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import numpy as np
from numpy import array
from numpy.testing import (assert_array_almost_equal, assert_array_equal,
assert_allclose,
assert_equal, assert_, assert_array_less,
suppress_warnings)
from pytest import raises as assert_raises
from scipy.fft import fft
from scipy.signal import windows, get_window, resample
window_funcs = [
('boxcar', ()),
('triang', ()),
('parzen', ()),
('bohman', ()),
('blackman', ()),
('nuttall', ()),
('blackmanharris', ()),
('flattop', ()),
('bartlett', ()),
('barthann', ()),
('hamming', ()),
('kaiser', (1,)),
('dpss', (2,)),
('gaussian', (0.5,)),
('general_gaussian', (1.5, 2)),
('chebwin', (1,)),
('cosine', ()),
('hann', ()),
('exponential', ()),
('taylor', ()),
('tukey', (0.5,)),
('lanczos', ()),
]
class TestBartHann:
def test_basic(self):
assert_allclose(windows.barthann(6, sym=True),
[0, 0.35857354213752, 0.8794264578624801,
0.8794264578624801, 0.3585735421375199, 0],
rtol=1e-15, atol=1e-15)
assert_allclose(windows.barthann(7),
[0, 0.27, 0.73, 1.0, 0.73, 0.27, 0],
rtol=1e-15, atol=1e-15)
assert_allclose(windows.barthann(6, False),
[0, 0.27, 0.73, 1.0, 0.73, 0.27],
rtol=1e-15, atol=1e-15)
class TestBartlett:
def test_basic(self):
assert_allclose(windows.bartlett(6), [0, 0.4, 0.8, 0.8, 0.4, 0])
assert_allclose(windows.bartlett(7), [0, 1/3, 2/3, 1.0, 2/3, 1/3, 0])
assert_allclose(windows.bartlett(6, False),
[0, 1/3, 2/3, 1.0, 2/3, 1/3])
class TestBlackman:
def test_basic(self):
assert_allclose(windows.blackman(6, sym=False),
[0, 0.13, 0.63, 1.0, 0.63, 0.13], atol=1e-14)
assert_allclose(windows.blackman(7, sym=False),
[0, 0.09045342435412804, 0.4591829575459636,
0.9203636180999081, 0.9203636180999081,
0.4591829575459636, 0.09045342435412804], atol=1e-8)
assert_allclose(windows.blackman(6),
[0, 0.2007701432625305, 0.8492298567374694,
0.8492298567374694, 0.2007701432625305, 0],
atol=1e-14)
assert_allclose(windows.blackman(7, True),
[0, 0.13, 0.63, 1.0, 0.63, 0.13, 0], atol=1e-14)
class TestBlackmanHarris:
def test_basic(self):
assert_allclose(windows.blackmanharris(6, False),
[6.0e-05, 0.055645, 0.520575, 1.0, 0.520575, 0.055645])
assert_allclose(windows.blackmanharris(7, sym=False),
[6.0e-05, 0.03339172347815117, 0.332833504298565,
0.8893697722232837, 0.8893697722232838,
0.3328335042985652, 0.03339172347815122])
assert_allclose(windows.blackmanharris(6),
[6.0e-05, 0.1030114893456638, 0.7938335106543362,
0.7938335106543364, 0.1030114893456638, 6.0e-05])
assert_allclose(windows.blackmanharris(7, sym=True),
[6.0e-05, 0.055645, 0.520575, 1.0, 0.520575, 0.055645,
6.0e-05])
class TestTaylor:
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_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_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)
class TestBohman:
def test_basic(self):
assert_allclose(windows.bohman(6),
[0, 0.1791238937062839, 0.8343114522576858,
0.8343114522576858, 0.1791238937062838, 0])
assert_allclose(windows.bohman(7, sym=True),
[0, 0.1089977810442293, 0.6089977810442293, 1.0,
0.6089977810442295, 0.1089977810442293, 0])
assert_allclose(windows.bohman(6, False),
[0, 0.1089977810442293, 0.6089977810442293, 1.0,
0.6089977810442295, 0.1089977810442293])
class TestBoxcar:
def test_basic(self):
assert_allclose(windows.boxcar(6), [1, 1, 1, 1, 1, 1])
assert_allclose(windows.boxcar(7), [1, 1, 1, 1, 1, 1, 1])
assert_allclose(windows.boxcar(6, False), [1, 1, 1, 1, 1, 1])
cheb_odd_true = array([0.200938, 0.107729, 0.134941, 0.165348,
0.198891, 0.235450, 0.274846, 0.316836,
0.361119, 0.407338, 0.455079, 0.503883,
0.553248, 0.602637, 0.651489, 0.699227,
0.745266, 0.789028, 0.829947, 0.867485,
0.901138, 0.930448, 0.955010, 0.974482,
0.988591, 0.997138, 1.000000, 0.997138,
0.988591, 0.974482, 0.955010, 0.930448,
0.901138, 0.867485, 0.829947, 0.789028,
0.745266, 0.699227, 0.651489, 0.602637,
0.553248, 0.503883, 0.455079, 0.407338,
0.361119, 0.316836, 0.274846, 0.235450,
0.198891, 0.165348, 0.134941, 0.107729,
0.200938])
