image-match/python/py/Lib/site-packages/scipy/signal/tests/test_windows.py

import math
import warnings

import numpy as np
from numpy import array
import pytest
from pytest import raises as assert_raises

from scipy.fft import fft
from scipy.signal import windows, get_window, resample
from scipy.signal.windows._windows import _WIN_FUNC_DATA, _WIN_FUNCS
from scipy._lib._array_api import (
    xp_assert_close, xp_assert_equal, array_namespace, is_torch, is_jax, is_cupy,
    assert_array_almost_equal, SCIPY_DEVICE, is_numpy, make_xp_test_case,
    make_xp_pytest_param, _xp_copy_to_numpy
)

skip_xp_backends = pytest.mark.skip_xp_backends
xfail_xp_backends = pytest.mark.xfail_xp_backends

lazy_xp_modules = [windows]


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', ()),
    ]


@make_xp_test_case(windows.barthann)
class TestBartHann:

    def test_basic(self, xp):
        xp_assert_close(windows.barthann(6, sym=True, xp=xp),
                        xp.asarray([0, 0.35857354213752, 0.8794264578624801,
                         0.8794264578624801, 0.3585735421375199, 0], dtype=xp.float64),
                        rtol=1e-15, atol=1e-15)
        xp_assert_close(windows.barthann(7, xp=xp),
                        xp.asarray([0, 0.27, 0.73, 1.0, 0.73, 0.27, 0],
                                   dtype=xp.float64),
                        rtol=1e-15, atol=1e-15)
        xp_assert_close(windows.barthann(6, False, xp=xp),
                        xp.asarray([0, 0.27, 0.73, 1.0, 0.73, 0.27], dtype=xp.float64),
                        rtol=1e-15, atol=1e-15)


@make_xp_test_case(windows.bartlett)
class TestBartlett:

    def test_basic(self, xp):
        xp_assert_close(windows.bartlett(6, xp=xp),
                        xp.asarray([0, 0.4, 0.8, 0.8, 0.4, 0], dtype=xp.float64))
        xp_assert_close(windows.bartlett(7, xp=xp),
                        xp.asarray([0, 1/3, 2/3, 1.0, 2/3, 1/3, 0], dtype=xp.float64))
        xp_assert_close(windows.bartlett(6, False, xp=xp),
                        xp.asarray([0, 1/3, 2/3, 1.0, 2/3, 1/3], dtype=xp.float64))


@make_xp_test_case(windows.blackman)
class TestBlackman:

    def test_basic(self, xp):
        xp_assert_close(windows.blackman(6, sym=False, xp=xp),
                        xp.asarray([0, 0.13, 0.63, 1.0, 0.63, 0.13], dtype=xp.float64),
                        atol=1e-14)
        xp_assert_close(windows.blackman(7, sym=False, xp=xp),
                        xp.asarray([0, 0.09045342435412804, 0.4591829575459636,
                                    0.9203636180999081, 0.9203636180999081,
                                    0.4591829575459636, 0.09045342435412804],
                                    dtype=xp.float64),
                        atol=1e-8)
        xp_assert_close(windows.blackman(6, xp=xp),
                        xp.asarray([0, 0.2007701432625305, 0.8492298567374694,
                                    0.8492298567374694, 0.2007701432625305, 0],
                                    dtype=xp.float64),
                        atol=1e-14)
        xp_assert_close(windows.blackman(7, True, xp=xp),
                        xp.asarray([0, 0.13, 0.63, 1.0, 0.63, 0.13, 0],
                        dtype=xp.float64), atol=1e-14)


@make_xp_test_case(windows.blackmanharris)
class TestBlackmanHarris:

    def test_basic(self, xp):
        xp_assert_close(windows.blackmanharris(6, False, xp=xp),
                        xp.asarray([6.0e-05, 0.055645, 0.520575,
                                    1.0, 0.520575, 0.055645], dtype=xp.float64))
        xp_assert_close(windows.blackmanharris(7, sym=False, xp=xp),
                        xp.asarray([6.0e-05, 0.03339172347815117, 0.332833504298565,
                                    0.8893697722232837, 0.8893697722232838,
                                    0.3328335042985652, 0.03339172347815122],
                                    dtype=xp.float64))
        xp_assert_close(windows.blackmanharris(6, xp=xp),
                        xp.asarray([6.0e-05, 0.1030114893456638, 0.7938335106543362,
                                    0.7938335106543364, 0.1030114893456638, 6.0e-05],
                                    dtype=xp.float64))
        xp_assert_close(windows.blackmanharris(7, sym=True, xp=xp),
                        xp.asarray([6.0e-05, 0.055645, 0.520575, 1.0, 0.520575,
                                    0.055645, 6.0e-05], dtype=xp.float64))


