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import numpy as np |
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from numpy import array |
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from numpy.testing import (assert_array_almost_equal, assert_array_equal, |
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assert_allclose, |
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assert_equal, assert_, assert_array_less, |
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suppress_warnings) |
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from pytest import raises as assert_raises |
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from scipy.fft import fft |
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from scipy.signal import windows, get_window, resample |
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window_funcs = [ |
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('boxcar', ()), |
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('triang', ()), |
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('parzen', ()), |
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('bohman', ()), |
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('blackman', ()), |
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('nuttall', ()), |
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('blackmanharris', ()), |
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('flattop', ()), |
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('bartlett', ()), |
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('barthann', ()), |
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('hamming', ()), |
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('kaiser', (1,)), |
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('dpss', (2,)), |
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('gaussian', (0.5,)), |
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('general_gaussian', (1.5, 2)), |
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('chebwin', (1,)), |
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('cosine', ()), |
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('hann', ()), |
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('exponential', ()), |
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('taylor', ()), |
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('tukey', (0.5,)), |
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('lanczos', ()), |
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] |
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class TestBartHann: |
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def test_basic(self): |
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assert_allclose(windows.barthann(6, sym=True), |
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[0, 0.35857354213752, 0.8794264578624801, |
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0.8794264578624801, 0.3585735421375199, 0], |
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rtol=1e-15, atol=1e-15) |
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assert_allclose(windows.barthann(7), |
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[0, 0.27, 0.73, 1.0, 0.73, 0.27, 0], |
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rtol=1e-15, atol=1e-15) |
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assert_allclose(windows.barthann(6, False), |
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[0, 0.27, 0.73, 1.0, 0.73, 0.27], |
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rtol=1e-15, atol=1e-15) |
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class TestBartlett: |
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def test_basic(self): |
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assert_allclose(windows.bartlett(6), [0, 0.4, 0.8, 0.8, 0.4, 0]) |
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assert_allclose(windows.bartlett(7), [0, 1/3, 2/3, 1.0, 2/3, 1/3, 0]) |
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assert_allclose(windows.bartlett(6, False), |
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[0, 1/3, 2/3, 1.0, 2/3, 1/3]) |
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class TestBlackman: |
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def test_basic(self): |
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assert_allclose(windows.blackman(6, sym=False), |
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[0, 0.13, 0.63, 1.0, 0.63, 0.13], atol=1e-14) |
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assert_allclose(windows.blackman(7, sym=False), |
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[0, 0.09045342435412804, 0.4591829575459636, |
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0.9203636180999081, 0.9203636180999081, |
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0.4591829575459636, 0.09045342435412804], atol=1e-8) |
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assert_allclose(windows.blackman(6), |
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[0, 0.2007701432625305, 0.8492298567374694, |
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0.8492298567374694, 0.2007701432625305, 0], |
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atol=1e-14) |
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assert_allclose(windows.blackman(7, True), |
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[0, 0.13, 0.63, 1.0, 0.63, 0.13, 0], atol=1e-14) |
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class TestBlackmanHarris: |
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def test_basic(self): |
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assert_allclose(windows.blackmanharris(6, False), |
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[6.0e-05, 0.055645, 0.520575, 1.0, 0.520575, 0.055645]) |
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assert_allclose(windows.blackmanharris(7, sym=False), |
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[6.0e-05, 0.03339172347815117, 0.332833504298565, |
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0.8893697722232837, 0.8893697722232838, |
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0.3328335042985652, 0.03339172347815122]) |
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assert_allclose(windows.blackmanharris(6), |
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[6.0e-05, 0.1030114893456638, 0.7938335106543362, |
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0.7938335106543364, 0.1030114893456638, 6.0e-05]) |
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assert_allclose(windows.blackmanharris(7, sym=True), |