cheb_even_true = array([0.203894, 0.107279, 0.133904,
0.163608, 0.196338, 0.231986,
0.270385, 0.311313, 0.354493,
0.399594, 0.446233, 0.493983,
0.542378, 0.590916, 0.639071,
0.686302, 0.732055, 0.775783,
0.816944, 0.855021, 0.889525,
0.920006, 0.946060, 0.967339,
0.983557, 0.994494, 1.000000,
1.000000, 0.994494, 0.983557,
0.967339, 0.946060, 0.920006,
0.889525, 0.855021, 0.816944,
0.775783, 0.732055, 0.686302,
0.639071, 0.590916, 0.542378,
0.493983, 0.446233, 0.399594,
0.354493, 0.311313, 0.270385,
0.231986, 0.196338, 0.163608,
0.133904, 0.107279, 0.203894])
class TestChebWin:
def test_basic(self):
with suppress_warnings() as sup:
sup.filter(UserWarning, "This window is not suitable")
assert_allclose(windows.chebwin(6, 100),
[0.1046401879356917, 0.5075781475823447, 1.0, 1.0,
0.5075781475823447, 0.1046401879356917])
assert_allclose(windows.chebwin(7, 100),
[0.05650405062850233, 0.316608530648474,
0.7601208123539079, 1.0, 0.7601208123539079,
0.316608530648474, 0.05650405062850233])
assert_allclose(windows.chebwin(6, 10),
[1.0, 0.6071201674458373, 0.6808391469897297,
0.6808391469897297, 0.6071201674458373, 1.0])
assert_allclose(windows.chebwin(7, 10),
[1.0, 0.5190521247588651, 0.5864059018130382,
0.6101519801307441, 0.5864059018130382,
0.5190521247588651, 1.0])
assert_allclose(windows.chebwin(6, 10, False),
[1.0, 0.5190521247588651, 0.5864059018130382,
0.6101519801307441, 0.5864059018130382,
0.5190521247588651])
def test_cheb_odd_high_attenuation(self):
with suppress_warnings() as sup:
sup.filter(UserWarning, "This window is not suitable")
cheb_odd = windows.chebwin(53, at=-40)
assert_array_almost_equal(cheb_odd, cheb_odd_true, decimal=4)
def test_cheb_even_high_attenuation(self):
with suppress_warnings() as sup:
sup.filter(UserWarning, "This window is not suitable")
cheb_even = windows.chebwin(54, at=40)
assert_array_almost_equal(cheb_even, cheb_even_true, decimal=4)
def test_cheb_odd_low_attenuation(self):
cheb_odd_low_at_true = array([1.000000, 0.519052, 0.586405,
0.610151, 0.586405, 0.519052,
1.000000])
with suppress_warnings() as sup:
sup.filter(UserWarning, "This window is not suitable")
cheb_odd = windows.chebwin(7, at=10)
assert_array_almost_equal(cheb_odd, cheb_odd_low_at_true, decimal=4)
def test_cheb_even_low_attenuation(self):
cheb_even_low_at_true = array([1.000000, 0.451924, 0.51027,
0.541338, 0.541338, 0.51027,
0.451924, 1.000000])
with suppress_warnings() as sup:
sup.filter(UserWarning, "This window is not suitable")
cheb_even = windows.chebwin(8, at=-10)
assert_array_almost_equal(cheb_even, cheb_even_low_at_true, decimal=4)
exponential_data = {
(4, None, 0.2, False):
array([4.53999297624848542e-05,
6.73794699908546700e-03, 1.00000000000000000e+00,
6.73794699908546700e-03]),
(4, None, 0.2, True): array([0.00055308437014783, 0.0820849986238988,
0.0820849986238988, 0.00055308437014783]),
(4, None, 1.0, False): array([0.1353352832366127, 0.36787944117144233, 1.,
0.36787944117144233]),
(4, None, 1.0, True): array([0.22313016014842982, 0.60653065971263342,
0.60653065971263342, 0.22313016014842982]),
(4, 2, 0.2, False):
array([4.53999297624848542e-05, 6.73794699908546700e-03,
1.00000000000000000e+00, 6.73794699908546700e-03]),
(4, 2, 0.2, True): None,
(4, 2, 1.0, False): array([0.1353352832366127, 0.36787944117144233, 1.,
0.36787944117144233]),
(4, 2, 1.0, True): None,
(5, None, 0.2, True):
array([4.53999297624848542e-05,
6.73794699908546700e-03, 1.00000000000000000e+00,
6.73794699908546700e-03, 4.53999297624848542e-05]),
(5, None, 1.0, True): array([0.1353352832366127, 0.36787944117144233, 1.,
0.36787944117144233, 0.1353352832366127]),
(5, 2, 0.2, True): None,
(5, 2, 1.0, True): None
}
def test_exponential():
for k, v in exponential_data.items():
if v is None:
assert_raises(ValueError, windows.exponential, *k)
else:
win = windows.exponential(*k)
assert_allclose(win, v, rtol=1e-14)
class TestFlatTop:
def test_basic(self):
assert_allclose(windows.flattop(6, sym=False),
[-0.000421051, -0.051263156, 0.19821053, 1.0,
0.19821053, -0.051263156])