@make_xp_test_case(windows.taylor)
class TestTaylor:

    def test_normalized(self, xp):
        """Tests windows of small length that are normalized to 1. See the
        documentation for the Taylor window for more information on
        normalization.
        """
        xp_assert_close(windows.taylor(1, 2, 15, xp=xp),
                        xp.asarray([1.0], dtype=xp.float64))
        xp_assert_close(
            windows.taylor(5, 2, 15, xp=xp),
            xp.asarray([0.75803341, 0.90757699, 1.0, 0.90757699, 0.75803341],
                       dtype=xp.float64)
        )
        xp_assert_close(
            windows.taylor(6, 2, 15, xp=xp),
            xp.asarray([
                0.7504082, 0.86624416, 0.98208011, 0.98208011, 0.86624416,
                0.7504082
            ], dtype=xp.float64)
        )

    def test_non_normalized(self, xp):
        """Test windows of small length that are not normalized to 1. See
        the documentation for the Taylor window for more information on
        normalization.
        """
        xp_assert_close(
            windows.taylor(5, 2, 15, norm=False, xp=xp),
            xp.asarray([
                0.87508054, 1.04771499, 1.15440894, 1.04771499, 0.87508054
            ], dtype=xp.float64)
        )
        xp_assert_close(
            windows.taylor(6, 2, 15, norm=False, xp=xp),
            xp.asarray([
                0.86627793, 1.0, 1.13372207, 1.13372207, 1.0, 0.86627793
            ], dtype=xp.float64)
        )

    def test_correctness(self, xp):
        """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, xp=xp)
        f_np = fft(_xp_copy_to_numpy(w), N_fft)

        spec = 20 * np.log10(np.abs(f_np / np.max(f_np)))

        first_zero = np.argmax(np.diff(spec) > 0)

        PSLL = np.max(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 math.isclose(PSLL, -35.1672, abs_tol=1)
        assert math.isclose(BW_3dB, 1.1822, abs_tol=0.1)
        assert math.isclose(BW_18dB, 2.6112, abs_tol=0.1)


@make_xp_test_case(windows.bohman)
class TestBohman:

    def test_basic(self, xp):
        xp_assert_close(windows.bohman(6, xp=xp),
                        xp.asarray([0, 0.1791238937062839, 0.8343114522576858,
                                    0.8343114522576858, 0.1791238937062838, 0],
                                    dtype=xp.float64))
        xp_assert_close(windows.bohman(7, sym=True, xp=xp),
                        xp.asarray([0, 0.1089977810442293, 0.6089977810442293, 1.0,
                                    0.6089977810442295, 0.1089977810442293, 0],
                                    dtype=xp.float64))
        xp_assert_close(windows.bohman(6, False, xp=xp),
                        xp.asarray([0, 0.1089977810442293, 0.6089977810442293, 1.0,
                                    0.6089977810442295, 0.1089977810442293],
                                    dtype=xp.float64))


@make_xp_test_case(windows.boxcar)
class TestBoxcar:

    def test_basic(self, xp):
        xp_assert_close(windows.boxcar(6, xp=xp),
                        xp.asarray([1.0, 1, 1, 1, 1, 1], dtype=xp.float64))
        xp_assert_close(windows.boxcar(7, xp=xp),
                        xp.asarray([1.0, 1, 1, 1, 1, 1, 1], dtype=xp.float64))
        xp_assert_close(windows.boxcar(6, False, xp=xp),
                        xp.asarray([1.0, 1, 1, 1, 1, 1], dtype=xp.float64))


cheb_odd_true = [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 = [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]


@make_xp_test_case(windows.chebwin)
class TestChebWin:

    def test_basic(self, xp):
        with warnings.catch_warnings():
            warnings.filterwarnings(
                "ignore", "This window is not suitable", UserWarning)
            xp_assert_close(windows.chebwin(6, 100, xp=xp),
                            xp.asarray([0.1046401879356917, 0.5075781475823447,
                                        1.0, 1.0,
                                        0.5075781475823447, 0.1046401879356917],
                                        dtype=xp.float64),
                            atol=1e-8
            )
            xp_assert_close(windows.chebwin(7, 100, xp=xp),
                            xp.asarray([0.05650405062850233, 0.316608530648474,
                                        0.7601208123539079, 1.0, 0.7601208123539079,
                                        0.316608530648474, 0.05650405062850233],
                                        dtype=xp.float64))
            xp_assert_close(windows.chebwin(6, 10, xp=xp),
                            xp.asarray([1.0, 0.6071201674458373, 0.6808391469897297,
                                        0.6808391469897297, 0.6071201674458373, 1.0],
                                        dtype=xp.float64))
            xp_assert_close(windows.chebwin(7, 10, xp=xp),
                            xp.asarray([1.0, 0.5190521247588651, 0.5864059018130382,
                                        0.6101519801307441, 0.5864059018130382,
                                        0.5190521247588651, 1.0], dtype=xp.float64))
            xp_assert_close(windows.chebwin(6, 10, False, xp=xp),
                            xp.asarray([1.0, 0.5190521247588651, 0.5864059018130382,
                                        0.6101519801307441, 0.5864059018130382,
                                        0.5190521247588651], dtype=xp.float64))

    def test_cheb_odd_high_attenuation(self, xp):
        with warnings.catch_warnings():
            warnings.filterwarnings(
                "ignore", "This window is not suitable", UserWarning)
            cheb_odd = windows.chebwin(53, at=-40, xp=xp)
        assert_array_almost_equal(cheb_odd, xp.asarray(cheb_odd_true), decimal=4)

    def test_cheb_even_high_attenuation(self, xp):
        with warnings.catch_warnings():
            warnings.filterwarnings(
                "ignore", "This window is not suitable", UserWarning)
            cheb_even = windows.chebwin(54, at=40, xp=xp)
        assert_array_almost_equal(cheb_even, xp.asarray(cheb_even_true), decimal=4)

