def test_non_normalized(self):
"""Test windows of small length that are not normalized to 1. See
the documentation for the Taylor window for more information on
normalization.
"""
assert_allclose(
windows.taylor(5, 2, 15, norm=False),
np.array(
[0.87508054, 1.04771499, 1.15440894, 1.04771499, 0.87508054]))
assert_allclose(
windows.taylor(6, 2, 15, norm=False),
np.array(
[0.86627793, 1.0, 1.13372207, 1.13372207, 1.0, 0.86627793]))
def test_normalized(self):
"""Tests windows of small length that are normalized to 1. See the
documentation for the Taylor window for more information on
normalization.
"""
assert_allclose(windows.taylor(1, 2, 15), 1.0)
assert_allclose(
windows.taylor(5, 2, 15),
np.array([0.75803341, 0.90757699, 1.0, 0.90757699, 0.75803341]))
assert_allclose(
windows.taylor(6, 2, 15),
np.array([
0.7504082, 0.86624416, 0.98208011, 0.98208011, 0.86624416,
0.7504082
]))
def test_correctness(self):
"""This test ensures the correctness of the implemented Taylor
Windowing function. A Taylor Window of 1024 points is created, its FFT
is taken, and the Peak Sidelobe Level (PSLL) and 3dB and 18dB bandwidth
are found and checked.
A publication from Sandia National Laboratories was used as reference
for the correctness values [1]_.
References
-----
.. [1] Armin Doerry, "Catalog of Window Taper Functions for
Sidelobe Control", 2017.
https://www.researchgate.net/profile/Armin_Doerry/publication/316281181_Catalog_of_Window_Taper_Functions_for_Sidelobe_Control/links/58f92cb2a6fdccb121c9d54d/Catalog-of-Window-Taper-Functions-for-Sidelobe-Control.pdf
"""
M_win = 1024
N_fft = 131072
# Set norm=False for correctness as the values obtained from the
# scientific publication do not normalize the values. Normalizing
# changes the sidelobe level from the desired value.
w = windows.taylor(M_win, nbar=4, sll=35, norm=False, sym=False)
f = fft(w, N_fft)
spec = 20 * np.log10(np.abs(f / np.amax(f)))
first_zero = np.argmax(np.diff(spec) > 0)
PSLL = np.amax(spec[first_zero:-first_zero])
BW_3dB = 2 * np.argmax(spec <= -3.0102999566398121) / N_fft * M_win
BW_18dB = 2 * np.argmax(spec <= -18.061799739838872) / N_fft * M_win
assert_allclose(PSLL, -35.1672, atol=1)
assert_allclose(BW_3dB, 1.1822, atol=0.1)
assert_allclose(BW_18dB, 2.6112, atol=0.1)
def test_simple(self):
assert_allclose(windows.taylor(1, 2, -15), 1.0)
assert_allclose(windows.taylor(5, 2, -15),
np.array([0.75803341, 0.90757699, 1.0,
0.90757699, 0.75803341]))