assert_allclose(windows.flattop(7, sym=False),
[-0.000421051, -0.03684078115492348,
0.01070371671615342, 0.7808739149387698,
0.7808739149387698, 0.01070371671615342,
-0.03684078115492348])
assert_allclose(windows.flattop(6),
[-0.000421051, -0.0677142520762119, 0.6068721525762117,
0.6068721525762117, -0.0677142520762119,
-0.000421051])
assert_allclose(windows.flattop(7, True),
[-0.000421051, -0.051263156, 0.19821053, 1.0,
0.19821053, -0.051263156, -0.000421051])
class TestGaussian:
def test_basic(self):
assert_allclose(windows.gaussian(6, 1.0),
[0.04393693362340742, 0.3246524673583497,
0.8824969025845955, 0.8824969025845955,
0.3246524673583497, 0.04393693362340742])
assert_allclose(windows.gaussian(7, 1.2),
[0.04393693362340742, 0.2493522087772962,
0.7066482778577162, 1.0, 0.7066482778577162,
0.2493522087772962, 0.04393693362340742])
assert_allclose(windows.gaussian(7, 3),
[0.6065306597126334, 0.8007374029168081,
0.9459594689067654, 1.0, 0.9459594689067654,
0.8007374029168081, 0.6065306597126334])
assert_allclose(windows.gaussian(6, 3, False),
[0.6065306597126334, 0.8007374029168081,
0.9459594689067654, 1.0, 0.9459594689067654,
0.8007374029168081])
class TestGeneralCosine:
def test_basic(self):
assert_allclose(windows.general_cosine(5, [0.5, 0.3, 0.2]),
[0.4, 0.3, 1, 0.3, 0.4])
assert_allclose(windows.general_cosine(4, [0.5, 0.3, 0.2], sym=False),
[0.4, 0.3, 1, 0.3])
class TestGeneralHamming:
def test_basic(self):
assert_allclose(windows.general_hamming(5, 0.7),
[0.4, 0.7, 1.0, 0.7, 0.4])
assert_allclose(windows.general_hamming(5, 0.75, sym=False),
[0.5, 0.6727457514, 0.9522542486,
0.9522542486, 0.6727457514])
assert_allclose(windows.general_hamming(6, 0.75, sym=True),
[0.5, 0.6727457514, 0.9522542486,
0.9522542486, 0.6727457514, 0.5])
class TestHamming:
def test_basic(self):
assert_allclose(windows.hamming(6, False),
[0.08, 0.31, 0.77, 1.0, 0.77, 0.31])
assert_allclose(windows.hamming(7, sym=False),
[0.08, 0.2531946911449826, 0.6423596296199047,
0.9544456792351128, 0.9544456792351128,
0.6423596296199047, 0.2531946911449826])
assert_allclose(windows.hamming(6),
[0.08, 0.3978521825875242, 0.9121478174124757,
0.9121478174124757, 0.3978521825875242, 0.08])
assert_allclose(windows.hamming(7, sym=True),
[0.08, 0.31, 0.77, 1.0, 0.77, 0.31, 0.08])
class TestHann:
def test_basic(self):
assert_allclose(windows.hann(6, sym=False),
[0, 0.25, 0.75, 1.0, 0.75, 0.25],
rtol=1e-15, atol=1e-15)
assert_allclose(windows.hann(7, sym=False),
[0, 0.1882550990706332, 0.6112604669781572,
0.9504844339512095, 0.9504844339512095,
0.6112604669781572, 0.1882550990706332],
rtol=1e-15, atol=1e-15)
assert_allclose(windows.hann(6, True),
[0, 0.3454915028125263, 0.9045084971874737,
0.9045084971874737, 0.3454915028125263, 0],
rtol=1e-15, atol=1e-15)
assert_allclose(windows.hann(7),
[0, 0.25, 0.75, 1.0, 0.75, 0.25, 0],
rtol=1e-15, atol=1e-15)
class TestKaiser:
def test_basic(self):
assert_allclose(windows.kaiser(6, 0.5),
[0.9403061933191572, 0.9782962393705389,
0.9975765035372042, 0.9975765035372042,
0.9782962393705389, 0.9403061933191572])
assert_allclose(windows.kaiser(7, 0.5),
[0.9403061933191572, 0.9732402256999829,
0.9932754654413773, 1.0, 0.9932754654413773,
0.9732402256999829, 0.9403061933191572])
assert_allclose(windows.kaiser(6, 2.7),
[0.2603047507678832, 0.6648106293528054,
0.9582099802511439, 0.9582099802511439,
0.6648106293528054, 0.2603047507678832])
assert_allclose(windows.kaiser(7, 2.7),
[0.2603047507678832, 0.5985765418119844,
0.8868495172060835, 1.0, 0.8868495172060835,
0.5985765418119844, 0.2603047507678832])
assert_allclose(windows.kaiser(6, 2.7, False),
[0.2603047507678832, 0.5985765418119844,
0.8868495172060835, 1.0, 0.8868495172060835,
0.5985765418119844])
class TestKaiserBesselDerived:
def test_basic(self):
M = 100
w = windows.kaiser_bessel_derived(M, beta=4.0)
w2 = windows.get_window(('kaiser bessel derived', 4.0),
M, fftbins=False)
assert_allclose(w, w2)
# Test for Princen-Bradley condition
assert_allclose(w[:M // 2] ** 2 + w[-M // 2:] ** 2, 1.)