    def test_cheb_odd_low_attenuation(self, xp):
        cheb_odd_low_at_true = xp.asarray([1.000000, 0.519052, 0.586405,
                                           0.610151, 0.586405, 0.519052,
                                           1.000000], dtype=xp.float64)
        with warnings.catch_warnings():
            warnings.filterwarnings(
                "ignore", "This window is not suitable", UserWarning)
            cheb_odd = windows.chebwin(7, at=10, xp=xp)
        assert_array_almost_equal(cheb_odd, cheb_odd_low_at_true, decimal=4)

    def test_cheb_even_low_attenuation(self, xp):
        cheb_even_low_at_true = xp.asarray([1.000000, 0.451924, 0.51027,
                                            0.541338, 0.541338, 0.51027,
                                            0.451924, 1.000000], dtype=xp.float64)
        with warnings.catch_warnings():
            warnings.filterwarnings(
                "ignore", "This window is not suitable", UserWarning)
            cheb_even = windows.chebwin(8, at=-10, xp=xp)
        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
}


@make_xp_test_case(windows.exponential)
def test_exponential(xp):
    for k, v in exponential_data.items():
        if v is None:
            assert_raises(ValueError, windows.exponential, *k, xp=xp)
        else:
            win = windows.exponential(*k, xp=xp)
            xp_assert_close(win, xp.asarray(v), rtol=1e-14)


@make_xp_test_case(windows.flattop)
class TestFlatTop:

    def test_basic(self, xp):
        xp_assert_close(windows.flattop(6, sym=False, xp=xp),
                        xp.asarray([-0.000421051, -0.051263156, 0.19821053, 1.0,
                                     0.19821053, -0.051263156], dtype=xp.float64))
        xp_assert_close(windows.flattop(7, sym=False, xp=xp),
                        xp.asarray([-0.000421051, -0.03684078115492348,
                                     0.01070371671615342, 0.7808739149387698,
                                     0.7808739149387698, 0.01070371671615342,
                                    -0.03684078115492348], dtype=xp.float64))
        xp_assert_close(windows.flattop(6, xp=xp),
                        xp.asarray([-0.000421051, -0.0677142520762119,
                                     0.6068721525762117, 0.6068721525762117,
                                    -0.0677142520762119, -0.000421051],
                                    dtype=xp.float64))
        xp_assert_close(windows.flattop(7, True, xp=xp),
                        xp.asarray([-0.000421051, -0.051263156, 0.19821053, 1.0,
                                     0.19821053, -0.051263156, -0.000421051],
                                     dtype=xp.float64))


@make_xp_test_case(windows.gaussian)
class TestGaussian:

    def test_basic(self, xp):
        xp_assert_close(windows.gaussian(6, 1.0, xp=xp),
                        xp.asarray([0.04393693362340742, 0.3246524673583497,
                                    0.8824969025845955, 0.8824969025845955,
                                    0.3246524673583497, 0.04393693362340742],
                                    dtype=xp.float64))
        xp_assert_close(windows.gaussian(7, 1.2, xp=xp),
                        xp.asarray([0.04393693362340742, 0.2493522087772962,
                                    0.7066482778577162, 1.0, 0.7066482778577162,
                                    0.2493522087772962, 0.04393693362340742],
                                    dtype=xp.float64))
        xp_assert_close(windows.gaussian(7, 3, xp=xp),
                        xp.asarray([0.6065306597126334, 0.8007374029168081,
                                    0.9459594689067654, 1.0, 0.9459594689067654,
                                    0.8007374029168081, 0.6065306597126334],
                                    dtype=xp.float64))
        xp_assert_close(windows.gaussian(6, 3, False, xp=xp),
                        xp.asarray([0.6065306597126334, 0.8007374029168081,
                                    0.9459594689067654, 1.0, 0.9459594689067654,
                                    0.8007374029168081], dtype=xp.float64))


@make_xp_test_case(windows.general_cosine)
class TestGeneralCosine:

    def test_basic(self, xp):
        a = xp.asarray([0.5, 0.3, 0.2])
        xp_assert_close(windows.general_cosine(5, a),
                        xp.asarray([0.4, 0.3, 1, 0.3, 0.4], dtype=xp.float64))

        a = xp.asarray([0.5, 0.3, 0.2])
        xp_assert_close(windows.general_cosine(4, a, sym=False),
                        xp.asarray([0.4, 0.3, 1, 0.3], dtype=xp.float64))


@make_xp_test_case(windows.general_hamming)
class TestGeneralHamming:

    def test_basic(self, xp):
        xp_assert_close(windows.general_hamming(5, 0.7, xp=xp),
                        xp.asarray([0.4, 0.7, 1.0, 0.7, 0.4], dtype=xp.float64))
        xp_assert_close(windows.general_hamming(5, 0.75, sym=False, xp=xp),
                        xp.asarray([0.5, 0.6727457514, 0.9522542486,
                                    0.9522542486, 0.6727457514], dtype=xp.float64))
        xp_assert_close(windows.general_hamming(6, 0.75, sym=True, xp=xp),
                        xp.asarray([0.5, 0.6727457514, 0.9522542486,
                                    0.9522542486, 0.6727457514, 0.5], dtype=xp.float64))