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[6.0e-05, 0.055645, 0.520575, 1.0, 0.520575, 0.055645, |
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6.0e-05]) |
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class TestTaylor: |
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def test_normalized(self): |
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"""Tests windows of small length that are normalized to 1. See the |
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documentation for the Taylor window for more information on |
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normalization. |
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""" |
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assert_allclose(windows.taylor(1, 2, 15), 1.0) |
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assert_allclose( |
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windows.taylor(5, 2, 15), |
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np.array([0.75803341, 0.90757699, 1.0, 0.90757699, 0.75803341]) |
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) |
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assert_allclose( |
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windows.taylor(6, 2, 15), |
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np.array([ |
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0.7504082, 0.86624416, 0.98208011, 0.98208011, 0.86624416, |
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0.7504082 |
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]) |
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) |
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def test_non_normalized(self): |
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"""Test windows of small length that are not normalized to 1. See |
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the documentation for the Taylor window for more information on |
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normalization. |
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""" |
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assert_allclose( |
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windows.taylor(5, 2, 15, norm=False), |
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np.array([ |
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0.87508054, 1.04771499, 1.15440894, 1.04771499, 0.87508054 |
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]) |
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) |
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assert_allclose( |
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windows.taylor(6, 2, 15, norm=False), |
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np.array([ |
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0.86627793, 1.0, 1.13372207, 1.13372207, 1.0, 0.86627793 |
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]) |
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) |
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def test_correctness(self): |
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"""This test ensures the correctness of the implemented Taylor |
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Windowing function. A Taylor Window of 1024 points is created, its FFT |
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is taken, and the Peak Sidelobe Level (PSLL) and 3dB and 18dB bandwidth |
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are found and checked. |
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A publication from Sandia National Laboratories was used as reference |
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for the correctness values [1]_. |
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References |
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----- |
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.. [1] Armin Doerry, "Catalog of Window Taper Functions for |
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Sidelobe Control", 2017. |
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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 |
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""" |
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M_win = 1024 |
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N_fft = 131072 |
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w = windows.taylor(M_win, nbar=4, sll=35, norm=False, sym=False) |
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f = fft(w, N_fft) |
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spec = 20 * np.log10(np.abs(f / np.amax(f))) |
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first_zero = np.argmax(np.diff(spec) > 0) |
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PSLL = np.amax(spec[first_zero:-first_zero]) |
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BW_3dB = 2*np.argmax(spec <= -3.0102999566398121) / N_fft * M_win |
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BW_18dB = 2*np.argmax(spec <= -18.061799739838872) / N_fft * M_win |
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assert_allclose(PSLL, -35.1672, atol=1) |
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assert_allclose(BW_3dB, 1.1822, atol=0.1) |
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assert_allclose(BW_18dB, 2.6112, atol=0.1) |
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class TestBohman: |
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def test_basic(self): |
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assert_allclose(windows.bohman(6), |
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[0, 0.1791238937062839, 0.8343114522576858, |
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0.8343114522576858, 0.1791238937062838, 0]) |
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assert_allclose(windows.bohman(7, sym=True), |
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[0, 0.1089977810442293, 0.6089977810442293, 1.0, |
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0.6089977810442295, 0.1089977810442293, 0]) |
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assert_allclose(windows.bohman(6, False), |
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[0, 0.1089977810442293, 0.6089977810442293, 1.0, |
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0.6089977810442295, 0.1089977810442293]) |
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class TestBoxcar: |
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def test_basic(self): |
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assert_allclose(windows.boxcar(6), [1, 1, 1, 1, 1, 1]) |
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assert_allclose(windows.boxcar(7), [1, 1, 1, 1, 1, 1, 1]) |
