237 lines
7.1 KiB
Python
237 lines
7.1 KiB
Python
from scipy.signal import chirp, spectrogram
|
|
import numpy as np
|
|
import matplotlib.pyplot as plt
|
|
|
|
def amp_freq_mod():
|
|
# amplitude modulation
|
|
t = np.linspace(0, 20 * np.pi, 1000, endpoint=False)
|
|
t1 = t[0:200]
|
|
t2 = t[200:600]
|
|
t3 = t[600:800]
|
|
t4 = t[800:]
|
|
|
|
plt.figure(1)
|
|
signal_unmod = np.sin(t)
|
|
plt.plot(t, signal_unmod)
|
|
plt.title("Unmodulated signal")
|
|
plt.xlabel('time')
|
|
plt.ylabel('Amplitude')
|
|
plt.tight_layout()
|
|
plt.savefig('unmodulated.png')
|
|
plt.show()
|
|
|
|
plt.figure(2)
|
|
signal_ampmod = np.hstack((np.sin(t1), 0.2 * np.sin(t2), np.sin(t3), 0.2 * np.sin(t4)))
|
|
plt.plot(t, signal_ampmod)
|
|
plt.title("Amplitude modulation")
|
|
plt.xlabel('time')
|
|
plt.ylabel('Amplitude')
|
|
plt.tight_layout()
|
|
plt.savefig('amplitude_modulation.png')
|
|
plt.show()
|
|
|
|
# frequency modulation
|
|
plt.figure(3)
|
|
signal_ampmod = np.hstack((np.sin(t1), np.sin(0.5*t2), np.sin(t3), np.sin(0.5*t4)))
|
|
plt.plot(t, signal_ampmod)
|
|
plt.title("Frequency modulation")
|
|
plt.xlabel('time')
|
|
plt.ylabel('Amplitude')
|
|
plt.tight_layout()
|
|
plt.savefig('frequency_modulation.png')
|
|
plt.show()
|
|
|
|
def chirps():
|
|
# chirp example
|
|
fs = 8000
|
|
T = 10
|
|
t = np.linspace(0, T, T*fs, endpoint=False)
|
|
|
|
upchirp = chirp(t, f0=0, f1=5, t1=10, method='linear')
|
|
plt.figure(1)
|
|
plt.plot(t, upchirp)
|
|
plt.title("Chirp")
|
|
plt.xlabel('time')
|
|
plt.ylabel('Amplitude')
|
|
plt.tight_layout()
|
|
plt.savefig('chirp.png')
|
|
plt.show()
|
|
|
|
|
|
#######################################
|
|
# LoRa chirps
|
|
fs = 8000
|
|
T = 10
|
|
t = np.linspace(0, T, T*fs, endpoint=False)
|
|
|
|
upchirp = chirp(t, f0=250, f1=1750, t1=10, method='linear')
|
|
|
|
ff, tt, Sxx = spectrogram(upchirp, fs=fs, noverlap=256, nperseg=512,
|
|
nfft=2048)
|
|
|
|
# Chirp explanation
|
|
plt.figure(2)
|
|
plt.yticks([250, 1000, 1750], ['f_start', 'f_center', 'f_end'] )
|
|
plt.xticks([0,10], [0, 't_symb'])
|
|
plt.pcolormesh(tt, ff[:513], Sxx[:513])
|
|
plt.title("Chirp spectrogram")
|
|
plt.xlabel('time')
|
|
plt.ylabel('frequency')
|
|
plt.tight_layout()
|
|
plt.savefig('chirp_spectrogram.png')
|
|
plt.show()
|
|
|
|
# LoRa upchirp
|
|
plt.figure(3)
|
|
plt.yticks([250, 1000, 1750], ['868.1 MHz - 62.5 kHz', '868.1 MHz', '868.1 MHz + 62.5 kHz'] )
|
|
plt.xticks([0,10], [0, 't_symb'])
|
|
plt.pcolormesh(tt, ff[:513], Sxx[:513])
|
|
plt.title("LoRa Up-Chirp")
|
|
plt.xlabel('time')
|
|
plt.ylabel('frequency')
|
|
plt.tight_layout()
|
|
plt.savefig('lora_upchirp.png')
|
|
plt.show()
|
|
|
|
|
|
# downchirp
|
|
downchirp = chirp(t, f0=1750, f1=250, t1=10, method='linear')
|
|
|
|
ff, tt, Sxx = spectrogram(downchirp, fs=fs, noverlap=256, nperseg=512,
|
|
nfft=2048)
|
|
|
|
|
|
plt.figure(4)
|
|
plt.yticks([250, 1000, 1750], ['868.1 MHz - 62.5 kHz', '868.1 MHz', '868.1 MHz + 62.5 kHz'] )
|
|
plt.xticks([0,10], [0, 't_symb'])
|
|
plt.pcolormesh(tt, ff[:513], Sxx[:513])
|
|
plt.title("LoRa Down-Chirp")
|
|
plt.xlabel('time')
|
|
plt.ylabel('frequency')
|
|
plt.tight_layout()
|
|
plt.savefig('lora_downchirp.png')
|
|
plt.show()
|
|
|
|
def symbol():
|
|
# symbol example
|
|
fs = 8000
|
|
T = 10
|
|
t = np.linspace(0, T, T*fs, endpoint=False)
|
|
|
|
fracs = [0.7, 0.7, 0.99, 0.9, 0.8, 0.5]
|
|
for i in range(0,6):
|
|
frac = fracs[i]
|
|
t_jump = T * (1 - frac)
|
|
|
|
# 250, 500, 750, 1000, 1250, 1500, 1750
|
|
t1 = (frac)*T