@make_xp_test_case(windows.hamming)
class TestHamming:

    def test_basic(self, xp):
        xp_assert_close(windows.hamming(6, False, xp=xp),
                        xp.asarray([0.08, 0.31, 0.77, 1.0, 0.77, 0.31],
                                   dtype=xp.float64))
        xp_assert_close(windows.hamming(7, sym=False, xp=xp),
                        xp.asarray([0.08, 0.2531946911449826, 0.6423596296199047,
                                    0.9544456792351128, 0.9544456792351128,
                                    0.6423596296199047, 0.2531946911449826],
                                    dtype=xp.float64))
        xp_assert_close(windows.hamming(6, xp=xp),
                        xp.asarray([0.08, 0.3978521825875242, 0.9121478174124757,
                                    0.9121478174124757, 0.3978521825875242, 0.08],
                                    dtype=xp.float64))
        xp_assert_close(windows.hamming(7, sym=True, xp=xp),
                        xp.asarray([0.08, 0.31, 0.77, 1.0, 0.77, 0.31, 0.08],
                                   dtype=xp.float64))


@make_xp_test_case(windows.hann)
class TestHann:

    def test_basic(self, xp):
        xp_assert_close(windows.hann(6, sym=False, xp=xp),
                        xp.asarray([0, 0.25, 0.75, 1.0, 0.75, 0.25], dtype=xp.float64),
                        rtol=1e-15, atol=1e-15)
        xp_assert_close(windows.hann(7, sym=False, xp=xp),
                        xp.asarray([0, 0.1882550990706332, 0.6112604669781572,
                                    0.9504844339512095, 0.9504844339512095,
                                    0.6112604669781572, 0.1882550990706332],
                                    dtype=xp.float64),
                        rtol=1e-15, atol=1e-15)
        xp_assert_close(windows.hann(6, True, xp=xp),
                        xp.asarray([0, 0.3454915028125263, 0.9045084971874737,
                                    0.9045084971874737, 0.3454915028125263, 0],
                                    dtype=xp.float64),
                        rtol=1e-15, atol=1e-15)
        xp_assert_close(windows.hann(7, xp=xp),
                        xp.asarray([0, 0.25, 0.75, 1.0, 0.75, 0.25, 0],
                        dtype=xp.float64),
                        rtol=1e-15, atol=1e-15)


@make_xp_test_case(windows.kaiser)
class TestKaiser:

    def test_basic(self, xp):
        xp_assert_close(windows.kaiser(6, 0.5, xp=xp),
                        xp.asarray([0.9403061933191572, 0.9782962393705389,
                                    0.9975765035372042, 0.9975765035372042,
                                    0.9782962393705389, 0.9403061933191572],
                                    dtype=xp.float64))
        xp_assert_close(windows.kaiser(7, 0.5, xp=xp),
                        xp.asarray([0.9403061933191572, 0.9732402256999829,
                                    0.9932754654413773, 1.0, 0.9932754654413773,
                                    0.9732402256999829, 0.9403061933191572],
                                    dtype=xp.float64))
        xp_assert_close(windows.kaiser(6, 2.7, xp=xp),
                        xp.asarray([0.2603047507678832, 0.6648106293528054,
                                    0.9582099802511439, 0.9582099802511439,
                                    0.6648106293528054, 0.2603047507678832],
                                    dtype=xp.float64))
        xp_assert_close(windows.kaiser(7, 2.7, xp=xp),
                        xp.asarray([0.2603047507678832, 0.5985765418119844,
                                    0.8868495172060835, 1.0, 0.8868495172060835,
                                    0.5985765418119844, 0.2603047507678832],
                                    dtype=xp.float64))
        xp_assert_close(windows.kaiser(6, 2.7, False, xp=xp),
                        xp.asarray([0.2603047507678832, 0.5985765418119844,
                                    0.8868495172060835, 1.0, 0.8868495172060835,
                                    0.5985765418119844], dtype=xp.float64))


@make_xp_test_case(windows.kaiser_bessel_derived)
class TestKaiserBesselDerived:

    def test_basic(self, xp):
        # cover case `M < 1`
        w = windows.kaiser_bessel_derived(0.5, beta=4.0, xp=xp)
        xp_assert_equal(w, xp.asarray([]))

        M = 100
        w = windows.kaiser_bessel_derived(M, beta=4.0, xp=xp)
        w2 = windows.get_window(('kaiser bessel derived', 4.0),
                                M, fftbins=False, xp=xp)
        xp_assert_close(w, w2)

        # Test for Princen-Bradley condition
        actual = w[:M // 2] ** 2 + w[-M // 2:] ** 2
        xp_assert_close(actual, xp.ones(actual.shape, dtype=actual.dtype))

        # 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
        actual = windows.kaiser_bessel_derived(2, beta=np.pi / 2, xp=xp)[:1]
        desired = xp.ones_like(actual) * math.sqrt(2) / 2.0
        xp_assert_close(actual, desired)

        xp_assert_close(windows.kaiser_bessel_derived(4, beta=np.pi / 2, xp=xp)[:2],
                        xp.asarray([0.518562710536, 0.855039598640], dtype=xp.float64))

        xp_assert_close(windows.kaiser_bessel_derived(6, beta=np.pi / 2, xp=xp)[:3],
                        xp.asarray([0.436168993154, 0.707106781187, 0.899864772847],
                                   dtype=xp.float64))

    def test_exceptions(self, xp):
        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., xp=xp)