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assert_allclose(windows.boxcar(6, False), [1, 1, 1, 1, 1, 1]) |
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cheb_odd_true = array([0.200938, 0.107729, 0.134941, 0.165348, |
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0.198891, 0.235450, 0.274846, 0.316836, |
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0.361119, 0.407338, 0.455079, 0.503883, |
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0.553248, 0.602637, 0.651489, 0.699227, |
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0.745266, 0.789028, 0.829947, 0.867485, |
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0.901138, 0.930448, 0.955010, 0.974482, |
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0.988591, 0.997138, 1.000000, 0.997138, |
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0.988591, 0.974482, 0.955010, 0.930448, |
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0.901138, 0.867485, 0.829947, 0.789028, |
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0.745266, 0.699227, 0.651489, 0.602637, |
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0.553248, 0.503883, 0.455079, 0.407338, |
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0.361119, 0.316836, 0.274846, 0.235450, |
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0.198891, 0.165348, 0.134941, 0.107729, |
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0.200938]) |
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cheb_even_true = array([0.203894, 0.107279, 0.133904, |
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0.163608, 0.196338, 0.231986, |
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0.270385, 0.311313, 0.354493, |
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0.399594, 0.446233, 0.493983, |
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0.542378, 0.590916, 0.639071, |
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0.686302, 0.732055, 0.775783, |
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0.816944, 0.855021, 0.889525, |
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0.920006, 0.946060, 0.967339, |
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0.983557, 0.994494, 1.000000, |
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1.000000, 0.994494, 0.983557, |
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0.967339, 0.946060, 0.920006, |
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0.889525, 0.855021, 0.816944, |
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0.775783, 0.732055, 0.686302, |
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0.639071, 0.590916, 0.542378, |
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0.493983, 0.446233, 0.399594, |
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0.354493, 0.311313, 0.270385, |
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0.231986, 0.196338, 0.163608, |
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0.133904, 0.107279, 0.203894]) |
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class TestChebWin: |
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def test_basic(self): |
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with suppress_warnings() as sup: |
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sup.filter(UserWarning, "This window is not suitable") |
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assert_allclose(windows.chebwin(6, 100), |
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[0.1046401879356917, 0.5075781475823447, 1.0, 1.0, |
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0.5075781475823447, 0.1046401879356917]) |
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assert_allclose(windows.chebwin(7, 100), |
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[0.05650405062850233, 0.316608530648474, |
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0.7601208123539079, 1.0, 0.7601208123539079, |
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0.316608530648474, 0.05650405062850233]) |
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assert_allclose(windows.chebwin(6, 10), |
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[1.0, 0.6071201674458373, 0.6808391469897297, |
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0.6808391469897297, 0.6071201674458373, 1.0]) |
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assert_allclose(windows.chebwin(7, 10), |
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[1.0, 0.5190521247588651, 0.5864059018130382, |
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0.6101519801307441, 0.5864059018130382, |
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0.5190521247588651, 1.0]) |
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assert_allclose(windows.chebwin(6, 10, False), |
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[1.0, 0.5190521247588651, 0.5864059018130382, |
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0.6101519801307441, 0.5864059018130382, |
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0.5190521247588651]) |
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def test_cheb_odd_high_attenuation(self): |
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with suppress_warnings() as sup: |
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sup.filter(UserWarning, "This window is not suitable") |
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cheb_odd = windows.chebwin(53, at=-40) |
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assert_array_almost_equal(cheb_odd, cheb_odd_true, decimal=4) |
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def test_cheb_even_high_attenuation(self): |
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with suppress_warnings() as sup: |
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sup.filter(UserWarning, "This window is not suitable") |
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cheb_even = windows.chebwin(54, at=40) |
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assert_array_almost_equal(cheb_even, cheb_even_true, decimal=4) |
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def test_cheb_odd_low_attenuation(self): |
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cheb_odd_low_at_true = array([1.000000, 0.519052, 0.586405, |
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0.610151, 0.586405, 0.519052, |
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1.000000]) |
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with suppress_warnings() as sup: |
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sup.filter(UserWarning, "This window is not suitable") |
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cheb_odd = windows.chebwin(7, at=10) |
