def robust_hilbert(sig, increase_n=False):
"""Compute the Hilbert transform, ignoring any boundaries that are NaN.
Parameters
----------
sig : 1d array
Time series.
increase_n : bool, optional, default: False
If True, zero pad the signal to length the next power of 2 for the Hilbert transform.
This is because :func:`scipy.signal.hilbert` can be very slow for some signal lengths.
Returns
-------
sig_hilb : 1d array
The Hilbert transform of the input signal.
"""
# Extract the signal that is not nan
sig_nonan, sig_nans = remove_nans(sig)
# Compute Hilbert transform of signal without nans
if increase_n:
sig_len = len(sig_nonan)
n_components = 2**(int(np.log2(sig_len)) + 1)
sig_hilb_nonan = hilbert(sig_nonan, n_components)[:sig_len]
else:
sig_hilb_nonan = hilbert(sig_nonan)
# Fill in output hilbert with nans on edges
sig_hilb = restore_nans(sig_hilb_nonan, sig_nans, dtype=complex)
return sig_hilb
def robust_hilbert(sig):
"""Compute the Hilbert transform, ignoring any boundaries that are NaN.
Parameters
----------
sig : 1d array
Time series.
Returns
-------
sig_hilb : 1d array
The analytic signal, of which the imaginary part is the Hilbert transform of the input.
Examples
--------
Compute the analytic signal, using zero padding:
>>> from neurodsp.sim import sim_combined
>>> sig = sim_combined(n_seconds=10, fs=500,
... components={'sim_powerlaw': {}, 'sim_oscillation': {'freq': 10}})
>>> sig_hilb = robust_hilbert(sig)
"""
# Extract the signal that is not nan
sig_nonan, sig_nans = remove_nans(sig)
# Compute Hilbert transform of signal without nans
sig_hilb_nonan = hilbert(sig_nonan)
# Fill in output hilbert with nans on edges
sig_hilb = restore_nans(sig_hilb_nonan, sig_nans, dtype=complex)
return sig_hilb
def freq_by_time(sig, fs, f_range=None, remove_edges=True, **filter_kwargs):
"""Compute the instantaneous frequency of a time series.
Parameters
----------
sig : 1d array
Time series.
fs : float
Sampling rate, in Hz.
f_range : tuple of float or None, optional default: None
Filter range, in Hz, as (low, high). If None, no filtering is applied.
remove_edges : bool, optional, default: True
If True, replace samples that are within half of the filter's length to the edge with nan.
This removes edge artifacts from the filtered signal. Only used if `f_range` is defined.
**filter_kwargs
Keyword parameters to pass to `filter_signal`.
Returns
-------
i_f : 1d array
Instantaneous frequency time series.
Notes
-----
This function assumes monotonic phase, so phase slips will be processed as high frequencies.
Examples
--------
Compute the instantaneous frequency, for the alpha range:
>>> from neurodsp.sim import sim_combined
>>> sig = sim_combined(n_seconds=10, fs=500,
... components={'sim_powerlaw': {}, 'sim_oscillation' : {'freq': 10}})
>>> instant_freq = freq_by_time(sig, fs=500, f_range=(8, 12))
"""
# Calculate instantaneous phase, from which we can compute instantaneous frequency
pha = phase_by_time(sig, fs, f_range, remove_edges, **filter_kwargs)
# If filter edges were removed, temporarily drop nans for subsequent operations
pha, nans = remove_nans(pha)
# Differentiate the unwrapped phase, to estimate frequency as the rate of change of phase
pha_unwrapped = np.unwrap(pha)
pha_diff = np.diff(pha_unwrapped)
# Convert differentiated phase to frequency
i_f = fs * pha_diff / (2 * np.pi)
# Prepend nan value to re-align with original signal (necessary due to differentiation)
i_f = np.insert(i_f, 0, np.nan)
# Restore nans, to re-align signal if filter edges were removed
i_f = restore_nans(i_f, nans)
return i_f
def robust_hilbert(sig, increase_n=False):
"""Compute the Hilbert transform, ignoring any boundaries that are NaN.
Parameters
----------
sig : 1d array
Time series.
increase_n : bool, optional, default: False
If True, zero pad the signal's length to the next power of 2 for the Hilbert transform.
This is because ``scipy.signal.hilbert`` can be very slow for some signal lengths.
Returns
-------
sig_hilb : 1d array
The analytic signal, of which the imaginary part is the Hilbert transform of the input.
Examples
--------
Compute the analytic signal, using zero padding:
>>> from neurodsp.sim import sim_combined
>>> sig = sim_combined(n_seconds=10, fs=500,
... components={'sim_powerlaw': {}, 'sim_oscillation': {'freq': 10}})
>>> sig_hilb = robust_hilbert(sig, increase_n=True)
"""
# Extract the signal that is not nan
sig_nonan, sig_nans = remove_nans(sig)
# Compute Hilbert transform of signal without nans
if increase_n:
sig_len = len(sig_nonan)
n_components = 2**(int(np.log2(sig_len)) + 1)
sig_hilb_nonan = hilbert(sig_nonan, n_components)[:sig_len]
else:
sig_hilb_nonan = hilbert(sig_nonan)
# Fill in output hilbert with nans on edges
sig_hilb = restore_nans(sig_hilb_nonan, sig_nans, dtype=complex)
return sig_hilb