1714 lines
62 KiB
Python
1714 lines
62 KiB
Python
import sys
|
|
|
|
import numpy as np
|
|
from numpy.testing import (assert_, assert_approx_equal,
|
|
assert_allclose, assert_array_equal, assert_equal,
|
|
assert_array_almost_equal_nulp, suppress_warnings)
|
|
import pytest
|
|
from pytest import raises as assert_raises
|
|
|
|
from scipy import signal
|
|
from scipy.fft import fftfreq, rfftfreq, fft, irfft
|
|
from scipy.integrate import trapezoid
|
|
from scipy.signal import (periodogram, welch, lombscargle, coherence,
|
|
spectrogram, check_COLA, check_NOLA)
|
|
from scipy.signal.windows import hann
|
|
from scipy.signal._spectral_py import _spectral_helper
|
|
|
|
# Compare ShortTimeFFT.stft() / ShortTimeFFT.istft() with stft() / istft():
|
|
from scipy.signal.tests._scipy_spectral_test_shim import stft_compare as stft
|
|
from scipy.signal.tests._scipy_spectral_test_shim import istft_compare as istft
|
|
from scipy.signal.tests._scipy_spectral_test_shim import csd_compare as csd
|
|
|
|
|
|
class TestPeriodogram:
|
|
def test_real_onesided_even(self):
|
|
x = np.zeros(16)
|
|
x[0] = 1
|
|
f, p = periodogram(x)
|
|
assert_allclose(f, np.linspace(0, 0.5, 9))
|
|
q = np.ones(9)
|
|
q[0] = 0
|
|
q[-1] /= 2.0
|
|
q /= 8
|
|
assert_allclose(p, q)
|
|
|
|
def test_real_onesided_odd(self):
|
|
x = np.zeros(15)
|
|
x[0] = 1
|
|
f, p = periodogram(x)
|
|
assert_allclose(f, np.arange(8.0)/15.0)
|
|
q = np.ones(8)
|
|
q[0] = 0
|
|
q *= 2.0/15.0
|
|
assert_allclose(p, q, atol=1e-15)
|
|
|
|
def test_real_twosided(self):
|
|
x = np.zeros(16)
|
|
x[0] = 1
|
|
f, p = periodogram(x, return_onesided=False)
|
|
assert_allclose(f, fftfreq(16, 1.0))
|
|
q = np.full(16, 1/16.0)
|
|
q[0] = 0
|
|
assert_allclose(p, q)
|
|
|
|
def test_real_spectrum(self):
|
|
x = np.zeros(16)
|
|
x[0] = 1
|
|
f, p = periodogram(x, scaling='spectrum')
|
|
g, q = periodogram(x, scaling='density')
|
|
assert_allclose(f, np.linspace(0, 0.5, 9))
|
|
assert_allclose(p, q/16.0)
|
|
|
|
def test_integer_even(self):
|
|
x = np.zeros(16, dtype=int)
|
|
x[0] = 1
|
|
f, p = periodogram(x)
|
|
assert_allclose(f, np.linspace(0, 0.5, 9))
|
|
q = np.ones(9)
|
|
q[0] = 0
|
|
q[-1] /= 2.0
|
|
q /= 8
|
|
assert_allclose(p, q)
|
|
|
|
def test_integer_odd(self):
|
|
x = np.zeros(15, dtype=int)
|
|
x[0] = 1
|
|
f, p = periodogram(x)
|
|
assert_allclose(f, np.arange(8.0)/15.0)
|
|
q = np.ones(8)
|
|
q[0] = 0
|
|
q *= 2.0/15.0
|
|
assert_allclose(p, q, atol=1e-15)
|
|
|
|
def test_integer_twosided(self):
|
|
x = np.zeros(16, dtype=int)
|
|
x[0] = 1
|
|
f, p = periodogram(x, return_onesided=False)
|
|
assert_allclose(f, fftfreq(16, 1.0))
|
|
q = np.full(16, 1/16.0)
|
|
q[0] = 0
|
|
assert_allclose(p, q)
|
|
|
|
def test_complex(self):
|
|
x = np.zeros(16, np.complex128)
|
|
x[0] = 1.0 + 2.0j
|
|
f, p = periodogram(x, return_onesided=False)
|
|
assert_allclose(f, fftfreq(16, 1.0))
|
|
q = np.full(16, 5.0/16.0)
|
|
q[0] = 0
|
|
assert_allclose(p, q)
|
|
|
|
def test_unk_scaling(self):
|
|
assert_raises(ValueError, periodogram, np.zeros(4, np.complex128),
|
|
scaling='foo')
|
|
|
|
@pytest.mark.skipif(
|
|
sys.maxsize <= 2**32,
|
|
reason="On some 32-bit tolerance issue"
|
|
)
|
|
def test_nd_axis_m1(self):
|
|
x = np.zeros(20, dtype=np.float64)
|
|
x = x.reshape((2,1,10))
|
|
x[:,:,0] = 1.0
|
|
f, p = periodogram(x)
|
|
assert_array_equal(p.shape, (2, 1, 6))
|
|
assert_array_almost_equal_nulp(p[0,0,:], p[1,0,:], 60)
|
|
f0, p0 = periodogram(x[0,0,:])
|
|
assert_array_almost_equal_nulp(p0[np.newaxis,:], p[1,:], 60)
|
|
|
|
@pytest.mark.skipif(
|
|
sys.maxsize <= 2**32,
|
|
reason="On some 32-bit tolerance issue"
|
|
)
|
|
def test_nd_axis_0(self):
|
|
x = np.zeros(20, dtype=np.float64)
|
|
x = x.reshape((10,2,1))
|
|
x[0,:,:] = 1.0
|
|
f, p = periodogram(x, axis=0)
|
|
assert_array_equal(p.shape, (6,2,1))
|
|
assert_array_almost_equal_nulp(p[:,0,0], p[:,1,0], 60)
|
|
f0, p0 = periodogram(x[:,0,0])
|
|
assert_array_almost_equal_nulp(p0, p[:,1,0])
|
|
|
|
def test_window_external(self):
|
|
x = np.zeros(16)
|
|
x[0] = 1
|
|
f, p = periodogram(x, 10, 'hann')
|
|
win = signal.get_window('hann', 16)
|
|
fe, pe = periodogram(x, 10, win)
|
|
assert_array_almost_equal_nulp(p, pe)
|
|
assert_array_almost_equal_nulp(f, fe)
|
|
win_err = signal.get_window('hann', 32)
|
|
assert_raises(ValueError, periodogram, x,
|
|
10, win_err) # win longer than signal
|
|
|
|
def test_padded_fft(self):
|
|
x = np.zeros(16)
|
|
x[0] = 1
|
|
f, p = periodogram(x)
|
|
fp, pp = periodogram(x, nfft=32)
|
|
assert_allclose(f, fp[::2])
|
|
assert_allclose(p, pp[::2])
|
|
assert_array_equal(pp.shape, (17,))
|
|
|
|
def test_empty_input(self):
|
|
f, p = periodogram([])
|
|
assert_array_equal(f.shape, (0,))
|
|
assert_array_equal(p.shape, (0,))
|
|
for shape in [(0,), (3,0), (0,5,2)]:
|
|
f, p = periodogram(np.empty(shape))
|
|
assert_array_equal(f.shape, shape)
|
|
assert_array_equal(p.shape, shape)
|
|
|
|
def test_empty_input_other_axis(self):
|
|
for shape in [(3,0), (0,5,2)]:
|
|
f, p = periodogram(np.empty(shape), axis=1)
|
|
assert_array_equal(f.shape, shape)
|
|
assert_array_equal(p.shape, shape)
|
|
|
|
def test_short_nfft(self):
|
|
x = np.zeros(18)
|
|
x[0] = 1
|
|
f, p = periodogram(x, nfft=16)
|
|
assert_allclose(f, np.linspace(0, 0.5, 9))
|
|
q = np.ones(9)
|
|
q[0] = 0
|
|
q[-1] /= 2.0
|
|
q /= 8
|
|
assert_allclose(p, q)
|
|
|
|
def test_nfft_is_xshape(self):
|
|
x = np.zeros(16)
|
|
x[0] = 1
|
|
f, p = periodogram(x, nfft=16)
|
|
assert_allclose(f, np.linspace(0, 0.5, 9))
|
|
q = np.ones(9)
|
|
q[0] = 0
|
|
q[-1] /= 2.0
|
|
q /= 8
|
|
assert_allclose(p, q)
|
|
|
|
def test_real_onesided_even_32(self):
|
|
x = np.zeros(16, 'f')
|
|
x[0] = 1
|
|
f, p = periodogram(x)
|
|
assert_allclose(f, np.linspace(0, 0.5, 9))
|
|
q = np.ones(9, 'f')
|
|
q[0] = 0
|
|
q[-1] /= 2.0
|
|
q /= 8
|
|
assert_allclose(p, q)
|
|
assert_(p.dtype == q.dtype)
|
|
|
|
def test_real_onesided_odd_32(self):
|
|
x = np.zeros(15, 'f')
|
|
x[0] = 1
|
|
f, p = periodogram(x)
|
|
assert_allclose(f, np.arange(8.0)/15.0)
|
|
q = np.ones(8, 'f')
|
|
q[0] = 0
|
|
q *= 2.0/15.0
|
|
assert_allclose(p, q, atol=1e-7)
|
|
assert_(p.dtype == q.dtype)
|
|
|
|
def test_real_twosided_32(self):
|
|
x = np.zeros(16, 'f')
|
|
x[0] = 1
|
|
f, p = periodogram(x, return_onesided=False)
|
|
assert_allclose(f, fftfreq(16, 1.0))
|
|
q = np.full(16, 1/16.0, 'f')
|
|
q[0] = 0
|
|
assert_allclose(p, q)
|
|
assert_(p.dtype == q.dtype)
|
|
|
|
def test_complex_32(self):
|
|
x = np.zeros(16, 'F')
|
|
x[0] = 1.0 + 2.0j
|
|
f, p = periodogram(x, return_onesided=False)
|
|
assert_allclose(f, fftfreq(16, 1.0))
|
|
q = np.full(16, 5.0/16.0, 'f')
|
|
q[0] = 0
|
|
assert_allclose(p, q)
|
|
assert_(p.dtype == q.dtype)
|
|
|
|
def test_shorter_window_error(self):
|
|
x = np.zeros(16)
|
|
x[0] = 1
|
|
win = signal.get_window('hann', 10)
|
|
expected_msg = ('the size of the window must be the same size '
|
|
'of the input on the specified axis')
|
|
with assert_raises(ValueError, match=expected_msg):
|
|
periodogram(x, window=win)
|
|
|
|
|
|
class TestWelch:
|
|
