesem Abschnitt geht es um den in Aufgabe 11 beschriebenen Fall, in dem $t_0 > T$ gilt. In diesem Abschnitt geht es um den in Aufgabe 11 beschriebenen Fall, in dem $t_0 > T$ gilt.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
def receiver_compensation_filter(t0, T): def receiver_compensation_filter(t0, T):
if t0 > T: if t0 > T:
# Kompensationsfilter # Kompensationsfilter
H2 = 1/(1+0.4*np.cos(2*np.pi*f_ax*T))*rect(f_ax/(2*fg)) H2 = 1/(1+0.4*np.cos(2*np.pi*f_ax*T))*rect(f_ax/(2*fg))
print("Kompensiere") print("Kompensiere")
else: else:
H2 = np.ones_like(F) H2 = np.ones_like(F)
print("Kompensation nicht nötig") print("Kompensation nicht nötig")
return H2 return H2
H2 = receiver_compensation_filter(t0, T) H2 = receiver_compensation_filter(t0, T)
# Plot # Plot
fig,ax=plt.subplots(); ax.plot(f_ax, np.abs(H2), 'rwth:blue'); fig,ax=plt.subplots(); ax.plot(f_ax, np.abs(H2), 'rwth:blue');
ax.set_xlabel(r'$\rightarrow f$ [Hz]', bbox=rwth_plots.wbbox); ax.set_ylabel(r'$\uparrow |H_2(f)|$'); ax.set_xlabel(r'$\rightarrow f$ [Hz]', bbox=rwth_plots.wbbox); ax.set_ylabel(r'$\uparrow |H_2(f)|$');
ax.set_xlim([-2*fg, 2*fg]); rwth_plots.axis(ax); ax.set_xlim([-2*fg, 2*fg]); rwth_plots.axis(ax);
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Filterung und Vergleich von $F_\mathrm{e}(f)$ mit $F(f)$ Filterung und Vergleich von $F_\mathrm{e}(f)$ mit $F(f)$
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
def receiver_compensate(fe, H2): def receiver_compensate(fe, H2):
# Fourier-Transformation # Fourier-Transformation
Fe,_ = rwth_transforms.dft(fe, fs) Fe,_ = rwth_transforms.dft(fe, fs)
# Kompensation (im Frequenzbereich) # Kompensation (im Frequenzbereich)
Fe2 = Fe*H2 Fe2 = Fe*H2
# Inverse Fourier-Transformation # Inverse Fourier-Transformation
fe2 = np.real(rwth_transforms.idft(Fe2, len(t))) fe2 = np.real(rwth_transforms.idft(Fe2, len(t)))
return (fe2, Fe2, Fe) return (fe2, Fe2, Fe)
fe2, Fe2, Fe = receiver_compensate(fe, H2) fe2, Fe2, Fe = receiver_compensate(fe, H2)
# Plot # Plot
fig, axs = plt.subplots(2,2, figsize=(8,4)); fig, axs = plt.subplots(2,2, figsize=(8,4));
ax = axs[0,0]; ax.plot(f_ax, np.abs(F), 'rwth:blue', label=r'$|F(f)|$'); ax = axs[0,0]; ax.plot(f_ax, np.abs(F), 'rwth:blue', label=r'$|F(f)|$');
ax.plot(f_ax, np.abs(Fe), 'rwth:green', label=r'$|F_\mathrm{e}(f)|$'); ax.plot(f_ax, np.abs(Fe), 'rwth:green', label=r'$|F_\mathrm{e}(f)|$');
ax.set_xlabel(r'$\rightarrow f$ [Hz]', bbox=rwth_plots.wbbox); ax.set_xlabel(r'$\rightarrow f$ [Hz]', bbox=rwth_plots.wbbox);
ax.set_xlim([-fg, fg]); ax.legend(); rwth_plots.axis(ax); ax.set_xlim([-fg, fg]); ax.legend(); rwth_plots.axis(ax);
ax = axs[0,1]; ax.plot(f_ax, np.abs(F), 'rwth:blue'); ax = axs[0,1]; ax.plot(f_ax, np.abs(F), 'rwth:blue');
ax.plot(f_ax, np.abs(Fe), 'rwth:green'); ax.plot(f_ax, np.abs(Fe), 'rwth:green');
