def test_spectrogram_linearity(self):
"""Test the linearity property of the spectrogram."""
signal, _ = fmlin(128, 0.1, 0.4)
window = kaiser(17, 3 * np.pi)
tfr1, _, _ = cohen.Spectrogram(signal, n_fbins=64,
fwindow=window).run()
tfr2, _, _ = cohen.Spectrogram(signal * 2, n_fbins=64,
fwindow=window).run()
x = np.sum(np.sum(tfr2))
y = np.sum(np.sum(tfr1))
self.assertEqual(x / y, 4)
def test_spectrogram_energy_conservation(self):
"""Test the energy conservation property of the spectrogram."""
signal, _ = fmlin(128, 0.1, 0.4)
window = kaiser(17, 3 * np.pi)
tfr, ts, freqs = cohen.Spectrogram(signal, n_fbins=64, fwindow=window).run()
e_sig = (np.abs(signal) ** 2).sum()
self.assertAlmostEqual(tfr.sum().sum() / 64, e_sig)
def test_spectrogram_time_invariance(self):
"""Test the time invariance property of the spectrogram."""
signal, _ = fmlin(128, 0.1, 0.4)
window = kaiser(17, 3 * np.pi)
tfr, ts, freqs = cohen.Spectrogram(signal, n_fbins=64, fwindow=window).run()
shift = 64
timeshifted_signal = np.roll(signal, shift)
timeshifted_tfr, _, _ = cohen.Spectrogram(timeshifted_signal, n_fbins=64,
fwindow=window).run()
rolled_tfr = np.roll(tfr, shift, axis=1)
# the time invariance property holds mostly qualitatively. The shifted
# TFR is not numerically indentical to the rolled TFR, having
# differences at the edges; so clip with two TFRs where there are
# discontinuities in the TFR.
edge = 10
xx = np.c_[timeshifted_tfr[:, edge:(shift - edge)],
timeshifted_tfr[:, (shift + edge):-edge]]
yy = np.c_[rolled_tfr[:, edge:(shift - edge)],
rolled_tfr[:, (shift + edge):-edge]]
np.testing.assert_allclose(xx, yy)
def test_spectrogram_reality(self):
"""Test the reality property of the spectrogram."""
signal, _ = fmlin(128, 0.1, 0.4)
window = kaiser(17, 3 * np.pi)
tfr, _, _ = cohen.Spectrogram(signal, n_fbins=64, fwindow=window).run()
self.assertTrue(np.all(np.isreal(tfr)))
def test_spectrogram_non_negativity(self):
"""Test that the spectrogram is non negative."""
signal, _ = fmlin(128, 0.1, 0.4)
window = kaiser(17, 3 * np.pi)
tfr, _, _ = cohen.Spectrogram(signal, n_fbins=64, fwindow=window).run()
self.assertTrue(np.all(tfr >= 0))