# Test actual values from other implementations
# M = 2: sqrt(2) / 2
# M = 4: 0.518562710536, 0.855039598640
# M = 6: 0.436168993154, 0.707106781187, 0.899864772847
# Ref:https://github.com/scipy/scipy/pull/4747#issuecomment-172849418
assert_allclose(windows.kaiser_bessel_derived(2, beta=np.pi / 2)[:1],
np.sqrt(2) / 2)
assert_allclose(windows.kaiser_bessel_derived(4, beta=np.pi / 2)[:2],
[0.518562710536, 0.855039598640])
assert_allclose(windows.kaiser_bessel_derived(6, beta=np.pi / 2)[:3],
[0.436168993154, 0.707106781187, 0.899864772847])
def test_exceptions(self):
M = 100
# Assert ValueError for odd window length
msg = ("Kaiser-Bessel Derived windows are only defined for even "
"number of points")
with assert_raises(ValueError, match=msg):
windows.kaiser_bessel_derived(M + 1, beta=4.)
# Assert ValueError for non-symmetric setting
msg = ("Kaiser-Bessel Derived windows are only defined for "
"symmetric shapes")
with assert_raises(ValueError, match=msg):
windows.kaiser_bessel_derived(M + 1, beta=4., sym=False)
class TestNuttall:
def test_basic(self):
assert_allclose(windows.nuttall(6, sym=False),
[0.0003628, 0.0613345, 0.5292298, 1.0, 0.5292298,
0.0613345])
assert_allclose(windows.nuttall(7, sym=False),
[0.0003628, 0.03777576895352025, 0.3427276199688195,
0.8918518610776603, 0.8918518610776603,
0.3427276199688196, 0.0377757689535203])
assert_allclose(windows.nuttall(6),
[0.0003628, 0.1105152530498718, 0.7982580969501282,
0.7982580969501283, 0.1105152530498719, 0.0003628])
assert_allclose(windows.nuttall(7, True),
[0.0003628, 0.0613345, 0.5292298, 1.0, 0.5292298,
0.0613345, 0.0003628])
class TestParzen:
def test_basic(self):
assert_allclose(windows.parzen(6),
[0.009259259259259254, 0.25, 0.8611111111111112,
0.8611111111111112, 0.25, 0.009259259259259254])
assert_allclose(windows.parzen(7, sym=True),
[0.00583090379008747, 0.1574344023323616,
0.6501457725947521, 1.0, 0.6501457725947521,
0.1574344023323616, 0.00583090379008747])
assert_allclose(windows.parzen(6, False),
[0.00583090379008747, 0.1574344023323616,
0.6501457725947521, 1.0, 0.6501457725947521,
0.1574344023323616])
class TestTriang:
def test_basic(self):
assert_allclose(windows.triang(6, True),
[1/6, 1/2, 5/6, 5/6, 1/2, 1/6])
assert_allclose(windows.triang(7),
[1/4, 1/2, 3/4, 1, 3/4, 1/2, 1/4])
assert_allclose(windows.triang(6, sym=False),
[1/4, 1/2, 3/4, 1, 3/4, 1/2])
tukey_data = {
(4, 0.5, True): array([0.0, 1.0, 1.0, 0.0]),
(4, 0.9, True): array([0.0, 0.84312081893436686,
0.84312081893436686, 0.0]),
(4, 1.0, True): array([0.0, 0.75, 0.75, 0.0]),
(4, 0.5, False): array([0.0, 1.0, 1.0, 1.0]),
(4, 0.9, False): array([0.0, 0.58682408883346526,
1.0, 0.58682408883346526]),
(4, 1.0, False): array([0.0, 0.5, 1.0, 0.5]),
(5, 0.0, True): array([1.0, 1.0, 1.0, 1.0, 1.0]),
(5, 0.8, True): array([0.0, 0.69134171618254492,
1.0, 0.69134171618254492, 0.0]),
(5, 1.0, True): array([0.0, 0.5, 1.0, 0.5, 0.0]),
(6, 0): [1, 1, 1, 1, 1, 1],
(7, 0): [1, 1, 1, 1, 1, 1, 1],
(6, .25): [0, 1, 1, 1, 1, 0],
(7, .25): [0, 1, 1, 1, 1, 1, 0],
(6,): [0, 0.9045084971874737, 1.0, 1.0, 0.9045084971874735, 0],
(7,): [0, 0.75, 1.0, 1.0, 1.0, 0.75, 0],
(6, .75): [0, 0.5522642316338269, 1.0, 1.0, 0.5522642316338267, 0],
(7, .75): [0, 0.4131759111665348, 0.9698463103929542, 1.0,
0.9698463103929542, 0.4131759111665347, 0],
(6, 1): [0, 0.3454915028125263, 0.9045084971874737, 0.9045084971874737,
0.3454915028125263, 0],
(7, 1): [0, 0.25, 0.75, 1.0, 0.75, 0.25, 0],
}
class TestTukey:
def test_basic(self):
# Test against hardcoded data
for k, v in tukey_data.items():