ax.set_xlabel(r'$\rightarrow f$ [Hz]', bbox=rwth_plots.wbbox); ax.set_xlabel(r'$\rightarrow f$ [Hz]', bbox=rwth_plots.wbbox);
ax.set_xlim([0, fg/10]); rwth_plots.axis(ax); ax.set_xlim([0, fg/10]); rwth_plots.axis(ax);
ax = axs[1,0]; ax.plot(f_ax, np.abs(F), 'rwth:blue', label=r'$|F(f)|$'); ax = axs[1,0]; ax.plot(f_ax, np.abs(F), 'rwth:blue', label=r'$|F(f)|$');
ax.plot(f_ax, np.abs(Fe2), 'rwth:green', label=r'$|F_\mathrm{e}(f) \cdot H_2(f)|$'); ax.plot(f_ax, np.abs(Fe2), 'rwth:green', label=r'$|F_\mathrm{e}(f) \cdot H_2(f)|$');
ax.set_xlabel(r'$\rightarrow f$ [Hz]', bbox=rwth_plots.wbbox); ax.set_xlabel(r'$\rightarrow f$ [Hz]', bbox=rwth_plots.wbbox);
ax.set_xlim(axs[0,0].get_xlim()); ax.set_ylim(axs[0,0].get_ylim()); ax.legend(); rwth_plots.axis(ax); ax.set_xlim(axs[0,0].get_xlim()); ax.set_ylim(axs[0,0].get_ylim()); ax.legend(); rwth_plots.axis(ax);
ax = axs[1,1]; ax.plot(f_ax, np.abs(F), 'rwth:blue'); ax = axs[1,1]; ax.plot(f_ax, np.abs(F), 'rwth:blue');
ax.plot(f_ax, np.abs(Fe2), 'rwth:green'); ax.plot(f_ax, np.abs(Fe2), 'rwth:green');
ax.set_xlabel(r'$\rightarrow f$ [Hz]', bbox=rwth_plots.wbbox); ax.set_xlabel(r'$\rightarrow f$ [Hz]', bbox=rwth_plots.wbbox);
ax.set_xlim(axs[0,1].get_xlim()); ax.set_ylim(axs[0,1].get_ylim()); rwth_plots.axis(ax); ax.set_xlim(axs[0,1].get_xlim()); ax.set_ylim(axs[0,1].get_ylim()); rwth_plots.axis(ax);
rwth_media.audio_play(fTP, fs, r'$f(t)\ast h_\mathrm{LP}(t)$') rwth_media.audio_play(signal.resample(fTP, len(f0)), fs0, r'$f(t)\ast h_\mathrm{LP}(t)$')
rwth_media.audio_play(fe2, fs, r'$f_\mathrm{e}(t)\ast h_2(t)$') rwth_media.audio_play(signal.resample(fe2, len(f0)), fs0, r'$f_\mathrm{e}(t)\ast h_2(t)$')
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
### Interaktive Demo ### Interaktive Demo
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
fix,axs = plt.subplots(2,2, figsize=(8,8)); fix,axs = plt.subplots(2,2, figsize=(8,8));
@interact(t0byT = widgets.FloatSlider(min=0.5,max=1.25,step=0.25,value=0.5,description=r'$t_0/T$:', continuous_update=False)) @interact(t0byT = widgets.FloatSlider(min=0.5,max=1.25,step=0.25,value=0.5,description=r'$t_0/T$:', continuous_update=False))
def update_plot(t0byT): def update_plot(t0byT):
t0 = t0byT*T t0 = t0byT*T
# Sender: Träger mit Breite t0 # Sender: Träger mit Breite t0
m = sender_carrier(s, fa, t0) m = sender_carrier(s, fa, t0)
# Empfänger: Korrelationsfilter, Abtastung und Tiefpass # Empfänger: Korrelationsfilter, Abtastung und Tiefpass
y,g,ne,h = receiver_filter(m, n, s, t0) y,g,ne,h = receiver_filter(m, n, s, t0)
fe, ya, ya_nT = receiver_sampling_lp(y) fe, ya, ya_nT = receiver_sampling_lp(y)
# Empfänger: Kompensation # Empfänger: Kompensation
H2 = receiver_compensation_filter(t0, T) H2 = receiver_compensation_filter(t0, T)
fe2, Fe2, Fe = receiver_compensate(fe, H2) fe2, Fe2, Fe = receiver_compensate(fe, H2)