        # 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, xp=xp)


class TestNuttall:

    def test_basic(self, xp):
        xp_assert_close(windows.nuttall(6, sym=False, xp=xp),
                        xp.asarray([0.0003628, 0.0613345, 0.5292298, 1.0, 0.5292298,
                                    0.0613345], dtype=xp.float64))
        xp_assert_close(windows.nuttall(7, sym=False, xp=xp),
                        xp.asarray([0.0003628, 0.03777576895352025,
                                    0.3427276199688195,
                                    0.8918518610776603, 0.8918518610776603,
                                    0.3427276199688196, 0.0377757689535203],
                                    dtype=xp.float64))
        xp_assert_close(windows.nuttall(6, xp=xp),
                        xp.asarray([0.0003628, 0.1105152530498718,
                                    0.7982580969501282, 0.7982580969501283,
                                    0.1105152530498719, 0.0003628], dtype=xp.float64))
        xp_assert_close(windows.nuttall(7, True, xp=xp),
                        xp.asarray([0.0003628, 0.0613345, 0.5292298, 1.0,
                                    0.5292298, 0.0613345, 0.0003628], dtype=xp.float64))


@make_xp_test_case(windows.parzen)
class TestParzen:

    def test_basic(self, xp):
        xp_assert_close(windows.parzen(6, xp=xp),
                        xp.asarray([0.009259259259259254, 0.25, 0.8611111111111112,
                                    0.8611111111111112, 0.25, 0.009259259259259254],
                                    dtype=xp.float64))
        xp_assert_close(windows.parzen(7, sym=True, xp=xp),
                        xp.asarray([0.00583090379008747, 0.1574344023323616,
                                    0.6501457725947521, 1.0, 0.6501457725947521,
                                    0.1574344023323616, 0.00583090379008747],
                                    dtype=xp.float64))
        xp_assert_close(windows.parzen(6, False, xp=xp),
                        xp.asarray([0.00583090379008747, 0.1574344023323616,
                                    0.6501457725947521, 1.0, 0.6501457725947521,
                                    0.1574344023323616], dtype=xp.float64))


@make_xp_test_case(windows.triang)
class TestTriang:

    def test_basic(self, xp):

        xp_assert_close(windows.triang(6, True, xp=xp),
                        xp.asarray([1/6, 1/2, 5/6, 5/6, 1/2, 1/6], dtype=xp.float64))
        xp_assert_close(windows.triang(7, xp=xp),
                        xp.asarray([1/4, 1/2, 3/4, 1, 3/4, 1/2, 1/4], dtype=xp.float64))
        xp_assert_close(windows.triang(6, sym=False, xp=xp),
                        xp.asarray([1/4, 1/2, 3/4, 1, 3/4, 1/2], dtype=xp.float64))


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): [1.0, 1, 1, 1, 1, 1],
    (7, 0): [1.0, 1, 1, 1, 1, 1, 1],
    (6, .25): [0.0, 1, 1, 1, 1, 0],
    (7, .25): [0.0, 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],
}


@make_xp_test_case(windows.tukey)
class TestTukey:

    def test_basic(self, xp):
        # Test against hardcoded data
        for k, v in tukey_data.items():
            if v is None:
                assert_raises(ValueError, windows.tukey, *k, xp=xp)
            else:
                if is_torch(xp) and k in [(6,), (6, .75), (7, .75), (6,1)]:
                     atol_rtol = {'rtol': 3e-8, 'atol': 1e-8}
                else:
                     atol_rtol = {'rtol': 1e-15, 'atol': 1e-15 }

                win = windows.tukey(*k, xp=xp)
                xp_assert_close(win, xp.asarray(v),
                                check_dtype=False, **atol_rtol)

    def test_extremes(self, xp):
        # Test extremes of alpha correspond to boxcar and hann
        tuk0 = windows.tukey(100, 0, xp=xp)
        box0 = windows.boxcar(100, xp=xp)
        xp_assert_close(tuk0, box0)

        tuk1 = windows.tukey(100, 1, xp=xp)
        han1 = windows.hann(100, xp=xp)
        xp_assert_close(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
}


@make_xp_test_case(windows.dpss)
class TestDPSS:

    def test_basic(self, xp):
        # Test against hardcoded data
        for k, v in dpss_data.items():
            win, ratios = windows.dpss(*k, return_ratios=True, xp=xp)
            xp_assert_close(win, v[0], atol=1e-7, err_msg=k)
            xp_assert_close(ratios, v[1], rtol=1e-5, atol=1e-7, err_msg=k)

    def test_unity(self, xp):
        # Test unity value handling (gh-2221)
        for M in range(1, 21):
            # corrected w/approximation (default)
            win = windows.dpss(M, M / 2.1, xp=xp)
            expected = M % 2  # one for odd, none for even
            xp_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', xp=xp)
            if M > 2:
                # @M=2 the subsample doesn't do anything
                xp_assert_equal(np.isclose(win_sub, 1.).sum(), expected,
                             err_msg=f'{win_sub}')
                xp_assert_close(win, win_sub, rtol=0.03)  # within 3%
            # not the same, l2-norm
            win_2 = windows.dpss(M, M / 2.1, norm=2, xp=xp)
            expected = 1 if M == 1 else 0
            xp_assert_equal(np.isclose(win_2, 1.).sum(), expected,
                         err_msg=f'{win_2}')

    def test_extremes(self, xp):
        # Test extremes of alpha
        lam = windows.dpss(31, 6, 4, return_ratios=True, xp=xp)[1]
        xp_assert_close(lam, xp.ones_like(lam))
        lam = windows.dpss(31, 7, 4, return_ratios=True, xp=xp)[1]
        xp_assert_close(lam, xp.ones_like(lam))
        lam = windows.dpss(31, 8, 4, return_ratios=True, xp=xp)[1]
        xp_assert_close(lam, xp.ones_like(lam))

    def test_degenerate(self, xp):
        # 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