def test_real_onesided_even(self):
|
|
x = np.zeros(16)
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = welch(x, nperseg=8)
|
|
assert_allclose(f, np.linspace(0, 0.5, 5))
|
|
q = np.array([0.08333333, 0.15277778, 0.22222222, 0.22222222,
|
|
0.11111111])
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
|
|
def test_real_onesided_odd(self):
|
|
x = np.zeros(16)
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = welch(x, nperseg=9)
|
|
assert_allclose(f, np.arange(5.0)/9.0)
|
|
q = np.array([0.12477455, 0.23430933, 0.17072113, 0.17072113,
|
|
0.17072113])
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
|
|
def test_real_twosided(self):
|
|
x = np.zeros(16)
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = welch(x, nperseg=8, return_onesided=False)
|
|
assert_allclose(f, fftfreq(8, 1.0))
|
|
q = np.array([0.08333333, 0.07638889, 0.11111111, 0.11111111,
|
|
0.11111111, 0.11111111, 0.11111111, 0.07638889])
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
|
|
def test_real_spectrum(self):
|
|
x = np.zeros(16)
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = welch(x, nperseg=8, scaling='spectrum')
|
|
assert_allclose(f, np.linspace(0, 0.5, 5))
|
|
q = np.array([0.015625, 0.02864583, 0.04166667, 0.04166667,
|
|
0.02083333])
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
|
|
def test_integer_onesided_even(self):
|
|
x = np.zeros(16, dtype=int)
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = welch(x, nperseg=8)
|
|
assert_allclose(f, np.linspace(0, 0.5, 5))
|
|
q = np.array([0.08333333, 0.15277778, 0.22222222, 0.22222222,
|
|
0.11111111])
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
|
|
def test_integer_onesided_odd(self):
|
|
x = np.zeros(16, dtype=int)
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = welch(x, nperseg=9)
|
|
assert_allclose(f, np.arange(5.0)/9.0)
|
|
q = np.array([0.12477455, 0.23430933, 0.17072113, 0.17072113,
|
|
0.17072113])
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
|
|
def test_integer_twosided(self):
|
|
x = np.zeros(16, dtype=int)
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = welch(x, nperseg=8, return_onesided=False)
|
|
assert_allclose(f, fftfreq(8, 1.0))
|
|
q = np.array([0.08333333, 0.07638889, 0.11111111, 0.11111111,
|
|
0.11111111, 0.11111111, 0.11111111, 0.07638889])
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
|
|
def test_complex(self):
|
|
x = np.zeros(16, np.complex128)
|
|
x[0] = 1.0 + 2.0j
|
|
x[8] = 1.0 + 2.0j
|
|
f, p = welch(x, nperseg=8, return_onesided=False)
|
|
assert_allclose(f, fftfreq(8, 1.0))
|
|
q = np.array([0.41666667, 0.38194444, 0.55555556, 0.55555556,
|
|
0.55555556, 0.55555556, 0.55555556, 0.38194444])
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
|
|
def test_unk_scaling(self):
|
|
assert_raises(ValueError, welch, np.zeros(4, np.complex128),
|
|
scaling='foo', nperseg=4)
|
|
|
|
def test_detrend_linear(self):
|
|
x = np.arange(10, dtype=np.float64) + 0.04
|
|
f, p = welch(x, nperseg=10, detrend='linear')
|
|
assert_allclose(p, np.zeros_like(p), atol=1e-15)
|
|
|
|
def test_no_detrending(self):
|
|
x = np.arange(10, dtype=np.float64) + 0.04
|
|
f1, p1 = welch(x, nperseg=10, detrend=False)
|
|
f2, p2 = welch(x, nperseg=10, detrend=lambda x: x)
|
|
assert_allclose(f1, f2, atol=1e-15)
|
|
assert_allclose(p1, p2, atol=1e-15)
|
|
|
|
def test_detrend_external(self):
|
|
x = np.arange(10, dtype=np.float64) + 0.04
|
|
f, p = welch(x, nperseg=10,
|
|
detrend=lambda seg: signal.detrend(seg, type='l'))
|
|
assert_allclose(p, np.zeros_like(p), atol=1e-15)
|
|
|
|
def test_detrend_external_nd_m1(self):
|
|
x = np.arange(40, dtype=np.float64) + 0.04
|
|
x = x.reshape((2,2,10))
|
|
f, p = welch(x, nperseg=10,
|
|
detrend=lambda seg: signal.detrend(seg, type='l'))
|
|
assert_allclose(p, np.zeros_like(p), atol=1e-15)
|
|
|
|
def test_detrend_external_nd_0(self):
|
|
x = np.arange(20, dtype=np.float64) + 0.04
|
|
x = x.reshape((2,1,10))
|
|
x = np.moveaxis(x, 2, 0)
|
|
f, p = welch(x, nperseg=10, axis=0,
|
|
detrend=lambda seg: signal.detrend(seg, axis=0, type='l'))
|
|
assert_allclose(p, np.zeros_like(p), atol=1e-15)
|
|
|
|
def test_nd_axis_m1(self):
|
|
x = np.arange(20, dtype=np.float64) + 0.04
|
|
x = x.reshape((2,1,10))
|
|
f, p = welch(x, nperseg=10)
|
|
assert_array_equal(p.shape, (2, 1, 6))
|
|
assert_allclose(p[0,0,:], p[1,0,:], atol=1e-13, rtol=1e-13)
|
|
f0, p0 = welch(x[0,0,:], nperseg=10)
|
|
assert_allclose(p0[np.newaxis,:], p[1,:], atol=1e-13, rtol=1e-13)
|
|
|
|
def test_nd_axis_0(self):
|
|
x = np.arange(20, dtype=np.float64) + 0.04
|
|
x = x.reshape((10,2,1))
|
|
f, p = welch(x, nperseg=10, axis=0)
|
|
assert_array_equal(p.shape, (6,2,1))
|
|
assert_allclose(p[:,0,0], p[:,1,0], atol=1e-13, rtol=1e-13)
|
|
f0, p0 = welch(x[:,0,0], nperseg=10)
|
|
assert_allclose(p0, p[:,1,0], atol=1e-13, rtol=1e-13)
|
|
|
|
def test_window_external(self):
|
|
x = np.zeros(16)
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = welch(x, 10, 'hann', nperseg=8)
|
|
win = signal.get_window('hann', 8)
|
|
fe, pe = welch(x, 10, win, nperseg=None)
|
|
assert_array_almost_equal_nulp(p, pe)
|
|
assert_array_almost_equal_nulp(f, fe)
|
|
assert_array_equal(fe.shape, (5,)) # because win length used as nperseg
|
|
assert_array_equal(pe.shape, (5,))
|
|
assert_raises(ValueError, welch, x,
|
|
10, win, nperseg=4) # because nperseg != win.shape[-1]
|
|
win_err = signal.get_window('hann', 32)
|
|
assert_raises(ValueError, welch, x,
|
|
10, win_err, nperseg=None) # win longer than signal
|
|
|
|
def test_empty_input(self):
|
|
f, p = welch([])
|
|
assert_array_equal(f.shape, (0,))
|
|
assert_array_equal(p.shape, (0,))
|
|
for shape in [(0,), (3,0), (0,5,2)]:
|
|
f, p = welch(np.empty(shape))
|
|
assert_array_equal(f.shape, shape)
|
|
assert_array_equal(p.shape, shape)
|
|
|
|
def test_empty_input_other_axis(self):
|
|
for shape in [(3,0), (0,5,2)]:
|
|
f, p = welch(np.empty(shape), axis=1)
|
|
assert_array_equal(f.shape, shape)
|
|
assert_array_equal(p.shape, shape)
|
|
|
|
def test_short_data(self):
|
|
x = np.zeros(8)
|
|
x[0] = 1
|
|
#for string-like window, input signal length < nperseg value gives
|
|
#UserWarning, sets nperseg to x.shape[-1]
|
|
with suppress_warnings() as sup:
|
|
msg = "nperseg = 256 is greater than input length = 8, using nperseg = 8"
|
|
sup.filter(UserWarning, msg)
|
|
f, p = welch(x,window='hann') # default nperseg
|
|
f1, p1 = welch(x,window='hann', nperseg=256) # user-specified nperseg
|
|
f2, p2 = welch(x, nperseg=8) # valid nperseg, doesn't give warning
|
|
assert_allclose(f, f2)
|
|
assert_allclose(p, p2)
|
|
assert_allclose(f1, f2)
|
|
assert_allclose(p1, p2)
|
|
|
|
def test_window_long_or_nd(self):
|
|
assert_raises(ValueError, welch, np.zeros(4), 1, np.array([1,1,1,1,1]))
|
|
assert_raises(ValueError, welch, np.zeros(4), 1,
|
|
np.arange(6).reshape((2,3)))
|
|
|
|
def test_nondefault_noverlap(self):
|
|
x = np.zeros(64)
|
|
x[::8] = 1
|
|
f, p = welch(x, nperseg=16, noverlap=4)
|
|
q = np.array([0, 1./12., 1./3., 1./5., 1./3., 1./5., 1./3., 1./5.,
|
|
1./6.])