# Plot # Plot
if not axs[0,0].lines: if not axs[0,0].lines:
ax = axs[0,0]; ax.plot(t/T, m, 'rwth:blue'); ax = axs[0,0]; ax.plot(t/T, m, 'rwth:blue');
ax.set_xlabel(r'$\rightarrow t/T$', bbox=rwth_plots.wbbox); ax.set_ylabel(r'$\uparrow m(t)$', bbox=rwth_plots.wbbox); ax.set_xlabel(r'$\rightarrow t/T$', bbox=rwth_plots.wbbox); ax.set_ylabel(r'$\uparrow m(t)$', bbox=rwth_plots.wbbox);
ax.set_xlim([0,50]); ax.grid(); rwth_plots.axis(ax) ax.set_xlim([0,50]); ax.grid(); rwth_plots.axis(ax)
ax = axs[0,1]; ax.plot(t/T, y, 'rwth:blue'); ax = axs[0,1]; ax.plot(t/T, y, 'rwth:blue');
ax.set_xlabel(r'$\rightarrow t/T$', bbox=rwth_plots.wbbox); ax.set_ylabel(r'$\uparrow y(t)$', bbox=rwth_plots.wbbox); ax.set_xlabel(r'$\rightarrow t/T$', bbox=rwth_plots.wbbox); ax.set_ylabel(r'$\uparrow y(t)$', bbox=rwth_plots.wbbox);
ax.set_xlim(axs[0,0].get_xlim()); ax.grid(); rwth_plots.axis(ax) ax.set_xlim(axs[0,0].get_xlim()); ax.grid(); rwth_plots.axis(ax)
ax = axs[1,0]; ax.plot(t/T, fe, 'rwth:blue'); ax = axs[1,0]; ax.plot(t/T, fe, 'rwth:blue');
ax.set_xlabel(r'$\rightarrow t/T$', bbox=rwth_plots.wbbox); ax.set_ylabel(r'$\uparrow f_\mathrm{e}(t)$', bbox=rwth_plots.wbbox); ax.set_xlabel(r'$\rightarrow t/T$', bbox=rwth_plots.wbbox); ax.set_ylabel(r'$\uparrow f_\mathrm{e}(t)$', bbox=rwth_plots.wbbox);
ax.set_xlim(axs[0,0].get_xlim()); ax.grid(); rwth_plots.axis(ax) ax.set_xlim(axs[0,0].get_xlim()); ax.grid(); rwth_plots.axis(ax)
ax = axs[1,1]; ax.plot(t/T, fe, 'rwth:blue'); ax = axs[1,1]; ax.plot(t/T, fe, 'rwth:blue');
ax.set_xlabel(r'$\rightarrow t/T$', bbox=rwth_plots.wbbox); ax.set_ylabel(r'$\uparrow f_{\mathrm{e}}(t)\ast h_2(t)$', bbox=rwth_plots.wbbox); ax.set_xlabel(r'$\rightarrow t/T$', bbox=rwth_plots.wbbox); ax.set_ylabel(r'$\uparrow f_{\mathrm{e}}(t)\ast h_2(t)$', bbox=rwth_plots.wbbox);
ax.set_xlim(axs[0,0].get_xlim()); ax.grid(); rwth_plots.axis(ax) ax.set_xlim(axs[0,0].get_xlim()); ax.grid(); rwth_plots.axis(ax)
else: else:
axs[0,0].lines[0].set_ydata(m); axs[0,1].lines[0].set_ydata(y); axs[0,0].lines[0].set_ydata(m); axs[0,1].lines[0].set_ydata(y);
axs[1,0].lines[0].set_ydata(fe); axs[1,1].lines[0].set_ydata(fe2); axs[1,0].lines[0].set_ydata(fe); axs[1,1].lines[0].set_ydata(fe2);
``` ```
%% Cell type:markdown id: tags: %% 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). 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: Please attribute the work as follows:
*Christian Rohlfing, Übungsbeispiele zur Vorlesung "Informationsübertragung"*, gehalten von Jens-Rainer Ohm, 2020, Institut für Nachrichtentechnik, RWTH Aachen University. *Christian Rohlfing, Übungsbeispiele zur Vorlesung "Informationsübertragung"*, gehalten von Jens-Rainer Ohm, 2020, Institut für Nachrichtentechnik, RWTH Aachen University.
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