if v is None:
assert_raises(ValueError, windows.tukey, *k)
else:
win = windows.tukey(*k)
assert_allclose(win, v, rtol=1e-15, atol=1e-15)
def test_extremes(self):
# Test extremes of alpha correspond to boxcar and hann
tuk0 = windows.tukey(100, 0)
box0 = windows.boxcar(100)
assert_array_almost_equal(tuk0, box0)
tuk1 = windows.tukey(100, 1)
han1 = windows.hann(100)
assert_array_almost_equal(tuk1, han1)
dpss_data = {
# All values from MATLAB:
# * taper[1] of (3, 1.4, 3) sign-flipped
# * taper[3] of (5, 1.5, 5) sign-flipped
(4, 0.1, 2): ([[0.497943898, 0.502047681, 0.502047681, 0.497943898], [0.670487993, 0.224601537, -0.224601537, -0.670487993]], [0.197961815, 0.002035474]), # noqa: E501
(3, 1.4, 3): ([[0.410233151, 0.814504464, 0.410233151], [0.707106781, 0.0, -0.707106781], [0.575941629, -0.580157287, 0.575941629]], [0.999998093, 0.998067480, 0.801934426]), # noqa: E501
(5, 1.5, 5): ([[0.1745071052, 0.4956749177, 0.669109327, 0.495674917, 0.174507105], [0.4399493348, 0.553574369, 0.0, -0.553574369, -0.439949334], [0.631452756, 0.073280238, -0.437943884, 0.073280238, 0.631452756], [0.553574369, -0.439949334, 0.0, 0.439949334, -0.553574369], [0.266110290, -0.498935248, 0.600414741, -0.498935248, 0.266110290147157]], [0.999728571, 0.983706916, 0.768457889, 0.234159338, 0.013947282907567]), # noqa: E501
(100, 2, 4): ([[0.0030914414, 0.0041266922, 0.005315076, 0.006665149, 0.008184854, 0.0098814158, 0.011761239, 0.013829809, 0.016091597, 0.018549973, 0.02120712, 0.02406396, 0.027120092, 0.030373728, 0.033821651, 0.037459181, 0.041280145, 0.045276872, 0.049440192, 0.053759447, 0.058222524, 0.062815894, 0.067524661, 0.072332638, 0.077222418, 0.082175473, 0.087172252, 0.092192299, 0.097214376, 0.1022166, 0.10717657, 0.11207154, 0.11687856, 0.12157463, 0.12613686, 0.13054266, 0.13476986, 0.13879691, 0.14260302, 0.14616832, 0.14947401, 0.1525025, 0.15523755, 0.15766438, 0.15976981, 0.16154233, 0.16297223, 0.16405162, 0.16477455, 0.16513702, 0.16513702, 0.16477455, 0.16405162, 0.16297223, 0.16154233, 0.15976981, 0.15766438, 0.15523755, 0.1525025, 0.14947401, 0.14616832, 0.14260302, 0.13879691, 0.13476986, 0.13054266, 0.12613686, 0.12157463, 0.11687856, 0.11207154, 0.10717657, 0.1022166, 0.097214376, 0.092192299, 0.087172252, 0.082175473, 0.077222418, 0.072332638, 0.067524661, 0.062815894, 0.058222524, 0.053759447, 0.049440192, 0.045276872, 0.041280145, 0.037459181, 0.033821651, 0.030373728, 0.027120092, 0.02406396, 0.02120712, 0.018549973, 0.016091597, 0.013829809, 0.011761239, 0.0098814158, 0.008184854, 0.006665149, 0.005315076, 0.0041266922, 0.0030914414], [0.018064449, 0.022040342, 0.026325013, 0.030905288, 0.035764398, 0.040881982, 0.046234148, 0.051793558, 0.057529559, 0.063408356, 0.069393216, 0.075444716, 0.081521022, 0.087578202, 0.093570567, 0.099451049, 0.10517159, 0.11068356, 0.11593818, 0.12088699, 0.12548227, 0.12967752, 0.1334279, 0.13669069, 0.13942569, 0.1415957, 0.14316686, 0.14410905, 0.14439626, 0.14400686, 0.14292389, 0.1411353, 0.13863416, 0.13541876, 0.13149274, 0.12686516, 0.12155045, 0.1155684, 0.10894403, 0.10170748, 0.093893752, 0.08554251, 0.076697768, 0.067407559, 0.057723559, 0.04770068, 0.037396627, 0.026871428, 0.016186944, 