|
|
assert_allclose(p, q, atol=1e-12)
|
|
|
|
def test_bad_noverlap(self):
|
|
assert_raises(ValueError, welch, np.zeros(4), 1, 'hann', 2, 7)
|
|
|
|
def test_nfft_too_short(self):
|
|
assert_raises(ValueError, welch, np.ones(12), nfft=3, nperseg=4)
|
|
|
|
def test_real_onesided_even_32(self):
|
|
x = np.zeros(16, 'f')
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = welch(x, nperseg=8)
|
|
assert_allclose(f, np.linspace(0, 0.5, 5))
|
|
q = np.array([0.08333333, 0.15277778, 0.22222222, 0.22222222,
|
|
0.11111111], 'f')
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
assert_(p.dtype == q.dtype)
|
|
|
|
def test_real_onesided_odd_32(self):
|
|
x = np.zeros(16, 'f')
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = welch(x, nperseg=9)
|
|
assert_allclose(f, np.arange(5.0)/9.0)
|
|
q = np.array([0.12477458, 0.23430935, 0.17072113, 0.17072116,
|
|
0.17072113], 'f')
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
assert_(p.dtype == q.dtype)
|
|
|
|
def test_real_twosided_32(self):
|
|
x = np.zeros(16, 'f')
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = welch(x, nperseg=8, return_onesided=False)
|
|
assert_allclose(f, fftfreq(8, 1.0))
|
|
q = np.array([0.08333333, 0.07638889, 0.11111111,
|
|
0.11111111, 0.11111111, 0.11111111, 0.11111111,
|
|
0.07638889], 'f')
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
assert_(p.dtype == q.dtype)
|
|
|
|
def test_complex_32(self):
|
|
x = np.zeros(16, 'F')
|
|
x[0] = 1.0 + 2.0j
|
|
x[8] = 1.0 + 2.0j
|
|
f, p = welch(x, nperseg=8, return_onesided=False)
|
|
assert_allclose(f, fftfreq(8, 1.0))
|
|
q = np.array([0.41666666, 0.38194442, 0.55555552, 0.55555552,
|
|
0.55555558, 0.55555552, 0.55555552, 0.38194442], 'f')
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
assert_(p.dtype == q.dtype,
|
|
f'dtype mismatch, {p.dtype}, {q.dtype}')
|
|
|
|
def test_padded_freqs(self):
|
|
x = np.zeros(12)
|
|
|
|
nfft = 24
|
|
f = fftfreq(nfft, 1.0)[:nfft//2+1]
|
|
f[-1] *= -1
|
|
fodd, _ = welch(x, nperseg=5, nfft=nfft)
|
|
feven, _ = welch(x, nperseg=6, nfft=nfft)
|
|
assert_allclose(f, fodd)
|
|
assert_allclose(f, feven)
|
|
|
|
nfft = 25
|
|
f = fftfreq(nfft, 1.0)[:(nfft + 1)//2]
|
|
fodd, _ = welch(x, nperseg=5, nfft=nfft)
|
|
feven, _ = welch(x, nperseg=6, nfft=nfft)
|
|
assert_allclose(f, fodd)
|
|
assert_allclose(f, feven)
|
|
|
|
def test_window_correction(self):
|
|
A = 20
|
|
fs = 1e4
|
|
nperseg = int(fs//10)
|
|
fsig = 300
|
|
ii = int(fsig*nperseg//fs) # Freq index of fsig
|
|
|
|
tt = np.arange(fs)/fs
|
|
x = A*np.sin(2*np.pi*fsig*tt)
|
|
|
|
for window in ['hann', 'bartlett', ('tukey', 0.1), 'flattop']:
|
|
_, p_spec = welch(x, fs=fs, nperseg=nperseg, window=window,
|
|
scaling='spectrum')
|
|
freq, p_dens = welch(x, fs=fs, nperseg=nperseg, window=window,
|
|
scaling='density')
|
|
|
|
# Check peak height at signal frequency for 'spectrum'
|
|
assert_allclose(p_spec[ii], A**2/2.0)
|
|
# Check integrated spectrum RMS for 'density'
|
|
assert_allclose(np.sqrt(trapezoid(p_dens, freq)), A*np.sqrt(2)/2,
|
|
rtol=1e-3)
|
|
|
|
def test_axis_rolling(self):
|
|
np.random.seed(1234)
|
|
|
|
x_flat = np.random.randn(1024)
|
|
_, p_flat = welch(x_flat)
|
|
|
|
for a in range(3):
|
|
newshape = [1,]*3
|
|
newshape[a] = -1
|
|
x = x_flat.reshape(newshape)
|
|
|
|
_, p_plus = welch(x, axis=a) # Positive axis index
|
|
_, p_minus = welch(x, axis=a-x.ndim) # Negative axis index
|
|
|
|
assert_equal(p_flat, p_plus.squeeze(), err_msg=a)
|
|
assert_equal(p_flat, p_minus.squeeze(), err_msg=a-x.ndim)
|
|
|
|
def test_average(self):
|
|
x = np.zeros(16)
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = welch(x, nperseg=8, average='median')
|
|
assert_allclose(f, np.linspace(0, 0.5, 5))
|
|
q = np.array([.1, .05, 0., 1.54074396e-33, 0.])
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
|
|
assert_raises(ValueError, welch, x, nperseg=8,
|
|
average='unrecognised-average')
|
|
|
|
|
|
class TestCSD:
|
|
def test_pad_shorter_x(self):
|
|
x = np.zeros(8)
|
|
y = np.zeros(12)
|
|
|
|
f = np.linspace(0, 0.5, 7)
|
|
c = np.zeros(7,dtype=np.complex128)
|
|
f1, c1 = csd(x, y, nperseg=12)
|
|
|
|
assert_allclose(f, f1)
|
|
assert_allclose(c, c1)
|
|
|
|
def test_pad_shorter_y(self):
|
|
x = np.zeros(12)
|
|
y = np.zeros(8)
|
|
|
|
f = np.linspace(0, 0.5, 7)
|
|
c = np.zeros(7,dtype=np.complex128)
|
|
f1, c1 = csd(x, y, nperseg=12)
|
|
|
|
assert_allclose(f, f1)
|
|
assert_allclose(c, c1)
|
|
|
|
def test_real_onesided_even(self):
|
|
x = np.zeros(16)
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = csd(x, x, nperseg=8)
|
|
assert_allclose(f, np.linspace(0, 0.5, 5))
|
|
q = np.array([0.08333333, 0.15277778, 0.22222222, 0.22222222,
|
|
0.11111111])
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
|
|
def test_real_onesided_odd(self):
|
|
x = np.zeros(16)
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = csd(x, x, nperseg=9)
|
|
assert_allclose(f, np.arange(5.0)/9.0)
|
|
q = np.array([0.12477455, 0.23430933, 0.17072113, 0.17072113,
|
|
0.17072113])
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
|
|
def test_real_twosided(self):
|
|
x = np.zeros(16)
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = csd(x, x, nperseg=8, return_onesided=False)
|
|
assert_allclose(f, fftfreq(8, 1.0))
|
|
q = np.array([0.08333333, 0.07638889, 0.11111111, 0.11111111,
|
|
0.11111111, 0.11111111, 0.11111111, 0.07638889])
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
|
|
def test_real_spectrum(self):
|
|
x = np.zeros(16)
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = csd(x, x, nperseg=8, scaling='spectrum')
|
|
assert_allclose(f, np.linspace(0, 0.5, 5))
|
|
q = np.array([0.015625, 0.02864583, 0.04166667, 0.04166667,
|
|
0.02083333])
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
|
|
def test_integer_onesided_even(self):
|
|
x = np.zeros(16, dtype=int)
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = csd(x, x, nperseg=8)
|
|
assert_allclose(f, np.linspace(0, 0.5, 5))
|
|
q = np.array([0.08333333, 0.15277778, 0.22222222, 0.22222222,
|
|
0.11111111])
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
|
|
def test_integer_onesided_odd(self):
|
|