    @skip_xp_backends(np_only=True)
    def test_degenerate_signle_samples(self, xp):
        # Single samples
        w = windows.dpss(1, 1.)
        xp_assert_equal(w, [1.])
        w, ratio = windows.dpss(1, 1., return_ratios=True)
        xp_assert_equal(w, [1.])
        assert ratio == 1.
        w, ratio = windows.dpss(1, 1., Kmax=4, return_ratios=True)
        xp_assert_equal(w, [1.])
        assert isinstance(ratio, np.ndarray)
        xp_assert_equal(ratio, [1.])

        assert_raises(ValueError, windows.dpss, 4, 1.5, -1, xp=xp)  # Bad Kmax
        assert_raises(ValueError, windows.dpss, 4, 1.5, -5, xp=xp)
        assert_raises(TypeError, windows.dpss, 4, 1.5, 1.1, xp=xp)
        assert_raises(ValueError, windows.dpss, 3, 1.5, 3, xp=xp)  # NW must be < N/2.
        assert_raises(ValueError, windows.dpss, 3, -1, 3, xp=xp)  # NW must be pos
        assert_raises(ValueError, windows.dpss, 3, 0, 3, xp=xp)
        assert_raises(ValueError, windows.dpss, -1, 1, 3, xp=xp)  # negative M


@make_xp_test_case(windows.lanczos)
class TestLanczos:

    def test_basic(self, xp):
        # 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
        xp_assert_close(windows.lanczos(6, sym=False, xp=xp),
                        xp.asarray([0., 0.413496672,
                                    0.826993343, 1., 0.826993343,
                                    0.413496672], dtype=xp.float64),
                        atol=1e-9)
        xp_assert_close(windows.lanczos(6, xp=xp),
                        xp.asarray([0., 0.504551152,
                                    0.935489284, 0.935489284,
                                    0.504551152, 0.], dtype=xp.float64),
                        atol=1e-9)
        xp_assert_close(windows.lanczos(7, sym=True, xp=xp),
                        xp.asarray([0., 0.413496672,
                                    0.826993343, 1., 0.826993343,
                                    0.413496672, 0.], dtype=xp.float64),
                        atol=1e-9)

    def test_array_size(self, xp):
        for n in [0, 10, 11]:
            assert windows.lanczos(n, sym=False, xp=xp).shape[0] == n
            assert windows.lanczos(n, sym=True, xp=xp).shape[0] == n


@make_xp_test_case(windows.get_window)
class TestGetWindow:
    """Unit test for `scipy.signal.get_windows`. """

    def test_WIN_FUNC_DATA_integrity(self):
        """Verify that the `_windows._WIN_FUNC_DATA` dict is consistent.

          The keys of _WIN_FUNC_DATA are made of tuples of strings of allowed window
          names. Its values are 2-tuples made up of the window function and a
          entry characterizing the existence of window parameters as ``True``,
          ``False`` or ``'OPTIONAL'``.


          It is verified that the correct window name (i.e., corresponding to the
          function in the value tuple) is included in the key tuple. It is also checked
          that the second entry in the value tuple is either ``True``, ``False`` or
          ``'OPTIONAL'``.
          """
        for nn_, v_ in _WIN_FUNC_DATA.items():
            func_name = v_[0].__name__
            msg = f"Function name in {nn_} does not contain name of actual function!"
            assert func_name in nn_, msg
            assert v_[1] in (True, False, 'OPTIONAL')

    @make_xp_test_case(windows.boxcar)
    def test_boxcar(self, xp):
        w = windows.get_window('boxcar', 12, xp=xp)
        xp_assert_equal(w, xp.ones_like(w))

        # window is a tuple of len 1
        w = windows.get_window(('boxcar',), 16, xp=xp)
        xp_assert_equal(w, xp.ones_like(w))

    @make_xp_test_case(windows.chebwin)
    def test_cheb_odd(self, xp):
        with warnings.catch_warnings():
            warnings.filterwarnings(
                "ignore", "This window is not suitable", UserWarning)
            w = windows.get_window(('chebwin', -40), 53, fftbins=False, xp=xp)
        assert_array_almost_equal(
            w, xp.asarray(cheb_odd_true, dtype=xp.float64), decimal=4
        )

    @make_xp_test_case(windows.chebwin)
    def test_cheb_even(self, xp):
        with warnings.catch_warnings():
            warnings.filterwarnings(
                "ignore", "This window is not suitable", UserWarning)
            w = windows.get_window(('chebwin', 40), 54, fftbins=False, xp=xp)
        assert_array_almost_equal(w, xp.asarray(cheb_even_true), decimal=4)

    @make_xp_test_case(windows.dpss)
    def test_dpss(self, xp):
        win1 = windows.get_window(('dpss', 3), 64, fftbins=False, xp=xp)
        win2 = windows.dpss(64, 3, xp=xp)
        xp_assert_equal(win1, win2)

    @make_xp_test_case(windows.kaiser)
    def test_kaiser_float(self, xp):
        win1 = windows.get_window(7.2, 64, xp=xp)
        win2 = windows.kaiser(64, 7.2, False, xp=xp)
        if is_jax(xp):
            # On JAX with jit enabled, there is a very small discrepancy
            # in the results.
            xp_assert_close(win1, win2, rtol=xp.finfo(win1.dtype).eps)
        else:
            xp_assert_equal(win1, win2)

