def test_padded_align_odd() -> None:
"""
Test the padded cross-correlation method with two gaussian pulses of odd length.
"""
# make some time arrays and define a time delta
t = np.linspace(-2 * np.pi, 2 * np.pi, 100)
dt = 3.675 * (t[1] - t[0])
t = np.linspace(-1, 1, 199, endpoint=False)
# construct two identical gaussian pulses
x = np.real(signal.gausspulse(t, fc=5))
y = np.real(signal.gausspulse(t + dt, fc=5))
# compute the delay without any upsampling
d = align.xcorr_delay(x, y, 30)
# and apply the delay
y = align.apply_delay(y, d)
# and test the top-level call
ynew = align.align(x, y, method="xcorr", factor=30)
# and check that the alignment is within a certain known accuracy
assert np.std(np.abs(x - y)) < 0.005
assert np.std(np.abs(y - ynew)) < 5e-5
def test_fft_align() -> None:
"""
Test FFT phase shift alignment
"""
for N in [178, 179, 200, 201]:
# make some time arrays and define a time delta
t = np.linspace(-2 * np.pi, 2 * np.pi, N // 2)
dt = 3.675 * (t[1] - t[0])
t = np.linspace(-1, 1, N, endpoint=False)
true = dt / (t[1] - t[0])
# construct two identical gaussian pulses
x = np.real(signal.gausspulse(t, fc=5))
y = np.real(signal.gausspulse(t + dt, fc=5))
# compute the delay with upsampling
delay = align.fft_delay(x, y)
# and apply the delay
y = align.apply_delay(y, delay)
# use the top-level call
ynew = align.align(x, y, method="fft")
# and check that the alignment is within a certain known accuracy
assert np.abs(true - delay) < 1e-3
assert np.mean(np.abs(x - y)) < 1e-3
assert np.mean(np.abs(x - ynew)) < 2e-4
assert np.mean(np.abs(y - ynew)) < 3e-5
def test_gauss_align() -> None:
"""
Test Gaussian interpolation of unpadded cross correlation.
"""
# make some time arrays and define a time delta
t = np.linspace(-2 * np.pi, 2 * np.pi, 100)
dt = 3.675 * (t[1] - t[0])
t = np.linspace(-1, 1, 200, endpoint=False)
# construct two identical gaussian pulses
x = np.real(signal.gausspulse(t, fc=5))
y = np.real(signal.gausspulse(t + dt, fc=5))
# compute the delay with upsampling
d_padded = align.xcorr_delay(x, y, 30)
# compute the delay without any upsampling
d = align.xcorr_delay(x, y, fit="gauss")
# compute the new signal
y = align.apply_delay(y, d)
# and test the top-level call
ynew = align.align(x, y, method="xcorr", factor=30)
# and check that the alignment is within a certain known accuracy
assert np.abs(d - d_padded) < 0.05
assert np.mean(np.abs(x - y)) < 7e-4
assert np.mean(np.abs(x - ynew)) < 7e-4
assert np.mean(np.abs(y - ynew)) < 5e-5
def test_simple_align() -> None:
"""
Test the basic cross-correlation method with two gaussian pulses.
"""
# make some time arrays and define a time delta
t = np.linspace(-2 * np.pi, 2 * np.pi, 100)
dt = 3.675 * (t[1] - t[0])
t = np.linspace(-1, 1, 2 * 100, endpoint=False)
# construct two identical gaussian pulses
x = np.real(signal.gausspulse(t, fc=5))
y = np.real(signal.gausspulse(t + dt, fc=5))
# compute the delay without any upsampling
d = align.xcorr_delay(x, y)
# and apply the delay
y = align.apply_delay(y, d)
# and check that the alignment is within a certain accuracy
assert np.std(x - y) < 0.06