x = np.zeros(16, dtype=int)
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = csd(x, x, nperseg=9)
|
|
assert_allclose(f, np.arange(5.0)/9.0)
|
|
q = np.array([0.12477455, 0.23430933, 0.17072113, 0.17072113,
|
|
0.17072113])
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
|
|
def test_integer_twosided(self):
|
|
x = np.zeros(16, dtype=int)
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = csd(x, x, nperseg=8, return_onesided=False)
|
|
assert_allclose(f, fftfreq(8, 1.0))
|
|
q = np.array([0.08333333, 0.07638889, 0.11111111, 0.11111111,
|
|
0.11111111, 0.11111111, 0.11111111, 0.07638889])
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
|
|
def test_complex(self):
|
|
x = np.zeros(16, np.complex128)
|
|
x[0] = 1.0 + 2.0j
|
|
x[8] = 1.0 + 2.0j
|
|
f, p = csd(x, x, nperseg=8, return_onesided=False)
|
|
assert_allclose(f, fftfreq(8, 1.0))
|
|
q = np.array([0.41666667, 0.38194444, 0.55555556, 0.55555556,
|
|
0.55555556, 0.55555556, 0.55555556, 0.38194444])
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
|
|
def test_unk_scaling(self):
|
|
assert_raises(ValueError, csd, np.zeros(4, np.complex128),
|
|
np.ones(4, np.complex128), scaling='foo', nperseg=4)
|
|
|
|
def test_detrend_linear(self):
|
|
x = np.arange(10, dtype=np.float64) + 0.04
|
|
f, p = csd(x, x, nperseg=10, detrend='linear')
|
|
assert_allclose(p, np.zeros_like(p), atol=1e-15)
|
|
|
|
def test_no_detrending(self):
|
|
x = np.arange(10, dtype=np.float64) + 0.04
|
|
f1, p1 = csd(x, x, nperseg=10, detrend=False)
|
|
f2, p2 = csd(x, x, nperseg=10, detrend=lambda x: x)
|
|
assert_allclose(f1, f2, atol=1e-15)
|
|
assert_allclose(p1, p2, atol=1e-15)
|
|
|
|
def test_detrend_external(self):
|
|
x = np.arange(10, dtype=np.float64) + 0.04
|
|
f, p = csd(x, x, nperseg=10,
|
|
detrend=lambda seg: signal.detrend(seg, type='l'))
|
|
assert_allclose(p, np.zeros_like(p), atol=1e-15)
|
|
|
|
def test_detrend_external_nd_m1(self):
|
|
x = np.arange(40, dtype=np.float64) + 0.04
|
|
x = x.reshape((2,2,10))
|
|
f, p = csd(x, x, nperseg=10,
|
|
detrend=lambda seg: signal.detrend(seg, type='l'))
|
|
assert_allclose(p, np.zeros_like(p), atol=1e-15)
|
|
|
|
def test_detrend_external_nd_0(self):
|
|
x = np.arange(20, dtype=np.float64) + 0.04
|
|
x = x.reshape((2,1,10))
|
|
x = np.moveaxis(x, 2, 0)
|
|
f, p = csd(x, x, nperseg=10, axis=0,
|
|
detrend=lambda seg: signal.detrend(seg, axis=0, type='l'))
|
|
assert_allclose(p, np.zeros_like(p), atol=1e-15)
|
|
|
|
def test_nd_axis_m1(self):
|
|
x = np.arange(20, dtype=np.float64) + 0.04
|
|
x = x.reshape((2,1,10))
|
|
f, p = csd(x, x, nperseg=10)
|
|
assert_array_equal(p.shape, (2, 1, 6))
|
|
assert_allclose(p[0,0,:], p[1,0,:], atol=1e-13, rtol=1e-13)
|
|
f0, p0 = csd(x[0,0,:], x[0,0,:], nperseg=10)
|
|
assert_allclose(p0[np.newaxis,:], p[1,:], atol=1e-13, rtol=1e-13)
|
|
|
|
def test_nd_axis_0(self):
|
|
x = np.arange(20, dtype=np.float64) + 0.04
|
|
x = x.reshape((10,2,1))
|
|
f, p = csd(x, x, nperseg=10, axis=0)
|
|
assert_array_equal(p.shape, (6,2,1))
|
|
assert_allclose(p[:,0,0], p[:,1,0], atol=1e-13, rtol=1e-13)
|
|
f0, p0 = csd(x[:,0,0], x[:,0,0], nperseg=10)
|
|
assert_allclose(p0, p[:,1,0], atol=1e-13, rtol=1e-13)
|
|
|
|
def test_window_external(self):
|
|
x = np.zeros(16)
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = csd(x, x, 10, 'hann', 8)
|
|
win = signal.get_window('hann', 8)
|
|
fe, pe = csd(x, x, 10, win, nperseg=None)
|
|
assert_array_almost_equal_nulp(p, pe)
|
|
assert_array_almost_equal_nulp(f, fe)
|
|
assert_array_equal(fe.shape, (5,)) # because win length used as nperseg
|
|
assert_array_equal(pe.shape, (5,))
|
|
assert_raises(ValueError, csd, x, x,
|
|
10, win, nperseg=256) # because nperseg != win.shape[-1]
|
|
win_err = signal.get_window('hann', 32)
|
|
assert_raises(ValueError, csd, x, x,
|
|
10, win_err, nperseg=None) # because win longer than signal
|
|
|
|
def test_empty_input(self):
|
|
f, p = csd([],np.zeros(10))
|
|
assert_array_equal(f.shape, (0,))
|
|
assert_array_equal(p.shape, (0,))
|
|
|
|
f, p = csd(np.zeros(10),[])
|
|
assert_array_equal(f.shape, (0,))
|
|
assert_array_equal(p.shape, (0,))
|
|
|
|
for shape in [(0,), (3,0), (0,5,2)]:
|
|
f, p = csd(np.empty(shape), np.empty(shape))
|
|
assert_array_equal(f.shape, shape)
|
|
assert_array_equal(p.shape, shape)
|
|
|
|
f, p = csd(np.ones(10), np.empty((5,0)))
|
|
assert_array_equal(f.shape, (5,0))
|
|
assert_array_equal(p.shape, (5,0))
|
|
|
|
f, p = csd(np.empty((5,0)), np.ones(10))
|
|
assert_array_equal(f.shape, (5,0))
|
|
assert_array_equal(p.shape, (5,0))
|
|
|
|
def test_empty_input_other_axis(self):
|
|
for shape in [(3,0), (0,5,2)]:
|
|
f, p = csd(np.empty(shape), np.empty(shape), axis=1)
|
|
assert_array_equal(f.shape, shape)
|
|
assert_array_equal(p.shape, shape)
|
|
|
|
f, p = csd(np.empty((10,10,3)), np.zeros((10,0,1)), axis=1)
|
|
assert_array_equal(f.shape, (10,0,3))
|
|
assert_array_equal(p.shape, (10,0,3))
|
|
|
|
f, p = csd(np.empty((10,0,1)), np.zeros((10,10,3)), axis=1)
|
|
assert_array_equal(f.shape, (10,0,3))
|
|
assert_array_equal(p.shape, (10,0,3))
|
|
|
|
def test_short_data(self):
|
|
x = np.zeros(8)
|
|
x[0] = 1
|
|
|
|
#for string-like window, input signal length < nperseg value gives
|
|
#UserWarning, sets nperseg to x.shape[-1]
|
|
with suppress_warnings() as sup:
|
|
msg = "nperseg = 256 is greater than input length = 8, using nperseg = 8"
|
|
sup.filter(UserWarning, msg)
|
|
f, p = csd(x, x, window='hann') # default nperseg
|
|
f1, p1 = csd(x, x, window='hann', nperseg=256) # user-specified nperseg
|
|
f2, p2 = csd(x, x, nperseg=8) # valid nperseg, doesn't give warning
|
|
assert_allclose(f, f2)
|
|
assert_allclose(p, p2)
|
|
assert_allclose(f1, f2)
|
|
assert_allclose(p1, p2)
|
|
|
|
def test_window_long_or_nd(self):
|
|
assert_raises(ValueError, csd, np.zeros(4), np.ones(4), 1,
|
|
np.array([1,1,1,1,1]))
|
|
assert_raises(ValueError, csd, np.zeros(4), np.ones(4), 1,
|
|
np.arange(6).reshape((2,3)))
|
|
|
|
def test_nondefault_noverlap(self):
|
|
x = np.zeros(64)
|
|
x[::8] = 1
|
|
f, p = csd(x, x, nperseg=16, noverlap=4)
|
|
q = np.array([0, 1./12., 1./3., 1./5., 1./3., 1./5., 1./3., 1./5.,
|
|
1./6.])
