diff --git a/presentation/plots/.idea/markdown-navigator/profiles_settings.xml b/presentation/plots/.idea/markdown-navigator/profiles_settings.xml
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diff --git a/presentation/plots/.idea/misc.xml b/presentation/plots/.idea/misc.xml
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diff --git a/presentation/plots/.idea/workspace.xml b/presentation/plots/.idea/workspace.xml
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diff --git a/presentation/plots/amplitude_modulation.png b/presentation/plots/amplitude_modulation.png
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diff --git a/presentation/plots/chirp.png b/presentation/plots/chirp.png
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diff --git a/presentation/plots/chirp.py b/presentation/plots/chirp.py
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+++ b/presentation/plots/chirp.py
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+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 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()
+
+plt.show()
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