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assert_array_almost_equal(cheb_odd, cheb_odd_low_at_true, decimal=4) |
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def test_cheb_even_low_attenuation(self): |
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cheb_even_low_at_true = array([1.000000, 0.451924, 0.51027, |
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0.541338, 0.541338, 0.51027, |
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0.451924, 1.000000]) |
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with suppress_warnings() as sup: |
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sup.filter(UserWarning, "This window is not suitable") |
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cheb_even = windows.chebwin(8, at=-10) |
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assert_array_almost_equal(cheb_even, cheb_even_low_at_true, decimal=4) |
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exponential_data = { |
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(4, None, 0.2, False): |
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array([4.53999297624848542e-05, |
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6.73794699908546700e-03, 1.00000000000000000e+00, |
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6.73794699908546700e-03]), |
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(4, None, 0.2, True): array([0.00055308437014783, 0.0820849986238988, |
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0.0820849986238988, 0.00055308437014783]), |
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(4, None, 1.0, False): array([0.1353352832366127, 0.36787944117144233, 1., |
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0.36787944117144233]), |
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(4, None, 1.0, True): array([0.22313016014842982, 0.60653065971263342, |
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0.60653065971263342, 0.22313016014842982]), |
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(4, 2, 0.2, False): |
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array([4.53999297624848542e-05, 6.73794699908546700e-03, |
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1.00000000000000000e+00, 6.73794699908546700e-03]), |
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(4, 2, 0.2, True): None, |
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(4, 2, 1.0, False): array([0.1353352832366127, 0.36787944117144233, 1., |
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0.36787944117144233]), |
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(4, 2, 1.0, True): None, |
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(5, None, 0.2, True): |
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array([4.53999297624848542e-05, |
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6.73794699908546700e-03, 1.00000000000000000e+00, |
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6.73794699908546700e-03, 4.53999297624848542e-05]), |
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(5, None, 1.0, True): array([0.1353352832366127, 0.36787944117144233, 1., |
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0.36787944117144233, 0.1353352832366127]), |
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(5, 2, 0.2, True): None, |
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(5, 2, 1.0, True): None |
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} |
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def test_exponential(): |
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for k, v in exponential_data.items(): |
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if v is None: |
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assert_raises(ValueError, windows.exponential, *k) |
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else: |
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win = windows.exponential(*k) |
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assert_allclose(win, v, rtol=1e-14) |
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class TestFlatTop: |
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def test_basic(self): |
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assert_allclose(windows.flattop(6, sym=False), |
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[-0.000421051, -0.051263156, 0.19821053, 1.0, |
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0.19821053, -0.051263156]) |
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assert_allclose(windows.flattop(7, sym=False), |
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[-0.000421051, -0.03684078115492348, |
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0.01070371671615342, 0.7808739149387698, |
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0.7808739149387698, 0.01070371671615342, |
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-0.03684078115492348]) |
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assert_allclose(windows.flattop(6), |
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[-0.000421051, -0.0677142520762119, 0.6068721525762117, |
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0.6068721525762117, -0.0677142520762119, |
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-0.000421051]) |
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assert_allclose(windows.flattop(7, True), |
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[-0.000421051, -0.051263156, 0.19821053, 1.0, |
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0.19821053, -0.051263156, -0.000421051]) |
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class TestGaussian: |
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def test_basic(self): |
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assert_allclose(windows.gaussian(6, 1.0), |
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[0.04393693362340742, 0.3246524673583497, |
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0.8824969025845955, 0.8824969025845955, |
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0.3246524673583497, 0.04393693362340742]) |
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assert_allclose(windows.gaussian(7, 1.2), |
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[0.04393693362340742, 0.2493522087772962, |
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0.7066482778577162, 1.0, 0.7066482778577162, |
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0.2493522087772962, 0.04393693362340742]) |
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assert_allclose(windows.gaussian(7, 3), |
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[0.6065306597126334, 0.8007374029168081, |