|
|
assert_allclose(p, q, atol=1e-12)
|
|
|
|
def test_bad_noverlap(self):
|
|
assert_raises(ValueError, csd, np.zeros(4), np.ones(4), 1, 'hann',
|
|
2, 7)
|
|
|
|
def test_nfft_too_short(self):
|
|
assert_raises(ValueError, csd, np.ones(12), np.zeros(12), nfft=3,
|
|
nperseg=4)
|
|
|
|
def test_real_onesided_even_32(self):
|
|
x = np.zeros(16, 'f')
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = csd(x, x, nperseg=8)
|
|
assert_allclose(f, np.linspace(0, 0.5, 5))
|
|
q = np.array([0.08333333, 0.15277778, 0.22222222, 0.22222222,
|
|
0.11111111], 'f')
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
assert_(p.dtype == q.dtype)
|
|
|
|
def test_real_onesided_odd_32(self):
|
|
x = np.zeros(16, 'f')
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = csd(x, x, nperseg=9)
|
|
assert_allclose(f, np.arange(5.0)/9.0)
|
|
q = np.array([0.12477458, 0.23430935, 0.17072113, 0.17072116,
|
|
0.17072113], 'f')
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
assert_(p.dtype == q.dtype)
|
|
|
|
def test_real_twosided_32(self):
|
|
x = np.zeros(16, 'f')
|
|
x[0] = 1
|
|
x[8] = 1
|
|
f, p = csd(x, x, nperseg=8, return_onesided=False)
|
|
assert_allclose(f, fftfreq(8, 1.0))
|
|
q = np.array([0.08333333, 0.07638889, 0.11111111,
|
|
0.11111111, 0.11111111, 0.11111111, 0.11111111,
|
|
0.07638889], 'f')
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
assert_(p.dtype == q.dtype)
|
|
|
|
def test_complex_32(self):
|
|
x = np.zeros(16, 'F')
|
|
x[0] = 1.0 + 2.0j
|
|
x[8] = 1.0 + 2.0j
|
|
f, p = csd(x, x, nperseg=8, return_onesided=False)
|
|
assert_allclose(f, fftfreq(8, 1.0))
|
|
q = np.array([0.41666666, 0.38194442, 0.55555552, 0.55555552,
|
|
0.55555558, 0.55555552, 0.55555552, 0.38194442], 'f')
|
|
assert_allclose(p, q, atol=1e-7, rtol=1e-7)
|
|
assert_(p.dtype == q.dtype,
|
|
f'dtype mismatch, {p.dtype}, {q.dtype}')
|
|
|
|
def test_padded_freqs(self):
|
|
x = np.zeros(12)
|
|
y = np.ones(12)
|
|
|
|
nfft = 24
|
|
f = fftfreq(nfft, 1.0)[:nfft//2+1]
|
|
f[-1] *= -1
|
|
fodd, _ = csd(x, y, nperseg=5, nfft=nfft)
|
|
feven, _ = csd(x, y, nperseg=6, nfft=nfft)
|
|
assert_allclose(f, fodd)
|
|
assert_allclose(f, feven)
|
|
|
|
nfft = 25
|
|
f = fftfreq(nfft, 1.0)[:(nfft + 1)//2]
|
|
fodd, _ = csd(x, y, nperseg=5, nfft=nfft)
|
|
feven, _ = csd(x, y, nperseg=6, nfft=nfft)
|
|
assert_allclose(f, fodd)
|
|
assert_allclose(f, feven)
|
|
|
|
def test_copied_data(self):
|
|
x = np.random.randn(64)
|
|
y = x.copy()
|
|
|
|
_, p_same = csd(x, x, nperseg=8, average='mean',
|
|
return_onesided=False)
|
|
_, p_copied = csd(x, y, nperseg=8, average='mean',
|
|
return_onesided=False)
|
|
assert_allclose(p_same, p_copied)
|
|
|
|
_, p_same = csd(x, x, nperseg=8, average='median',
|
|
return_onesided=False)
|
|
_, p_copied = csd(x, y, nperseg=8, average='median',
|
|
return_onesided=False)
|
|
assert_allclose(p_same, p_copied)
|
|
|
|
|
|
class TestCoherence:
|
|
def test_identical_input(self):
|
|
x = np.random.randn(20)
|
|
y = np.copy(x) # So `y is x` -> False
|
|
|
|
f = np.linspace(0, 0.5, 6)
|
|
C = np.ones(6)
|
|
f1, C1 = coherence(x, y, nperseg=10)
|
|
|
|
assert_allclose(f, f1)
|
|
assert_allclose(C, C1)
|
|
|
|
def test_phase_shifted_input(self):
|
|
x = np.random.randn(20)
|
|
y = -x
|
|
|
|
f = np.linspace(0, 0.5, 6)
|
|
C = np.ones(6)
|
|
f1, C1 = coherence(x, y, nperseg=10)
|
|
|
|
assert_allclose(f, f1)
|
|
assert_allclose(C, C1)
|
|
|
|
|
|
class TestSpectrogram:
|
|
def test_average_all_segments(self):
|
|
x = np.random.randn(1024)
|
|
|
|
fs = 1.0
|
|
window = ('tukey', 0.25)
|
|
nperseg = 16
|
|
noverlap = 2
|
|
|
|
f, _, P = spectrogram(x, fs, window, nperseg, noverlap)
|
|
fw, Pw = welch(x, fs, window, nperseg, noverlap)
|
|
assert_allclose(f, fw)
|
|
assert_allclose(np.mean(P, axis=-1), Pw)
|
|
|
|
def test_window_external(self):
|
|
x = np.random.randn(1024)
|
|
|
|
fs = 1.0
|
|
window = ('tukey', 0.25)
|
|
nperseg = 16
|
|
noverlap = 2
|
|
f, _, P = spectrogram(x, fs, window, nperseg, noverlap)
|
|
|
|
win = signal.get_window(('tukey', 0.25), 16)
|
|
fe, _, Pe = spectrogram(x, fs, win, nperseg=None, noverlap=2)
|
|
assert_array_equal(fe.shape, (9,)) # because win length used as nperseg
|
|
assert_array_equal(Pe.shape, (9,73))
|
|
assert_raises(ValueError, spectrogram, x,
|
|
fs, win, nperseg=8) # because nperseg != win.shape[-1]
|
|
win_err = signal.get_window(('tukey', 0.25), 2048)
|
|
assert_raises(ValueError, spectrogram, x,
|
|
fs, win_err, nperseg=None) # win longer than signal
|
|
|
|
def test_short_data(self):
|
|
x = np.random.randn(1024)
|
|
fs = 1.0
|
|
|
|
#for string-like window, input signal length < nperseg value gives
|
|
#UserWarning, sets nperseg to x.shape[-1]
|
|
f, _, p = spectrogram(x, fs, window=('tukey',0.25)) # default nperseg
|
|
with suppress_warnings() as sup:
|
|
sup.filter(UserWarning,
|
|
"nperseg = 1025 is greater than input length = 1024, "
|
|
"using nperseg = 1024",)
|
|
f1, _, p1 = spectrogram(x, fs, window=('tukey',0.25),
|
|
nperseg=1025) # user-specified nperseg
|
|
f2, _, p2 = spectrogram(x, fs, nperseg=256) # to compare w/default
|
|
f3, _, p3 = spectrogram(x, fs, nperseg=1024) # compare w/user-spec'd
|
|
assert_allclose(f, f2)
|
|
assert_allclose(p, p2)
|
|
assert_allclose(f1, f3)
|
|
assert_allclose(p1, p3)
|
|
|
|
class TestLombscargle:
|
|
def test_frequency(self):
|
|
"""Test if frequency location of peak corresponds to frequency of
|
|
generated input signal.
|
|
"""
|
|
|
|
# Input parameters
|
|
ampl = 2.
|
|
w = 1.
|
|
phi = 0.5 * np.pi
|
|
nin = 100
|
|
nout = 1000
|
|
p = 0.7 # Fraction of points to select
|
|
|
|
# Randomly select a fraction of an array with timesteps
|
|
np.random.seed(2353425)
|
|
r = np.random.rand(nin)
|
|
t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
|
|
|
|
# Plot a sine wave for the selected times
|
|
x = ampl * np.sin(w*t + phi)
|
|
|
|
# Define the array of frequencies for which to compute the periodogram
|
|
f = np.linspace(0.01, 10., nout)
|
|
|
|
# Calculate Lomb-Scargle periodogram
|
|
P = lombscargle(t, x, f)
|
|
|
|
# Check if difference between found frequency maximum and input
|
|
# frequency is less than accuracy
|
|
delta = f[1] - f[0]
|
|
assert_(w - f[np.argmax(P)] < (delta/2.))
|
|
|
|
def test_amplitude(self):
|
|
# Test if height of peak in normalized Lomb-Scargle periodogram
|
|
# corresponds to amplitude of the generated input signal.
|
|
|
|
# Input parameters
|
|
ampl = 2.
|
|
w = 1.
|
|
phi = 0.5 * np.pi
|
|
nin = 100
|
|
nout = 1000
|
|
p = 0.7 # Fraction of points to select
|
|
|
|
# Randomly select a fraction of an array with timesteps
|
|
np.random.seed(2353425)
|
|
r = np.random.rand(nin)
|
|
t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
|
|
|
|
# Plot a sine wave for the selected times
|
|
x = ampl * np.sin(w*t + phi)
|
|
|
|
# Define the array of frequencies for which to compute the periodogram
|
|
f = np.linspace(0.01, 10., nout)
|
|
|
|
# Calculate Lomb-Scargle periodogram
|
|
pgram = lombscargle(t, x, f)
|
|
|
|
# Normalize
|
|
pgram = np.sqrt(4 * pgram / t.shape[0])
|
|
|
|
# Check if difference between found frequency maximum and input
|
|
# frequency is less than accuracy
|
|
assert_approx_equal(np.max(pgram), ampl, significant=2)
|
|
|
|
def test_precenter(self):
|
|
# Test if precenter gives the same result as manually precentering.
|
|
|
|
# Input parameters
|
|
ampl = 2.
|
|
w = 1.
|
|
phi = 0.5 * np.pi
|
|
nin = 100
|
|
nout = 1000
|
|
p = 0.7 # Fraction of points to select
|
|
offset = 0.15 # Offset to be subtracted in pre-centering
|
|
|
|
# Randomly select a fraction of an array with timesteps
|
|
np.random.seed(2353425)
|
|
r = np.random.rand(nin)
|
|
t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
|
|
|
|
# Plot a sine wave for the selected times
|
|
x = ampl * np.sin(w*t + phi) + offset
|
|
|
|
# Define the array of frequencies for which to compute the periodogram
|
|
f = np.linspace(0.01, 10., nout)
|
|
|
|
# Calculate Lomb-Scargle periodogram
|
|
pgram = lombscargle(t, x, f, precenter=True)
|
|
pgram2 = lombscargle(t, x - x.mean(), f, precenter=False)
|
|
|
|
# check if centering worked
|
|
assert_allclose(pgram, pgram2)
|
|
|
|
def test_normalize(self):
|
|
# Test normalize option of Lomb-Scarge.
|
|
|
|
# Input parameters
|
|
ampl = 2.
|
|
w = 1.
|
|
phi = 0.5 * np.pi
|
|
nin = 100
|
|
nout = 1000
|
|
p = 0.7 # Fraction of points to select
|
|
|
|
# Randomly select a fraction of an array with timesteps
|
|
np.random.seed(2353425)
|
|
r = np.random.rand(nin)
|
|
t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
|
|
|
|
# Plot a sine wave for the selected times
|
|
x = ampl * np.sin(w*t + phi)
|
|
|
|
# Define the array of frequencies for which to compute the periodogram
|
|
f = np.linspace(0.01, 10., nout)
|
|
|
|
# Calculate Lomb-Scargle periodogram
|
|
pgram = lombscargle(t, x, f)
|
|
pgram2 = lombscargle(t, x, f, normalize=True)
|
|
|
|
# check if normalization works as expected
|
|
assert_allclose(pgram * 2 / np.dot(x, x), pgram2)
|
|
assert_approx_equal(np.max(pgram2), 1.0, significant=2)
|
|
|
|
def test_wrong_shape(self):
|
|
t = np.linspace(0, 1, 1)
|
|
x = np.linspace(0, 1, 2)
|
|
f = np.linspace(0, 1, 3)
|
|
assert_raises(ValueError, lombscargle, t, x, f)
|
|
|
|
def test_zero_division(self):
|
|
t = np.zeros(1)
|
|
x = np.zeros(1)
|
|
f = np.zeros(1)
|
|
assert_raises(ZeroDivisionError, lombscargle, t, x, f)
|
|
|
|
def test_lombscargle_atan_vs_atan2(self):
|
|
# https://github.com/scipy/scipy/issues/3787
|
|
# This raised a ZeroDivisionError.
|
|
t = np.linspace(0, 10, 1000, endpoint=False)
|
|
x = np.sin(4*t)
|
|
f = np.linspace(0, 50, 500, endpoint=False) + 0.1
|
|
lombscargle(t, x, f*2*np.pi)
|
|
|
|
|
|
class TestSTFT:
|
|
def test_input_validation(self):
|
|
|
|
def chk_VE(match):
|
|
"""Assert for a ValueError matching regexp `match`.
