def test_stft_conjugation(self):
x = fmlin(128, 0, 0.2)[0]
h = np.conjugate(x)
lhs, _, _ = linear.ShortTimeFourierTransform(h).run()
rhs, _, _ = linear.ShortTimeFourierTransform(x[::-1]).run()
rhs = np.conjugate(rhs)
np.testing.assert_allclose(lhs, rhs)
def test_stft_translation(self):
"""Test the time-shift property of the Fourier transform."""
x = fmlin(128, 0.0, 0.2)[0]
tfrx, _, freqs = linear.ShortTimeFourierTransform(x).run()
x_shifted = np.roll(x, 64)
tfrxs, _, _ = linear.ShortTimeFourierTransform(x_shifted).run()
f_mul = np.exp(-1j * 2 * np.pi * 64 * freqs)
np.testing.assert_allclose(tfrxs, f_mul * tfrx)
def test_stft_modulation(self):
"""Test the modulation / frequency shifting property of STFT."""
x = fmlin(128, 0.0, 0.2)[0]
tfrx, _, _ = linear.ShortTimeFourierTransform(x).run()
f_0 = 0.3
h = np.exp(1j * 2 * np.pi * f_0 * np.arange(128)) * x
tfrh, _, _ = linear.ShortTimeFourierTransform(h).run()
tfrx_shifted = np.roll(tfrx, int(np.ceil(128 * 0.3)), axis=0)
self.assert_tfr_equal(tfrx_shifted, tfrh, tol=0.95)
def test_stft_linearity(self):
"""Test the linearity property of the Fourier transform."""
x = fmlin(128, 0.0, 0.2)[0]
y = fmlin(128, 0.3, 0.5)[0]
h = x + y
tfr, _, _ = linear.ShortTimeFourierTransform(h).run()
tfrx, _, _ = linear.ShortTimeFourierTransform(x).run()
tfry, _, _ = linear.ShortTimeFourierTransform(y).run()
np.testing.assert_allclose(tfr, tfrx + tfry)