def phase_randomize(D, random_state=0):
"""Randomly shift signal phases
For each timecourse (from each voxel and each subject), computes its DFT
and then randomly shifts the phase of each frequency before inverting
back into the time domain. This yields timecourses with the same power
spectrum (and thus the same autocorrelation) as the original timecourses,
but will remove any meaningful temporal relationships between the
timecourses.
This procedure is described in:
Simony E, Honey CJ, Chen J, Lositsky O, Yeshurun Y, Wiesel A, Hasson U
(2016) Dynamic reconfiguration of the default mode network during narrative
comprehension. Nat Commun 7.
Parameters
----------
D : voxel by time by subject ndarray
fMRI data to be phase randomized
random_state : RandomState or an int seed (0 by default)
A random number generator instance to define the state of the
random permutations generator.
Returns
----------
ndarray of same shape as D
phase randomized timecourses
"""
random_state = check_random_state(random_state)
F = fft(D, axis=1)
if D.shape[1] % 2 == 0:
pos_freq = np.arange(1, D.shape[1] // 2)
neg_freq = np.arange(D.shape[1] - 1, D.shape[1] // 2, -1)
else:
pos_freq = np.arange(1, (D.shape[1] - 1) // 2 + 1)
neg_freq = np.arange(D.shape[1] - 1, (D.shape[1] - 1) // 2, -1)
shift = random_state.rand(D.shape[0], len(pos_freq),
D.shape[2]) * 2 * math.pi
# Shift pos and neg frequencies symmetrically, to keep signal real
F[:, pos_freq, :] *= np.exp(1j * shift)
F[:, neg_freq, :] *= np.exp(-1j * shift)
return np.real(ifft(F, axis=1))
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