|
|
|
|
This little wrapper allows a more concise code layout.
|
|
"""
|
|
return pytest.raises(ValueError, match=match)
|
|
|
|
# Checks for check_COLA():
|
|
with chk_VE('nperseg must be a positive integer'):
|
|
check_COLA('hann', -10, 0)
|
|
with chk_VE('noverlap must be less than nperseg.'):
|
|
check_COLA('hann', 10, 20)
|
|
with chk_VE('window must be 1-D'):
|
|
check_COLA(np.ones((2, 2)), 10, 0)
|
|
with chk_VE('window must have length of nperseg'):
|
|
check_COLA(np.ones(20), 10, 0)
|
|
|
|
# Checks for check_NOLA():
|
|
with chk_VE('nperseg must be a positive integer'):
|
|
check_NOLA('hann', -10, 0)
|
|
with chk_VE('noverlap must be less than nperseg'):
|
|
check_NOLA('hann', 10, 20)
|
|
with chk_VE('window must be 1-D'):
|
|
check_NOLA(np.ones((2, 2)), 10, 0)
|
|
with chk_VE('window must have length of nperseg'):
|
|
check_NOLA(np.ones(20), 10, 0)
|
|
with chk_VE('noverlap must be a nonnegative integer'):
|
|
check_NOLA('hann', 64, -32)
|
|
|
|
x = np.zeros(1024)
|
|
z = stft(x)[2]
|
|
|
|
# Checks for stft():
|
|
with chk_VE('window must be 1-D'):
|
|
stft(x, window=np.ones((2, 2)))
|
|
with chk_VE('value specified for nperseg is different ' +
|
|
'from length of window'):
|
|
stft(x, window=np.ones(10), nperseg=256)
|
|
with chk_VE('nperseg must be a positive integer'):
|
|
stft(x, nperseg=-256)
|
|
with chk_VE('noverlap must be less than nperseg.'):
|
|
stft(x, nperseg=256, noverlap=1024)
|
|
with chk_VE('nfft must be greater than or equal to nperseg.'):
|
|
stft(x, nperseg=256, nfft=8)
|
|
|
|
# Checks for istft():
|
|
with chk_VE('Input stft must be at least 2d!'):
|
|
istft(x)
|
|
with chk_VE('window must be 1-D'):
|
|
istft(z, window=np.ones((2, 2)))
|
|
with chk_VE('window must have length of 256'):
|
|
istft(z, window=np.ones(10), nperseg=256)
|
|
with chk_VE('nperseg must be a positive integer'):
|
|
istft(z, nperseg=-256)
|
|
with chk_VE('noverlap must be less than nperseg.'):
|
|
istft(z, nperseg=256, noverlap=1024)
|
|
with chk_VE('nfft must be greater than or equal to nperseg.'):
|
|
istft(z, nperseg=256, nfft=8)
|
|
with pytest.warns(UserWarning, match="NOLA condition failed, " +
|
|
"STFT may not be invertible"):
|
|
istft(z, nperseg=256, noverlap=0, window='hann')
|
|
with chk_VE('Must specify differing time and frequency axes!'):
|
|
istft(z, time_axis=0, freq_axis=0)
|
|
|
|
# Checks for _spectral_helper():
|
|
with chk_VE("Unknown value for mode foo, must be one of: " +
|
|
r"\{'psd', 'stft'\}"):
|
|
_spectral_helper(x, x, mode='foo')
|
|
with chk_VE("x and y must be equal if mode is 'stft'"):
|
|
_spectral_helper(x[:512], x[512:], mode='stft')
|
|
with chk_VE("Unknown boundary option 'foo', must be one of: " +
|
|
r"\['even', 'odd', 'constant', 'zeros', None\]"):
|
|
_spectral_helper(x, x, boundary='foo')
|
|
|
|
scaling = "not_valid"
|
|
with chk_VE(fr"Parameter {scaling=} not in \['spectrum', 'psd'\]!"):
|
|
stft(x, scaling=scaling)
|
|
with chk_VE(fr"Parameter {scaling=} not in \['spectrum', 'psd'\]!"):
|
|
istft(z, scaling=scaling)
|
|
|
|
def test_check_COLA(self):
|
|
settings = [
|
|
('boxcar', 10, 0),
|
|
('boxcar', 10, 9),
|
|
('bartlett', 51, 26),
|
|
('hann', 256, 128),
|
|
('hann', 256, 192),
|
|
('blackman', 300, 200),
|
|
(('tukey', 0.5), 256, 64),
|
|
('hann', 256, 255),
|
|
]
|
|
|
|
for setting in settings:
|
|
msg = '{}, {}, {}'.format(*setting)
|
|
assert_equal(True, check_COLA(*setting), err_msg=msg)
|
|
|
|
def test_check_NOLA(self):
|
|
settings_pass = [
|
|
('boxcar', 10, 0),
|
|
('boxcar', 10, 9),
|
|
('boxcar', 10, 7),
|
|
('bartlett', 51, 26),
|
|
('bartlett', 51, 10),
|
|
('hann', 256, 128),
|
|
('hann', 256, 192),
|
|
('hann', 256, 37),
|
|
('blackman', 300, 200),
|
|
('blackman', 300, 123),
|
|
(('tukey', 0.5), 256, 64),
|
|
(('tukey', 0.5), 256, 38),
|
|
('hann', 256, 255),
|
|
('hann', 256, 39),
|
|
]
|
|
for setting in settings_pass:
|
|
msg = '{}, {}, {}'.format(*setting)
|
|
assert_equal(True, check_NOLA(*setting), err_msg=msg)
|
|
|
|
w_fail = np.ones(16)
|
|
w_fail[::2] = 0
|
|
settings_fail = [
|
|
(w_fail, len(w_fail), len(w_fail) // 2),
|
|
('hann', 64, 0),
|
|
]
|
|
for setting in settings_fail:
|
|
msg = '{}, {}, {}'.format(*setting)
|
|
assert_equal(False, check_NOLA(*setting), err_msg=msg)
|
|
|
|
def test_average_all_segments(self):
|
|
np.random.seed(1234)
|
|
x = np.random.randn(1024)
|
|
|
|
fs = 1.0
|
|
window = 'hann'
