ZH: use correct DTFT convention

Only affects phase determination.
Introduces a minus sign for the s_k terms and changes arctan2 parameters

simulations/airshower_beacon_simulation/lib/tests/lib

@@ -0,0 +1 @@
+../

simulations/airshower_beacon_simulation/lib/tests/test_beacon_fourier.py

@@ -0,0 +1,30 @@
+#!/usr/bin/env python3
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+import lib
+
+seed = 12345
+dt = 1 # ns
+t = np.arange(0, 10*int(1e3), dt)
+frequency = 45e-3 # GHz
+
+N = 5e2
+rng = np.random.default_rng(seed)
+
+phase_res = np.zeros(int(N))
+
+for i in range(int(N)):
+    phase = lib.phase_mod(np.pi*(2*rng.uniform(size=1) -1)) # rad
+    beacon = lib.sine_beacon(frequency, t, t0=0, phase=phase)
+
+    measured = lib.find_beacon_in_traces([beacon], t, frequency, frequency_fit=False)
+
+    phase_res[i] = lib.phase_mod(measured[1][0] - phase)
+
+fig, ax = plt.subplots()
+ax.set_xlabel("$\\varphi_{meas} - \\varphi_{true}$ [rad]")
+ax.set_ylabel("#")
+ax.hist(phase_res, bins='sqrt')
+plt.show()