0.0054063557, -0.0054063557, -0.016186944, -0.026871428, -0.037396627, -0.04770068, -0.057723559, -0.067407559, -0.076697768, -0.08554251, -0.093893752, -0.10170748, -0.10894403, -0.1155684, -0.12155045, -0.12686516, -0.13149274, -0.13541876, -0.13863416, -0.1411353, -0.14292389, -0.14400686, -0.14439626, -0.14410905, -0.14316686, -0.1415957, -0.13942569, -0.13669069, -0.1334279, -0.12967752, -0.12548227, -0.12088699, -0.11593818, -0.11068356, -0.10517159, -0.099451049, -0.093570567, -0.087578202, -0.081521022, -0.075444716, -0.069393216, -0.063408356, -0.057529559, -0.051793558, -0.046234148, -0.040881982, -0.035764398, -0.030905288, -0.026325013, -0.022040342, -0.018064449], [0.064817553, 0.072567801, 0.080292992, 0.087918235, 0.095367076, 0.10256232, 0.10942687, 0.1158846, 0.12186124, 0.12728523, 0.13208858, 0.13620771, 0.13958427, 0.14216587, 0.14390678, 0.14476863, 0.1447209, 0.14374148, 0.14181704, 0.13894336, 0.13512554, 0.13037812, 0.1247251, 0.11819984, 0.11084487, 0.10271159, 0.093859853, 0.084357497, 0.074279719, 0.063708406, 0.052731374, 0.041441525, 0.029935953, 0.018314987, 0.0066811877, -0.0048616765, -0.016209689, -0.027259848, -0.037911124, -0.048065512, -0.05762905, -0.066512804, -0.0746338, -0.081915903, -0.088290621, -0.09369783, -0.098086416, -0.10141482, -0.10365146, -0.10477512, -0.10477512, -0.10365146, -0.10141482, -0.098086416, -0.09369783, -0.088290621, -0.081915903, -0.0746338, -0.066512804, -0.05762905, -0.048065512, -0.037911124, -0.027259848, -0.016209689, -0.0048616765, 0.0066811877, 0.018314987, 0.029935953, 0.041441525, 0.052731374, 0.063708406, 0.074279719, 0.084357497, 0.093859853, 0.10271159, 0.11084487, 0.11819984, 0.1247251, 0.13037812, 0.13512554, 0.13894336, 0.14181704, 0.14374148, 0.1447209, 0.14476863, 0.14390678, 0.14216587, 0.13958427, 0.13620771, 0.13208858, 0.12728523, 0.12186124, 0.1158846, 0.10942687, 0.10256232, 0.095367076, 0.087918235, 0.080292992, 0.072567801, 0.064817553], [0.14985551, 0.15512305, 0.15931467, 0.16236806, 0.16423291, 0.16487165, 0.16426009, 0.1623879, 0.1592589, 0.15489114, 0.14931693, 0.14258255, 0.13474785, 0.1258857, 0.11608124, 0.10543095, 0.094041635, 0.082029213, 0.069517411, 0.056636348, 0.043521028, 0.030309756, 0.017142511, 0.0041592774, -0.0085016282, -0.020705223, -0.032321494, -0.043226982, -0.053306291, -0.062453515, -0.070573544, -0.077583253, -0.083412547, -0.088005244, -0.091319802, -0.093329861, -0.094024602, -0.093408915, -0.091503383, -0.08834406, -0.08398207, -0.078483012, -0.071926192, -0.064403681, -0.056019215, -0.046886954, -0.037130106, -0.026879442, -0.016271713, -0.005448, 0.005448, 0.016271713, 0.026879442, 0.037130106, 0.046886954, 0.056019215, 0.064403681, 0.071926192, 0.078483012, 0.08398207, 0.08834406, 0.091503383, 0.093408915, 0.094024602, 0.093329861, 0.091319802, 0.088005244, 0.083412547, 0.077583253, 0.070573544, 0.062453515, 0.053306291, 0.043226982, 0.032321494, 0.020705223, 0.0085016282, -0.0041592774, -0.017142511, -0.030309756, -0.043521028, -0.056636348, -0.069517411, -0.082029213, -0.094041635, -0.10543095, -0.11608124, -0.1258857, -0.13474785, -0.14258255, -0.14931693, -0.15489114, -0.1592589, -0.1623879, -0.16426009, -0.16487165, -0.16423291, -0.16236806, -0.15931467, -0.15512305, -0.14985551]], [0.999943140, 0.997571533, 0.959465463, 0.721862496]), # noqa: E501
}
class TestDPSS:
def test_basic(self):
# Test against hardcoded data
for k, v in dpss_data.items():
win, ratios = windows.dpss(*k, return_ratios=True)
assert_allclose(win, v[0], atol=1e-7, err_msg=k)
assert_allclose(ratios, v[1], rtol=1e-5, atol=1e-7, err_msg=k)
def test_unity(self):
# Test unity value handling (gh-2221)
for M in range(1, 21):
# corrected w/approximation (default)
win = windows.dpss(M, M / 2.1)
expected = M % 2 # one for odd, none for even
assert_equal(np.isclose(win, 1.).sum(), expected,
err_msg=f'{win}')