|
|
nperseg = 16
|
|
noverlap = 8
|
|
|
|
# Compare twosided, because onesided welch doubles non-DC terms to
|
|
# account for power at negative frequencies. stft doesn't do this,
|
|
# because it breaks invertibility.
|
|
f, _, Z = stft(x, fs, window, nperseg, noverlap, padded=False,
|
|
return_onesided=False, boundary=None)
|
|
fw, Pw = welch(x, fs, window, nperseg, noverlap, return_onesided=False,
|
|
scaling='spectrum', detrend=False)
|
|
|
|
assert_allclose(f, fw)
|
|
assert_allclose(np.mean(np.abs(Z)**2, axis=-1), Pw)
|
|
|
|
def test_permute_axes(self):
|
|
np.random.seed(1234)
|
|
x = np.random.randn(1024)
|
|
|
|
fs = 1.0
|
|
window = 'hann'
|
|
nperseg = 16
|
|
noverlap = 8
|
|
|
|
f1, t1, Z1 = stft(x, fs, window, nperseg, noverlap)
|
|
f2, t2, Z2 = stft(x.reshape((-1, 1, 1)), fs, window, nperseg, noverlap,
|
|
axis=0)
|
|
|
|
t3, x1 = istft(Z1, fs, window, nperseg, noverlap)
|
|
t4, x2 = istft(Z2.T, fs, window, nperseg, noverlap, time_axis=0,
|
|
freq_axis=-1)
|
|
|
|
assert_allclose(f1, f2)
|
|
assert_allclose(t1, t2)
|
|
assert_allclose(t3, t4)
|
|
assert_allclose(Z1, Z2[:, 0, 0, :])
|
|
assert_allclose(x1, x2[:, 0, 0])
|
|
|
|
@pytest.mark.parametrize('scaling', ['spectrum', 'psd'])
|
|
def test_roundtrip_real(self, scaling):
|
|
np.random.seed(1234)
|
|
|
|
settings = [
|
|
('boxcar', 100, 10, 0), # Test no overlap
|
|
('boxcar', 100, 10, 9), # Test high overlap
|
|
('bartlett', 101, 51, 26), # Test odd nperseg
|
|
('hann', 1024, 256, 128), # Test defaults
|
|
(('tukey', 0.5), 1152, 256, 64), # Test Tukey
|
|
('hann', 1024, 256, 255), # Test overlapped hann
|
|
]
|
|
|
|
for window, N, nperseg, noverlap in settings:
|
|
t = np.arange(N)
|
|
x = 10*np.random.randn(t.size)
|
|
|
|
_, _, zz = stft(x, nperseg=nperseg, noverlap=noverlap,
|
|
window=window, detrend=None, padded=False,
|
|
scaling=scaling)
|
|
|
|
tr, xr = istft(zz, nperseg=nperseg, noverlap=noverlap,
|
|
window=window, scaling=scaling)
|
|
|
|
msg = f'{window}, {noverlap}'
|
|
assert_allclose(t, tr, err_msg=msg)
|
|
assert_allclose(x, xr, err_msg=msg)
|
|
|
|
def test_roundtrip_not_nola(self):
|
|
np.random.seed(1234)
|
|
|
|
w_fail = np.ones(16)
|
|
w_fail[::2] = 0
|
|
settings = [
|
|
(w_fail, 256, len(w_fail), len(w_fail) // 2),
|
|
('hann', 256, 64, 0),
|
|
]
|
|
|
|
for window, N, nperseg, noverlap in settings:
|
|
msg = f'{window}, {N}, {nperseg}, {noverlap}'
|
|
assert not check_NOLA(window, nperseg, noverlap), msg
|
|
|
|
t = np.arange(N)
|
|
x = 10 * np.random.randn(t.size)
|
|
|
|
_, _, zz = stft(x, nperseg=nperseg, noverlap=noverlap,
|
|
window=window, detrend=None, padded=True,
|
|
boundary='zeros')
|
|
with pytest.warns(UserWarning, match='NOLA'):
|
|
tr, xr = istft(zz, nperseg=nperseg, noverlap=noverlap,
|
|
window=window, boundary=True)
|
|
|
|
assert np.allclose(t, tr[:len(t)]), msg
|
|
assert not np.allclose(x, xr[:len(x)]), msg
|
|
|
|
def test_roundtrip_nola_not_cola(self):
|
|
np.random.seed(1234)
|
|
|
|
settings = [
|
|
('boxcar', 100, 10, 3), # NOLA True, COLA False
|
|
('bartlett', 101, 51, 37), # NOLA True, COLA False
|
|
('hann', 1024, 256, 127), # NOLA True, COLA False
|
|
(('tukey', 0.5), 1152, 256, 14), # NOLA True, COLA False
|
|
('hann', 1024, 256, 5), # NOLA True, COLA False
|
|
]
|
|
|
|
for window, N, nperseg, noverlap in settings:
|
|
msg = f'{window}, {nperseg}, {noverlap}'
|
|
assert check_NOLA(window, nperseg, noverlap), msg
|
|
assert not check_COLA(window, nperseg, noverlap), msg
|
|
|
|
t = np.arange(N)
|
|
x = 10 * np.random.randn(t.size)
|
|
|
|
_, _, zz = stft(x, nperseg=nperseg, noverlap=noverlap,
|
|
window=window, detrend=None, padded=True,
|
|
boundary='zeros')
|
|
|
|
tr, xr = istft(zz, nperseg=nperseg, noverlap=noverlap,
|
|
window=window, boundary=True)
|
|
|
|
msg = f'{window}, {noverlap}'
|
|
assert_allclose(t, tr[:len(t)], err_msg=msg)
|
|
assert_allclose(x, xr[:len(x)], err_msg=msg)
|
|
|
|
def test_roundtrip_float32(self):
|
|
np.random.seed(1234)
|
|
|
|
settings = [('hann', 1024, 256, 128)]
|
|
|
|
for window, N, nperseg, noverlap in settings:
|
|
t = np.arange(N)
|
|
x = 10*np.random.randn(t.size)
|
|
x = x.astype(np.float32)
|
|
|
|
_, _, zz = stft(x, nperseg=nperseg, noverlap=noverlap,
|
|
window=window, detrend=None, padded=False)
|
|
|
|
tr, xr = istft(zz, nperseg=nperseg, noverlap=noverlap,
|
|
window=window)
|
|
|
|
msg = f'{window}, {noverlap}'
|
|
assert_allclose(t, t, err_msg=msg)
|
|
assert_allclose(x, xr, err_msg=msg, rtol=1e-4, atol=1e-5)
|
|
assert_(x.dtype == xr.dtype)
|
|
|
|
@pytest.mark.parametrize('scaling', ['spectrum', 'psd'])
|
|
def test_roundtrip_complex(self, scaling):
|
|
np.random.seed(1234)
|
|
|
|
settings = [
|
|
('boxcar', 100, 10, 0), # Test no overlap
|
|
('boxcar', 100, 10, 9), # Test high overlap
|
|
('bartlett', 101, 51, 26), # Test odd nperseg
|
|
('hann', 1024, 256, 128), # Test defaults
|
|
(('tukey', 0.5), 1152, 256, 64), # Test Tukey
|
|
('hann', 1024, 256, 255), # Test overlapped hann
|
|
]
|
|
|
|
for window, N, nperseg, noverlap in settings:
|
|
t = np.arange(N)
|
|
x = 10*np.random.randn(t.size) + 10j*np.random.randn(t.size)
|
|
|
|
_, _, zz = stft(x, nperseg=nperseg, noverlap=noverlap,
|
|
window=window, detrend=None, padded=False,
|
|
return_onesided=False, scaling=scaling)
|
|
|
|
tr, xr = istft(zz, nperseg=nperseg, noverlap=noverlap,
|
|
window=window, input_onesided=False,
|
|
scaling=scaling)
|
|
|
|
msg = f'{window}, {nperseg}, {noverlap}'
|
|
assert_allclose(t, tr, err_msg=msg)
|
|
assert_allclose(x, xr, err_msg=msg)
|
|
|
|
# Check that asking for onesided switches to twosided
|
|
with suppress_warnings() as sup:
|
|
sup.filter(UserWarning,
|
|
"Input data is complex, switching to return_onesided=False")
|
|
_, _, zz = stft(x, nperseg=nperseg, noverlap=noverlap,
|
|
window=window, detrend=None, padded=False,
|
|
return_onesided=True, scaling=scaling)
|
|
|
|
tr, xr = istft(zz, nperseg=nperseg, noverlap=noverlap,
|
|
window=window, input_onesided=False, scaling=scaling)
|
|
|
|
msg = f'{window}, {nperseg}, {noverlap}'
|
|
assert_allclose(t, tr, err_msg=msg)
|
|
assert_allclose(x, xr, err_msg=msg)
|
|
|
|
def test_roundtrip_boundary_extension(self):
|
|
np.random.seed(1234)
|
|
|
|
# Test against boxcar, since window is all ones, and thus can be fully
|
|
# recovered with no boundary extension
|
|
|
|
settings = [
|
|
('boxcar', 100, 10, 0), # Test no overlap
|
|
('boxcar', 100, 10, 9), # Test high overlap
|
|
]
|
|
|
|
for window, N, nperseg, noverlap in settings:
|
|
t = np.arange(N)
|
|
x = 10*np.random.randn(t.size)
|
|
|
|
_, _, zz = stft(x, nperseg=nperseg, noverlap=noverlap,
|
|
window=window, detrend=None, padded=True,
|
|
boundary=None)
|
|
|
|
_, xr = istft(zz, noverlap=noverlap, window=window, boundary=False)
|
|
|
|
for boundary in ['even', 'odd', 'constant', 'zeros']:
|
|
_, _, zz_ext = stft(x, nperseg=nperseg, noverlap=noverlap,
|
|
window=window, detrend=None, padded=True,
|
|
boundary=boundary)
|
|
|
|
_, xr_ext = istft(zz_ext, noverlap=noverlap, window=window,
|
|
boundary=True)
|
|
|
|
msg = f'{window}, {noverlap}, {boundary}'
|
|
assert_allclose(x, xr, err_msg=msg)
|
|
assert_allclose(x, xr_ext, err_msg=msg)
|
|
|
|
def test_roundtrip_padded_signal(self):
|
|
np.random.seed(1234)
|
|
|
|
settings = [
|
|
('boxcar', 101, 10, 0),
|
|
('hann', 1000, 256, 128),
|
|
]
|
|
|
|
for window, N, nperseg, noverlap in settings:
|
|
t = np.arange(N)
|
|
x = 10*np.random.randn(t.size)
|
|
|
|
_, _, zz = stft(x, nperseg=nperseg, noverlap=noverlap,
|
|
window=window, detrend=None, padded=True)
|
|
|
|
tr, xr = istft(zz, noverlap=noverlap, window=window)
|
|
|
|
msg = f'{window}, {noverlap}'
|
|
# Account for possible zero-padding at the end
|
|
assert_allclose(t, tr[:t.size], err_msg=msg)
|
|
assert_allclose(x, xr[:x.size], err_msg=msg)
|
|
|
|
def test_roundtrip_padded_FFT(self):
|
|
np.random.seed(1234)
|
|
|
|
settings = [
|
|
('hann', 1024, 256, 128, 512),
|
|
('hann', 1024, 256, 128, 501),
|
|
('boxcar', 100, 10, 0, 33),
|
|
(('tukey', 0.5), 1152, 256, 64, 1024),
|
|
]
|
|
|
|
for window, N, nperseg, noverlap, nfft in settings:
|
|
t = np.arange(N)
|
|
x = 10*np.random.randn(t.size)
|
|
xc = x*np.exp(1j*np.pi/4)
|
|
|
|
# real signal
|
|
_, _, z = stft(x, nperseg=nperseg, noverlap=noverlap, nfft=nfft,
|
|
window=window, detrend=None, padded=True)
|
|
|
|
# complex signal
|
|
_, _, zc = stft(xc, nperseg=nperseg, noverlap=noverlap, nfft=nfft,
|
|
window=window, detrend=None, padded=True,
|
|
return_onesided=False)
|
|
|
|
tr, xr = istft(z, nperseg=nperseg, noverlap=noverlap, nfft=nfft,
|
|
window=window)
|
|
|
|
tr, xcr = istft(zc, nperseg=nperseg, noverlap=noverlap, nfft=nfft,
|
|
window=window, input_onesided=False)
|
|
|
|
msg = f'{window}, {noverlap}'
|
|
assert_allclose(t, tr, err_msg=msg)
|
|
assert_allclose(x, xr, err_msg=msg)
|
|
assert_allclose(xc, xcr, err_msg=msg)
|
|
|
|
def test_axis_rolling(self):
|
|
np.random.seed(1234)
|
|
|
|
x_flat = np.random.randn(1024)
|
|
_, _, z_flat = stft(x_flat)
|
|
|
|
for a in range(3):
|
|
newshape = [1,]*3
|
|
newshape[a] = -1
|
|
x = x_flat.reshape(newshape)
|
|
|
|
_, _, z_plus = stft(x, axis=a) # Positive axis index
|
|
_, _, z_minus = stft(x, axis=a-x.ndim) # Negative axis index
|
|
|
|
assert_equal(z_flat, z_plus.squeeze(), err_msg=a)
|
|
assert_equal(z_flat, z_minus.squeeze(), err_msg=a-x.ndim)
|
|
|
|
# z_flat has shape [n_freq, n_time]
|
|
|
|
# Test vs. transpose
|
|
_, x_transpose_m = istft(z_flat.T, time_axis=-2, freq_axis=-1)
|
|
_, x_transpose_p = istft(z_flat.T, time_axis=0, freq_axis=1)
|
|
|
|
assert_allclose(x_flat, x_transpose_m, err_msg='istft transpose minus')
|
|
assert_allclose(x_flat, x_transpose_p, err_msg='istft transpose plus')
|
|
|
|
def test_roundtrip_scaling(self):
|
|
"""Verify behavior of scaling parameter. """
|
|
# Create 1024 sample cosine signal with amplitude 2:
|
|
X = np.zeros(513, dtype=complex)
|
|
X[256] = 1024
|
|
x = np.fft.irfft(X)
|
|
power_x = sum(x**2) / len(x) # power of signal x is 2
|
|
|
|
# Calculate magnitude-scaled STFT:
|
|
Zs = stft(x, boundary='even', scaling='spectrum')[2]
|
|
|
|
# Test round trip:
|
|
x1 = istft(Zs, boundary=True, scaling='spectrum')[1]
|
|
assert_allclose(x1, x)