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0.9459594689067654, 1.0, 0.9459594689067654, |
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0.8007374029168081, 0.6065306597126334]) |
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assert_allclose(windows.gaussian(6, 3, False), |
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[0.6065306597126334, 0.8007374029168081, |
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0.9459594689067654, 1.0, 0.9459594689067654, |
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0.8007374029168081]) |
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class TestGeneralCosine: |
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def test_basic(self): |
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assert_allclose(windows.general_cosine(5, [0.5, 0.3, 0.2]), |
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[0.4, 0.3, 1, 0.3, 0.4]) |
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assert_allclose(windows.general_cosine(4, [0.5, 0.3, 0.2], sym=False), |
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[0.4, 0.3, 1, 0.3]) |
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class TestGeneralHamming: |
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def test_basic(self): |
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assert_allclose(windows.general_hamming(5, 0.7), |
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|
[0.4, 0.7, 1.0, 0.7, 0.4]) |
|
|
assert_allclose(windows.general_hamming(5, 0.75, sym=False), |
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|
[0.5, 0.6727457514, 0.9522542486, |
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|
0.9522542486, 0.6727457514]) |
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assert_allclose(windows.general_hamming(6, 0.75, sym=True), |
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|
[0.5, 0.6727457514, 0.9522542486, |
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|
0.9522542486, 0.6727457514, 0.5]) |
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|
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class TestHamming: |
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|
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def test_basic(self): |
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assert_allclose(windows.hamming(6, False), |
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|
[0.08, 0.31, 0.77, 1.0, 0.77, 0.31]) |
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|
assert_allclose(windows.hamming(7, sym=False), |
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|
[0.08, 0.2531946911449826, 0.6423596296199047, |
|
|
0.9544456792351128, 0.9544456792351128, |
|
|
0.6423596296199047, 0.2531946911449826]) |
|
|
assert_allclose(windows.hamming(6), |
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|
[0.08, 0.3978521825875242, 0.9121478174124757, |
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|
0.9121478174124757, 0.3978521825875242, 0.08]) |
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assert_allclose(windows.hamming(7, sym=True), |
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[0.08, 0.31, 0.77, 1.0, 0.77, 0.31, 0.08]) |
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class TestHann: |
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|
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def test_basic(self): |
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assert_allclose(windows.hann(6, sym=False), |
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[0, 0.25, 0.75, 1.0, 0.75, 0.25], |
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|
rtol=1e-15, atol=1e-15) |
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|
assert_allclose(windows.hann(7, sym=False), |
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|
[0, 0.1882550990706332, 0.6112604669781572, |
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|
0.9504844339512095, 0.9504844339512095, |
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0.6112604669781572, 0.1882550990706332], |
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rtol=1e-15, atol=1e-15) |
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assert_allclose(windows.hann(6, True), |
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|
[0, 0.3454915028125263, 0.9045084971874737, |
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|
0.9045084971874737, 0.3454915028125263, 0], |
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|
rtol=1e-15, atol=1e-15) |
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assert_allclose(windows.hann(7), |
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|
[0, 0.25, 0.75, 1.0, 0.75, 0.25, 0], |
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rtol=1e-15, atol=1e-15) |
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class TestKaiser: |
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|
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def test_basic(self): |
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assert_allclose(windows.kaiser(6, 0.5), |
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[0.9403061933191572, 0.9782962393705389, |
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|
0.9975765035372042, 0.9975765035372042, |
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|
0.9782962393705389, 0.9403061933191572]) |
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assert_allclose(windows.kaiser(7, 0.5), |
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|
[0.9403061933191572, 0.9732402256999829, |
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|
0.9932754654413773, 1.0, 0.9932754654413773, |
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|
0.9732402256999829, 0.9403061933191572]) |
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assert_allclose(windows.kaiser(6, 2.7), |
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|
[0.2603047507678832, 0.6648106293528054, |
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|
0.9582099802511439, 0.9582099802511439, |
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|
0.6648106293528054, 0.2603047507678832]) |
|
|
assert_allclose(windows.kaiser(7, 2.7), |
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|
[0.2603047507678832, 0.5985765418119844, |
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|
0.8868495172060835, 1.0, 0.8868495172060835, |
|
|
0.5985765418119844, 0.2603047507678832]) |
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|
assert_allclose(windows.kaiser(6, 2.7, False), |
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|
[0.2603047507678832, 0.5985765418119844, |
|
|
0.8868495172060835, 1.0, 0.8868495172060835, |
|
|
0.5985765418119844]) |
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class TestKaiserBesselDerived: |