# corrected w/subsample delay (slower)
win_sub = windows.dpss(M, M / 2.1, norm='subsample')
if M > 2:
# @M=2 the subsample doesn't do anything
assert_equal(np.isclose(win_sub, 1.).sum(), expected,
err_msg=f'{win_sub}')
assert_allclose(win, win_sub, rtol=0.03) # within 3%
# not the same, l2-norm
win_2 = windows.dpss(M, M / 2.1, norm=2)
expected = 1 if M == 1 else 0
assert_equal(np.isclose(win_2, 1.).sum(), expected,
err_msg=f'{win_2}')
def test_extremes(self):
# Test extremes of alpha
lam = windows.dpss(31, 6, 4, return_ratios=True)[1]
assert_array_almost_equal(lam, 1.)
lam = windows.dpss(31, 7, 4, return_ratios=True)[1]
assert_array_almost_equal(lam, 1.)
lam = windows.dpss(31, 8, 4, return_ratios=True)[1]
assert_array_almost_equal(lam, 1.)
def test_degenerate(self):
# Test failures
assert_raises(ValueError, windows.dpss, 4, 1.5, -1) # Bad Kmax
assert_raises(ValueError, windows.dpss, 4, 1.5, -5)
assert_raises(TypeError, windows.dpss, 4, 1.5, 1.1)
assert_raises(ValueError, windows.dpss, 3, 1.5, 3) # NW must be < N/2.
assert_raises(ValueError, windows.dpss, 3, -1, 3) # NW must be pos
assert_raises(ValueError, windows.dpss, 3, 0, 3)
assert_raises(ValueError, windows.dpss, -1, 1, 3) # negative M
class TestLanczos:
def test_basic(self):
# Analytical results:
# sinc(x) = sinc(-x)
# sinc(pi) = 0, sinc(0) = 1
# Hand computation on WolframAlpha:
# sinc(2 pi / 3) = 0.413496672
# sinc(pi / 3) = 0.826993343
# sinc(3 pi / 5) = 0.504551152
# sinc(pi / 5) = 0.935489284
assert_allclose(windows.lanczos(6, sym=False),
[0., 0.413496672,
0.826993343, 1., 0.826993343,
0.413496672],
atol=1e-9)
assert_allclose(windows.lanczos(6),
[0., 0.504551152,
0.935489284, 0.935489284,
0.504551152, 0.],
atol=1e-9)
assert_allclose(windows.lanczos(7, sym=True),
[0., 0.413496672,
0.826993343, 1., 0.826993343,
0.413496672, 0.],
atol=1e-9)
def test_array_size(self):
for n in [0, 10, 11]:
assert_equal(len(windows.lanczos(n, sym=False)), n)
assert_equal(len(windows.lanczos(n, sym=True)), n)
class TestGetWindow:
def test_boxcar(self):
w = windows.get_window('boxcar', 12)
assert_array_equal(w, np.ones_like(w))
# window is a tuple of len 1
w = windows.get_window(('boxcar',), 16)
assert_array_equal(w, np.ones_like(w))
def test_cheb_odd(self):
with suppress_warnings() as sup:
sup.filter(UserWarning, "This window is not suitable")
w = windows.get_window(('chebwin', -40), 53, fftbins=False)
assert_array_almost_equal(w, cheb_odd_true, decimal=4)
def test_cheb_even(self):
with suppress_warnings() as sup:
sup.filter(UserWarning, "This window is not suitable")
w = windows.get_window(('chebwin', 40), 54, fftbins=False)
assert_array_almost_equal(w, cheb_even_true, decimal=4)
def test_dpss(self):
win1 = windows.get_window(('dpss', 3), 64, fftbins=False)
win2 = windows.dpss(64, 3)
assert_array_almost_equal(win1, win2, decimal=4)
def test_kaiser_float(self):
win1 = windows.get_window(7.2, 64)
win2 = windows.kaiser(64, 7.2, False)
assert_allclose(win1, win2)
def test_invalid_inputs(self):
# Window is not a float, tuple, or string
assert_raises(ValueError, windows.get_window, set('hann'), 8)
# Unknown window type error
assert_raises(ValueError, windows.get_window, 'broken', 4)
def test_array_as_window(self):
# GitHub issue 3603
osfactor = 128
sig = np.arange(128)
win = windows.get_window(('kaiser', 8.0), osfactor // 2)
with assert_raises(ValueError, match='must have the same length'):
resample(sig, len(sig) * osfactor, window=win)
def test_general_cosine(self):
assert_allclose(get_window(('general_cosine', [0.5, 0.3, 0.2]), 4),
[0.4, 0.3, 1, 0.3])