|
|
|
|
# For a Hann-windowed 256 sample length FFT, we expect a peak at
|
|
# frequency 64 (since it is 1/4 the length of X) with a height of 1
|
|
# (half the amplitude). A Hann window of a perfectly centered sine has
|
|
# the magnitude [..., 0, 0, 0.5, 1, 0.5, 0, 0, ...].
|
|
# Note that in this case the 'even' padding works for the beginning
|
|
# but not for the end of the STFT.
|
|
assert_allclose(abs(Zs[63, :-1]), 0.5)
|
|
assert_allclose(abs(Zs[64, :-1]), 1)
|
|
assert_allclose(abs(Zs[65, :-1]), 0.5)
|
|
# All other values should be zero:
|
|
Zs[63:66, :-1] = 0
|
|
# Note since 'rtol' does not have influence here, atol needs to be set:
|
|
assert_allclose(Zs[:, :-1], 0, atol=np.finfo(Zs.dtype).resolution)
|
|
|
|
# Calculate two-sided psd-scaled STFT:
|
|
# - using 'even' padding since signal is axis symmetric - this ensures
|
|
# stationary behavior on the boundaries
|
|
# - using the two-sided transform allows determining the spectral
|
|
# power by `sum(abs(Zp[:, k])**2) / len(f)` for the k-th time slot.
|
|
Zp = stft(x, return_onesided=False, boundary='even', scaling='psd')[2]
|
|
|
|
# Calculate spectral power of Zd by summing over the frequency axis:
|
|
psd_Zp = np.sum(Zp.real**2 + Zp.imag**2, axis=0) / Zp.shape[0]
|
|
# Spectral power of Zp should be equal to the signal's power:
|
|
assert_allclose(psd_Zp, power_x)
|
|
|
|
# Test round trip:
|
|
x1 = istft(Zp, input_onesided=False, boundary=True, scaling='psd')[1]
|
|
assert_allclose(x1, x)
|
|
|
|
# The power of the one-sided psd-scaled STFT can be determined
|
|
# analogously (note that the two sides are not of equal shape):
|
|
Zp0 = stft(x, return_onesided=True, boundary='even', scaling='psd')[2]
|
|
|
|
# Since x is real, its Fourier transform is conjugate symmetric, i.e.,
|
|
# the missing 'second side' can be expressed through the 'first side':
|
|
Zp1 = np.conj(Zp0[-2:0:-1, :]) # 'second side' is conjugate reversed
|
|
assert_allclose(Zp[:129, :], Zp0)
|
|
assert_allclose(Zp[129:, :], Zp1)
|
|
|
|
# Calculate the spectral power:
|
|
s2 = (np.sum(Zp0.real ** 2 + Zp0.imag ** 2, axis=0) +
|
|
np.sum(Zp1.real ** 2 + Zp1.imag ** 2, axis=0))
|
|
psd_Zp01 = s2 / (Zp0.shape[0] + Zp1.shape[0])
|
|
assert_allclose(psd_Zp01, power_x)
|
|
|
|
# Test round trip:
|
|
x1 = istft(Zp0, input_onesided=True, boundary=True, scaling='psd')[1]
|
|
assert_allclose(x1, x)
|
|
|
|
|
|
class TestSampledSpectralRepresentations:
|
|
"""Check energy/power relations from `Spectral Analysis` section in the user guide.
|
|
|
|
A 32 sample cosine signal is used to compare the numerical to the expected results
|
|
stated in :ref:`tutorial_SpectralAnalysis` in
|
|
file ``doc/source/tutorial/signal.rst``
|
|
"""
|
|
n: int = 32 #: number of samples
|
|
T: float = 1/16 #: sampling interval
|
|
a_ref: float = 3 #: amplitude of reference
|
|
l_a: int = 3 #: index in fft for defining frequency of test signal
|
|
|
|
x_ref: np.ndarray #: reference signal
|
|
X_ref: np.ndarray #: two-sided FFT of x_ref
|
|
E_ref: float #: energy of signal
|
|
P_ref: float #: power of signal
|
|
|
|
def setup_method(self):
|
|
"""Create Cosine signal with amplitude a from spectrum. """
|
|
f = rfftfreq(self.n, self.T)
|
|
X_ref = np.zeros_like(f)
|
|
self.l_a = 3
|
|
X_ref[self.l_a] = self.a_ref/2 * self.n # set amplitude
|
|
self.x_ref = irfft(X_ref)
|
|
self.X_ref = fft(self.x_ref)
|
|
|
|
# Closed form expression for continuous-time signal:
|
|
self.E_ref = self.tau * self.a_ref**2 / 2 # energy of signal
|
|
self.P_ref = self.a_ref**2 / 2 # power of signal
|
|
|
|
@property
|
|
def tau(self) -> float:
|
|
"""Duration of signal. """
|
|
return self.n * self.T
|
|
|
|
@property
|
|
def delta_f(self) -> float:
|
|
"""Bin width """
|
|
return 1 / (self.n * self.T)
|
|
|
|
def test_reference_signal(self):
|
|
"""Test energy and power formulas. """
|
|
# Verify that amplitude is a:
|
|
assert_allclose(2*self.a_ref, np.ptp(self.x_ref), rtol=0.1)
|
|
# Verify that energy expression for sampled signal:
|
|
assert_allclose(self.T * sum(self.x_ref ** 2), self.E_ref)
|
|
|
|
# Verify that spectral energy and power formulas are correct:
|
|
sum_X_ref_squared = sum(self.X_ref.real**2 + self.X_ref.imag**2)
|
|
assert_allclose(self.T/self.n * sum_X_ref_squared, self.E_ref)
|
|
assert_allclose(1/self.n**2 * sum_X_ref_squared, self.P_ref)
|
|
|
|
def test_windowed_DFT(self):
|
|
"""Verify spectral representations of windowed DFT.
|
|
|
|
Furthermore, the scalings of `periodogram` and `welch` are verified.
|
|
"""
|
|
w = hann(self.n, sym=False)
|
|
c_amp, c_rms = abs(sum(w)), np.sqrt(sum(w.real**2 + w.imag**2))
|
|
Xw = fft(self.x_ref*w) # unnormalized windowed DFT
|
|
|
|
# Verify that the *spectrum* peak is consistent:
|
|
assert_allclose(self.tau * Xw[self.l_a] / c_amp, self.a_ref * self.tau / 2)
|
|
# Verify that the *amplitude spectrum* peak is consistent:
|
|
assert_allclose(Xw[self.l_a] / c_amp, self.a_ref/2)
|
|
|
|
# Verify spectral power/energy equals signal's power/energy:
|
|
X_ESD = self.tau * self.T * abs(Xw / c_rms)**2 # Energy Spectral Density
|
|
X_PSD = self.T * abs(Xw / c_rms)**2 # Power Spectral Density
|
|
assert_allclose(self.delta_f * sum(X_ESD), self.E_ref)
|
|
assert_allclose(self.delta_f * sum(X_PSD), self.P_ref)
|
|
|
|
# Verify scalings of periodogram:
|
|
kw = dict(fs=1/self.T, window=w, detrend=False, return_onesided=False)
|
|
_, P_mag = periodogram(self.x_ref, scaling='spectrum', **kw)
|
|
_, P_psd = periodogram(self.x_ref, scaling='density', **kw)
|
|
|
|
# Verify that periodogram calculates a squared magnitude spectrum:
|
|
float_res = np.finfo(P_mag.dtype).resolution
|
|
assert_allclose(P_mag, abs(Xw/c_amp)**2, atol=float_res*max(P_mag))
|
|
# Verify that periodogram calculates a PSD:
|
|
assert_allclose(P_psd, X_PSD, atol=float_res*max(P_psd))
|
|
|
|
# Ensure that scaling of welch is the same as of periodogram:
|
|
kw = dict(nperseg=len(self.x_ref), noverlap=0, **kw)
|
|
assert_allclose(welch(self.x_ref, scaling='spectrum', **kw)[1], P_mag,
|
|
atol=float_res*max(P_mag))
|
|
assert_allclose(welch(self.x_ref, scaling='density', **kw)[1], P_psd,
|
|
atol=float_res*max(P_psd))
|