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|
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def test_basic(self): |
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M = 100 |
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w = windows.kaiser_bessel_derived(M, beta=4.0) |
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|
w2 = windows.get_window(('kaiser bessel derived', 4.0), |
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M, fftbins=False) |
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|
assert_allclose(w, w2) |
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assert_allclose(w[:M // 2] ** 2 + w[-M // 2:] ** 2, 1.) |
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assert_allclose(windows.kaiser_bessel_derived(2, beta=np.pi / 2)[:1], |
|
|
np.sqrt(2) / 2) |
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assert_allclose(windows.kaiser_bessel_derived(4, beta=np.pi / 2)[:2], |
|
|
[0.518562710536, 0.855039598640]) |
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|
|
assert_allclose(windows.kaiser_bessel_derived(6, beta=np.pi / 2)[:3], |
|
|
[0.436168993154, 0.707106781187, 0.899864772847]) |
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|
|
|
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def test_exceptions(self): |
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|
M = 100 |
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|
|
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msg = ("Kaiser-Bessel Derived windows are only defined for even " |
|
|
"number of points") |
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|
with assert_raises(ValueError, match=msg): |
|
|
windows.kaiser_bessel_derived(M + 1, beta=4.) |
|
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|
|
|
|
|
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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) |
|
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|
|
|
|
|
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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): |
|
|
|
|
|
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): |
|
|
|
|
|
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 = { |
|
|
|
|
|
|
|
|
|
|
|
(4, 0.1, 2): ([[0.497943898, 0.502047681, 0.502047681, 0.497943898], [0.670487993, 0.224601537, -0.224601537, -0.670487993]], [0.197961815, 0.002035474]), |
|
|
(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]), |
|
|
(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]), |
|
|
(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]), |
|
|
} |
|
|
|
|
|
|
|
|
class TestDPSS: |
|
|
|
|
|
def test_basic(self): |
|
|
|
|
|
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) |
|
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assert_allclose(ratios, v[1], rtol=1e-5, atol=1e-7, err_msg=k) |
|
|
|
|
|
def test_unity(self): |
|
|
|
|
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for M in range(1, 21): |
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|
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|
win = windows.dpss(M, M / 2.1) |
|
|
expected = M % 2 |
|
|
assert_equal(np.isclose(win, 1.).sum(), expected, |
|
|
err_msg=f'{win}') |
|
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|
|
|
win_sub = windows.dpss(M, M / 2.1, norm='subsample') |
|
|
if M > 2: |
|
|
|
|
|
assert_equal(np.isclose(win_sub, 1.).sum(), expected, |
|
|
err_msg=f'{win_sub}') |
|
|
assert_allclose(win, win_sub, rtol=0.03) |
|
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|
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|
win_2 = windows.dpss(M, M / 2.1, norm=2) |
|
|
expected = 1 if M == 1 else 0 |
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assert_equal(np.isclose(win_2, 1.).sum(), expected, |
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|
err_msg=f'{win_2}') |
|
|
|
|
|
def test_extremes(self): |
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|
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lam = windows.dpss(31, 6, 4, return_ratios=True)[1] |
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assert_array_almost_equal(lam, 1.) |
|
|
lam = windows.dpss(31, 7, 4, return_ratios=True)[1] |
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|
assert_array_almost_equal(lam, 1.) |
|
|
lam = windows.dpss(31, 8, 4, return_ratios=True)[1] |
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assert_array_almost_equal(lam, 1.) |
|
|
|
|
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def test_degenerate(self): |
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|
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assert_raises(ValueError, windows.dpss, 4, 1.5, -1) |
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|
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) |
|
|
assert_raises(ValueError, windows.dpss, 3, -1, 3) |
|
|
assert_raises(ValueError, windows.dpss, 3, 0, 3) |
|
|
assert_raises(ValueError, windows.dpss, -1, 1, 3) |
|
|
|
|
|
|
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|
class TestLanczos: |
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|
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def test_basic(self): |
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
assert_allclose(windows.lanczos(6, sym=False), |
|
|
[0., 0.413496672, |
|
|
0.826993343, 1., 0.826993343, |
|
|
0.413496672], |
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|
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]: |
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|
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)) |
|
|
|
|
|
|
|
|
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): |
|
|
|
|
|
assert_raises(ValueError, windows.get_window, set('hann'), 8) |
|
|
|
|
|
|
|
|
assert_raises(ValueError, windows.get_window, 'broken', 4) |
|
|
|
|
|
def test_array_as_window(self): |
|
|
|
|
|
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") |
|
|
|
|
|
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) |
|
|
|
|
|
|
|
|
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) |
|
|
|
|
|
|
|
|
assert_raises(ValueError, window, 5.5, *params) |
|
|
assert_raises(ValueError, window, -7, *params) |
|
|
|
|
|
|
|
|
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]) |
|
|
|
|
|
|
|
|
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') |
|
|
|
|
|
|
|
|
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) |
|
|
|
|
|
|
|
|
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]: |
|
|
|
|
|
w = win(4096) |
|
|
error = np.max(np.abs(w-np.flip(w))) |
|
|
assert_equal(error, 0.0) |
|
|
|
|
|
|
|
|
w = win(4097) |
|
|
error = np.max(np.abs(w-np.flip(w))) |
|
|
assert_equal(error, 0.0) |
|
|
|