|
|
|
|
symbol_p1 = chirp(t[0:int(frac*len(t))], f0=250, f1=1750, t1=T, method='linear')
|
|
symbol_p2 = chirp(t[int(frac*len(t)):], f0=250, f1=1750, t1=T, method='linear')
|
|
symbol = np.hstack((symbol_p2, symbol_p1))
|
|
ff, tt, Sxx = spectrogram(symbol, fs=fs, noverlap=256, nperseg=512,
|
|
nfft=2048)
|
|
|
|
#chirp = np.hstack((upchirp, upchirp))
|
|
#ff, tt, Sxx = spectrogram(chirp, fs=fs, noverlap=256, nperseg=512,
|
|
# nfft=2048)
|
|
|
|
plt.figure(5)
|
|
plt.yticks([250, 1000, 1750], ['868.1 MHz - 62.5 kHz', '868.1 MHz', '868.1 MHz + 62.5 kHz'] )
|
|
plt.pcolormesh(tt, ff[:513], Sxx[:513])
|
|
if i > 0:
|
|
plt.xticks([0, t_jump], [0, 't_jump'])
|
|
plt.plot([t_jump, t_jump], [0, 2000.0], 'r')
|
|
else:
|
|
plt.xticks([0, t_jump], [0, 't_jump'])
|
|
plt.gca().tick_params(axis='x', colors='white')
|
|
plt.title("LoRa Symbol")
|
|
plt.xlabel('time')
|
|
plt.ylabel('frequency')
|
|
plt.tight_layout()
|
|
plt.savefig('lora_symbols_{}.png'.format(i))
|
|
plt.show()
|
|
|
|
def demodulation():
|
|
# demodulation
|
|
fs = 8000
|
|
T = 10
|
|
t = np.linspace(0, T, T*fs, endpoint=False)
|
|
|
|
for i in range(0,3):
|
|
frac = 0.3
|
|
t_jump = T * (1 - frac)
|
|
|
|
# 250, 500, 750, 1000, 1250, 1500, 1750
|
|
t1 = (frac)*T
|
|
|
|
if i == 0:
|
|
symbol_p1 = chirp(t[0:int(frac*len(t))], f0=250, f1=1750, t1=T, method='linear')
|
|
symbol_p2 = chirp(t[int(frac*len(t)):], f0=250, f1=1750, t1=T, method='linear')
|
|
elif i == 1:
|
|
symbol_p1 = chirp(t[0:int(frac * len(t))], f0=1750, f1=250, t1=T, method='linear')
|
|
symbol_p2 = chirp(t[int(frac * len(t)):], f0=1750, f1=250, t1=T, method='linear')
|
|
elif i == 2:
|
|
symbol_p1 = chirp(t[0:int(frac * len(t))], f0=700, f1=700, t1=T, method='linear')
|
|
symbol_p2 = chirp(t[int(frac * len(t)):], f0=700, f1=700, t1=T, method='linear')
|
|
|
|
symbol = np.hstack((symbol_p2, symbol_p1))
|
|
ff, tt, Sxx = spectrogram(symbol, fs=fs, noverlap=256, nperseg=512,
|
|
nfft=2048)
|
|
|
|
#chirp = np.hstack((upchirp, upchirp))
|
|
#ff, tt, Sxx = spectrogram(chirp, fs=fs, noverlap=256, nperseg=512,
|
|
# nfft=2048)
|
|
|
|
plt.figure(5)
|
|
plt.yticks([250, 1000, 1750], ['868.1 MHz - 62.5 kHz', '868.1 MHz', '868.1 MHz + 62.5 kHz'] )
|
|
plt.pcolormesh(tt, ff[:513], Sxx[:513])
|
|
|
|
plt.title("LoRa Symbol")
|
|
plt.xlabel('time')
|
|
plt.ylabel('frequency')
|
|
plt.tight_layout()
|
|
plt.savefig('lora_demodulation_{}.png'.format(i))
|
|
plt.show()
|
|
|
|
|
|
def spreading_factor():
|
|
fs = 8000
|
|
T = 400
|
|
t = np.linspace(0, T, T * fs, endpoint=False)
|
|
|
|
chirps = np.array([0])
|
|
for i in range(3,-1,-1):
|
|
t_final = len(t)/2**i
|
|
chirp1 = chirp(t[0:t_final], f0=250, f1=1750, t1=T/2**i, method='linear')
|
|
|
|
chirps = np.hstack((chirps, chirp1))
|
|
|
|
ff, tt, Sxx = spectrogram(chirps, fs=fs, noverlap=256, nperseg=512,
|
|
nfft=2048)
|
|
|
|
plt.figure(5)
|
|
plt.yticks([250, 1000, 1750], ['868.1 MHz - 62.5 kHz', '868.1 MHz', '868.1 MHz + 62.5 kHz'])
|
|
plt.pcolormesh(tt, ff[:513], Sxx[:513])
|
|
|
|
plt.title("LoRa Spreading Factors")
|
|
plt.xlabel('time')
|
|
plt.ylabel('frequency')
|
|
plt.xticks([], [])
|
|
plt.gca().set_aspect(0.28)
|
|
|
|
for i in range(0,4):
|
|
plt.text(tt[int(2.0**i/2.0**3 * len(tt)-1)], 1800.0, 'SF = {}'.format(i + 7), color='white', horizontalalignment='right')
|
|
|
|
plt.tight_layout()
|
|
plt.savefig('lora_spreading_factors.png', dpi=400.0)
|
|
plt.show()
|
|
pass
|
|
|
|
|
|
#symbol()
|
|
#spreading_factor()
|
|
demodulation()
|
|
|
|
plt.show()
|