    @pytest.mark.parametrize('Nx', [-1, 3.0, np.float64(3)])
    @make_xp_test_case(windows.hann)
    def test_invalid_parameter_NX(self, Nx, xp):
        with pytest.raises(ValueError, match="^Parameter Nx=.*"):
            windows.get_window('hann', Nx, xp=xp)

    # noinspection PyTypeChecker
    def test_invalid_inputs(self, xp):
        """Raise all exceptions (except those concerning parameter `Nx`). """
        with pytest.raises(ValueError, match="^Parameter fftbins=.*"):
            windows.get_window('hann', 5, fftbins=1, xp=xp)
        with pytest.raises(ValueError, match="^Parameter window=.*"):
            windows.get_window(['hann',], 5, xp=xp)
        with pytest.raises(ValueError, match="^First tuple entry of parameter win.*"):
            windows.get_window((42,), 5, xp=xp)
        with pytest.raises(ValueError, match="^Invalid window name 'INVALID'.*"):
            windows.get_window('INVALID', 5, xp=xp)
        with pytest.raises(ValueError, match="^'hann' does not allow parameters.*"):
            windows.get_window(('hann', 1), 5, xp=xp)
        with pytest.raises(ValueError, match="^'kaiser' must have parameters.*"):
            windows.get_window('kaiser', 5, xp=xp)
        with pytest.raises(ValueError, match="^Window dpss must have one.*"):
            windows.get_window(('dpss', 1, 2), 5, xp=xp)
        with pytest.raises(ValueError, match="^'general_cosine' does not accept.*"):
            xp_ = xp or np  # ensure parameter xp_ is not None
            windows.get_window(('general cosine', [1, 2]), 5, xp=xp_)

    @make_xp_test_case(windows.bartlett)
    def test_symmetric_periodic(self, xp):
        """Ensure that suffixes `_periodic` and `_symmetric` work for window names. """
        w_sym = windows.bartlett(5, sym=True, xp=xp)
        xp_assert_close(get_window('bartlett', 5, fftbins=False, xp=xp), w_sym)
        xp_assert_close(get_window('bartlett_symmetric', 5, xp=xp), w_sym)
        # overwrite parameter `fftbins`:
        xp_assert_close(get_window('bartlett_symmetric', 5, fftbins=True, xp=xp), w_sym)

        w_per = windows.bartlett(5, sym=False, xp=xp)
        xp_assert_close(get_window('bartlett', 5, xp=xp), w_per)
        xp_assert_close(get_window('bartlett', 5, fftbins=True, xp=xp), w_per)
        xp_assert_close(get_window('bartlett_periodic', 5, xp=xp), w_per)
        # overwrite parameter `fftbins`:
        xp_assert_close(get_window('bartlett_periodic', 5, fftbins=False, xp=xp),
                        w_per)

    @make_xp_test_case(windows.kaiser)
    def test_array_as_window(self, xp):
        # github issue 3603
        osfactor = 128
        sig = xp.arange(128)

        win = windows.get_window(('kaiser', 8.0), osfactor // 2, xp=xp)
        mesg = "^window must" if is_cupy(xp) else "^window.shape="
        with assert_raises(ValueError, match=mesg):
            resample(sig, sig.shape[0] * osfactor, window=win)

    @make_xp_test_case(windows.general_cosine)
    def test_general_cosine(self, xp):
        xp_assert_close(get_window(('general_cosine', xp.asarray([0.5, 0.3, 0.2])), 4),
                        xp.asarray([0.4, 0.3, 1, 0.3], dtype=xp.float64))
        xp_assert_close(get_window(('general_cosine', xp.asarray([0.5, 0.3, 0.2])), 4,
                                   fftbins=False),
                        xp.asarray([0.4, 0.55, 0.55, 0.4], dtype=xp.float64))

        with pytest.raises(ValueError):
            get_window(('general_cosine', [0.5, 0.3, 0.2]), 4, xp=xp)

    @make_xp_test_case(windows.general_hamming)
    def test_general_hamming(self, xp):
        xp_assert_close(get_window(('general_hamming', 0.7), 5, xp=xp),
                        xp.asarray([0.4, 0.6072949, 0.9427051, 0.9427051, 0.6072949],
                                   dtype=xp.float64))
        xp_assert_close(get_window(('general_hamming', 0.7), 5, fftbins=False, xp=xp),
                        xp.asarray([0.4, 0.7, 1.0, 0.7, 0.4], dtype=xp.float64))

    @make_xp_test_case(windows.lanczos)
    def test_lanczos(self, xp):
        xp_assert_close(get_window('lanczos', 6, xp=xp),
                        xp.asarray([0., 0.413496672, 0.826993343, 1., 0.826993343,
                                    0.413496672], dtype=xp.float64), atol=1e-9)
        xp_assert_close(get_window('lanczos', 6, fftbins=False, xp=xp),
                        xp.asarray([0., 0.504551152, 0.935489284, 0.935489284,
                                    0.504551152, 0.], dtype=xp.float64), atol=1e-9)
        xp_assert_close(get_window('lanczos', 6, xp=xp),
                        get_window('sinc', 6, xp=xp))

    def test_xp_default(self, xp):
        # no explicit xp= argument, default to numpy
        win = get_window('lanczos', 6)
        assert isinstance(win, np.ndarray)

        win = get_window('lanczos', 6, xp=xp)
        if not is_numpy(xp):
            assert not isinstance(win, np.ndarray)


