def test_psd():
n_times = data.shape[-1]
freqs, pxx = signal.welch(data, sfreq,
window=signal.get_window('boxcar', n_times),
return_onesided=True, scaling='spectrum')
ps, freqs2 = power_spectrum(sfreq, data, return_db=False)
assert_almost_equal(freqs, freqs2)
assert_almost_equal(pxx, ps)
def test_psd():
n_channels, n_times = data.shape
_data = data[None, ...]
# Only test output shape when `method='welch'` or `method='multitaper'`
# since it is actually just a wrapper for MNE functions:
psd_welch, _ = power_spectrum(sfreq, _data, psd_method='welch')
psd_multitaper, _ = power_spectrum(sfreq, _data, psd_method='multitaper')
psd_fft, freqs_fft = power_spectrum(sfreq, _data, psd_method='fft')
assert_equal(psd_welch.shape, (1, n_channels, n_times // 2 + 1))
assert_equal(psd_multitaper.shape, (1, n_channels, n_times // 2 + 1))
assert_equal(psd_fft.shape, (1, n_channels, n_times // 2 + 1))
# Compare result obtained with `method='fft'` to the Scipy's result
# (implementation of Welch's method with rectangular window):
expected_freqs, expected_psd = signal.welch(data,
sfreq,
window=signal.get_window(
'boxcar', data.shape[-1]),
return_onesided=True,
scaling='density')
assert_almost_equal(expected_freqs, freqs_fft)
assert_almost_equal(expected_psd, psd_fft[0, ...])
def test_power_spectrum():
ps, freqs = power_spectrum(sfreq, data, return_db=False)
_data = data - np.mean(data, axis=-1)[:, None]
assert_almost_equal(np.mean(_data ** 2, axis=-1), np.sum(ps, axis=-1))
raw.filter(.5, None, fir_design='firwin')
###############################################################################
# Estimate the slope (and the intercept) of the PSD. We use here a single
# MEG channel during the full recording to estimate the slope and the
# intercept.
data, _ = raw[0, :2048]
# data = epochs.get_data()[0, 1, :].reshape((1, -1))
sfreq = raw.info['sfreq']
# Compute the (one-sided) PSD using FFT. The ``mask`` variable allows to
# select only the part of the PSD which corresponds to frequencies between
# 0.1Hz and 40Hz (the data used in this example is already low-pass filtered
# at 40Hz).
psd, freqs = power_spectrum(sfreq, data)
mask = np.logical_and(0.1 <= freqs, freqs <= 40)
psd, freqs = psd[0, mask], freqs[mask]
# Estimate the slope (and the intercept) of the PSD. The function
# :func:`compute_spect_slope` assumes that the PSD of the signal is of the
# form: ``psd[f] = b / (f ** a)``. The coefficients a and b are respectively
# called *slope* and *intercept* of the Power Spectral Density. The values of
# the variables ``slope`` and ``intercept`` differ from the values returned
# by ``compute_spect_slope`` because, in the feature function, the linear
# regression fit is done in the log10-log10 scale.
intercept, slope, _, _ = compute_spect_slope(sfreq, data, fmin=1., fmax=40.)
print('The estimated slope (respectively intercept) is: %1.2f (resp. %1.3e)' %
(slope, intercept))
# Plot the PSD together with the ``b / (f ** a)`` curve (estimated decay of