def test_demodulate_sinusoidalModulation():
'Test demodulation with a linear phase modulation.'
# Create linear phase evolution
# (i.e. the corresponding signal `y` is only the carrier frequency)
Fs = 200.
f0 = 27.
t = np.arange(0, 10, 1. / Fs)
ph0 = 2 * np.pi * f0 * t
# Sinusoidal phase modulation
# Error *decreases* as `fm` and/or `phm` decrease
fm = 5e-2 # if Fs = 200 MHz, then here fm = 50 kHz
phm = 1e-2 * np.cos(2 * np.pi * fm * t)
# Create signal
A0 = 1.
y = A0 * np.cos(ph0 + phm)
# Attempt to demodulate
# Note: High frequency noise/V-shape of error between
# calculated phase `ph` and true phase `ph0 + phm`
# *decreases* as Q is increased (e.g. the low pass filtering
# in `decimate(...)` is cleaning up the signal/removing errors).
Q = 20
A, ph, valid = demodulate(y, Q=Q, decimate_kwargs={})
np.testing.assert_allclose(A[valid], A0, atol=1e-5)
np.testing.assert_allclose(ph[valid], (ph0 + phm)[::Q][valid], atol=1e-5)
def test_demodulate_carrierOnly():
'Test demodulation on (nearly) perfect carrier wave.'
# Create linear phase evolution
# (i.e. the corresponding signal `y` is only the carrier frequency)
Fs = 200.
f0 = 27.
t = np.arange(0, 10, 1. / Fs)
ph0 = 2 * np.pi * f0 * t
# Create signal
A0 = 1.
y = A0 * np.cos(ph0)
# Attempt to demodulate
A, ph, valid = demodulate(y, Q=1, decimate_kwargs={})
np.testing.assert_allclose(A, A0, atol=1e-11)
np.testing.assert_allclose(ph, ph0, atol=1e-11)