assert_allclose(get_window(('general_cosine', [0.5, 0.3, 0.2]), 4,
fftbins=False),
[0.4, 0.55, 0.55, 0.4])
def test_general_hamming(self):
assert_allclose(get_window(('general_hamming', 0.7), 5),
[0.4, 0.6072949, 0.9427051, 0.9427051, 0.6072949])
assert_allclose(get_window(('general_hamming', 0.7), 5, fftbins=False),
[0.4, 0.7, 1.0, 0.7, 0.4])
def test_lanczos(self):
assert_allclose(get_window('lanczos', 6),
[0., 0.413496672, 0.826993343, 1., 0.826993343,
0.413496672], atol=1e-9)
assert_allclose(get_window('lanczos', 6, fftbins=False),
[0., 0.504551152, 0.935489284, 0.935489284,
0.504551152, 0.], atol=1e-9)
assert_allclose(get_window('lanczos', 6), get_window('sinc', 6))
def test_windowfunc_basics():
for window_name, params in window_funcs:
window = getattr(windows, window_name)
with suppress_warnings() as sup:
sup.filter(UserWarning, "This window is not suitable")
# Check symmetry for odd and even lengths
w1 = window(8, *params, sym=True)
w2 = window(7, *params, sym=False)
assert_array_almost_equal(w1[:-1], w2)
w1 = window(9, *params, sym=True)
w2 = window(8, *params, sym=False)
assert_array_almost_equal(w1[:-1], w2)
# Check that functions run and output lengths are correct
assert_equal(len(window(6, *params, sym=True)), 6)
assert_equal(len(window(6, *params, sym=False)), 6)
assert_equal(len(window(7, *params, sym=True)), 7)
assert_equal(len(window(7, *params, sym=False)), 7)
# Check invalid lengths
assert_raises(ValueError, window, 5.5, *params)
assert_raises(ValueError, window, -7, *params)
# Check degenerate cases
assert_array_equal(window(0, *params, sym=True), [])
assert_array_equal(window(0, *params, sym=False), [])
assert_array_equal(window(1, *params, sym=True), [1])
assert_array_equal(window(1, *params, sym=False), [1])
# Check dtype
assert_(window(0, *params, sym=True).dtype == 'float')
assert_(window(0, *params, sym=False).dtype == 'float')
assert_(window(1, *params, sym=True).dtype == 'float')
assert_(window(1, *params, sym=False).dtype == 'float')
assert_(window(6, *params, sym=True).dtype == 'float')
assert_(window(6, *params, sym=False).dtype == 'float')
# Check normalization
assert_array_less(window(10, *params, sym=True), 1.01)
assert_array_less(window(10, *params, sym=False), 1.01)
assert_array_less(window(9, *params, sym=True), 1.01)
assert_array_less(window(9, *params, sym=False), 1.01)
# Check that DFT-even spectrum is purely real for odd and even
assert_allclose(fft(window(10, *params, sym=False)).imag,
0, atol=1e-14)
assert_allclose(fft(window(11, *params, sym=False)).imag,
0, atol=1e-14)
def test_needs_params():
for winstr in ['kaiser', 'ksr', 'kaiser_bessel_derived', 'kbd',
'gaussian', 'gauss', 'gss',
'general gaussian', 'general_gaussian',
'general gauss', 'general_gauss', 'ggs',
'dss', 'dpss', 'general cosine', 'general_cosine',
'chebwin', 'cheb', 'general hamming', 'general_hamming',
]:
assert_raises(ValueError, get_window, winstr, 7)
def test_not_needs_params():
for winstr in ['barthann',
'bartlett',
'blackman',
'blackmanharris',
'bohman',
'boxcar',
'cosine',
'flattop',
'hamming',
'nuttall',
'parzen',
'taylor',
'exponential',
'poisson',
'tukey',
'tuk',
'triangle',
'lanczos',
'sinc',
]:
win = get_window(winstr, 7)
assert_equal(len(win), 7)
def test_symmetric():
for win in [windows.lanczos]:
# Even sampling points
w = win(4096)
error = np.max(np.abs(w-np.flip(w)))
assert_equal(error, 0.0)
# Odd sampling points
w = win(4097)
error = np.max(np.abs(w-np.flip(w)))
assert_equal(error, 0.0)
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