@skip_xp_backends("dask.array", reason="https://github.com/dask/dask/issues/2620")
@pytest.mark.parametrize(
    "window,window_name,params",
    [
        make_xp_pytest_param(getattr(windows, window_name), window_name, params)
        for window_name, params in window_funcs
    ]
)
def test_windowfunc_basics(window, window_name, params, xp):
    window = getattr(windows, window_name)
    if is_jax(xp) and window_name in ['taylor', 'chebwin']:
        pytest.skip(reason=f'{window_name = }: item assignment')
    if window_name in ['dpss']:
        if is_cupy(xp):
            pytest.skip(reason='dpss window is not implemented for cupy')
        if is_torch(xp) and SCIPY_DEVICE != 'cpu':
            pytest.skip(reason='needs eight_tridiagonal which is CPU only')

    with warnings.catch_warnings():
        warnings.filterwarnings(
            "ignore", "This window is not suitable", UserWarning)
        # Check symmetry for odd and even lengths
        w1 = window(8, *params, sym=True, xp=xp)
        w2 = window(7, *params, sym=False, xp=xp)
        xp_assert_close(w1[:-1], w2)

        w1 = window(9, *params, sym=True, xp=xp)
        w2 = window(8, *params, sym=False, xp=xp)
        xp_assert_close(w1[:-1], w2)

        # Check that functions run and output lengths are correct
        assert window(6, *params, sym=True, xp=xp).shape[0] == 6
        assert window(6, *params, sym=False, xp=xp).shape[0] == 6
        assert window(7, *params, sym=True, xp=xp).shape[0] == 7
        assert window(7, *params, sym=False, xp=xp).shape[0] == 7

        # Check invalid lengths
        assert_raises(ValueError, window, 5.5, *params, xp=xp)
        assert_raises(ValueError, window, -7, *params, xp=xp)

        # Check degenerate cases
        xp_assert_equal(window(0, *params, sym=True, xp=xp),
                        xp.asarray([], dtype=xp.float64))
        xp_assert_equal(window(0, *params, sym=False, xp=xp),
                        xp.asarray([], dtype=xp.float64))
        xp_assert_equal(window(1, *params, sym=True, xp=xp),
                        xp.asarray([1.], dtype=xp.float64))
        xp_assert_equal(window(1, *params, sym=False, xp=xp),
                        xp.asarray([1.], dtype=xp.float64))

        # Check dtype
        assert window(0, *params, sym=True, xp=xp).dtype == xp.float64
        assert window(0, *params, sym=False, xp=xp).dtype == xp.float64
        assert window(1, *params, sym=True, xp=xp).dtype == xp.float64
        assert window(1, *params, sym=False, xp=xp).dtype == xp.float64
        assert window(6, *params, sym=True, xp=xp).dtype == xp.float64
        assert window(6, *params, sym=False, xp=xp).dtype == xp.float64

        # Check normalization
        assert xp.all(window(10, *params, sym=True, xp=xp) < 1.01)
        assert xp.all(window(10, *params, sym=False, xp=xp) < 1.01)
        assert xp.all(window(9, *params, sym=True, xp=xp) < 1.01)
        assert xp.all(window(9, *params, sym=False, xp=xp) < 1.01)

        # Check that DFT-even spectrum is purely real for odd and even
        res = fft(window(10, *params, sym=False, xp=xp))
        res = xp.imag(res)
        xp_assert_close(res, xp.zeros_like(res), atol=1e-14)

        res = fft(window(11, *params, sym=False, xp=xp))
        res = xp.imag(res)
        xp_assert_close(res, xp.zeros_like(res), atol=1e-14)


@make_xp_test_case(get_window)
def test_needs_params(xp):
    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, xp=xp)


_winstr = ['barthann',
           'bartlett',
           'blackman',
           'blackmanharris',
           'bohman',
           'boxcar',
           'cosine',
           'flattop',
           'hamming',
           'nuttall',
           'parzen',
           'taylor',
           'exponential',
           'poisson',
           'tukey',
           'tuk',
           'triangle',
           'lanczos',
           'sinc',
]


@pytest.mark.parametrize(
    'window,winstr',
    [
        make_xp_pytest_param(_WIN_FUNCS[winstr][0], winstr)
        for winstr in _winstr
    ]
)
@make_xp_test_case(get_window)
def test_not_needs_params(xp, window, winstr):
    if is_jax(xp) and winstr in ['taylor']:
        pytest.skip(reason=f'{winstr}: item assignment')
    win = get_window(winstr, 7, xp=xp)
    assert win.shape[0] == 7


@make_xp_test_case(windows.lanczos)
def test_symmetric(xp):

    for win in [windows.lanczos]:
        # Even sampling points
        w = win(4096, xp=xp)
        flip = array_namespace(w).flip
        error = xp.max(xp.abs(w - flip(w)))
        xp_assert_equal(error, xp.asarray(0.0), check_dtype=False, check_0d=False)

        # Odd sampling points
        w = win(4097, xp=xp)
        error = xp.max(xp.abs(w - flip(w)))
        xp_assert_equal(error, xp.asarray(0.0), check_dtype=False, check_0d=False)