import numpy as np
[docs]def absolute_band_power(psd, fs, target_band):
"""This method computes the absolute band power of the signal in the given
band using the power spectral density (PSD).
Parameters
----------
psd : numpy array
PSD of the signal with shape [n_epochs, n_samples, n_channels]. Some
of these dimensions may not exist in advance. In these case, create new
axis using np.newaxis. E.g., non-epoched single-channel psd with
shape [n_samples] can be passed to this function with psd[numpy.newaxis,
..., numpy.newaxis]. Afterwards, you may use numpy.squeeze to eliminate
those axes.
fs : int
Sampling frequency of the signal
target_band : numpy 2D array
Frequency band where to calculate the power in Hz. E.g., [8, 13]
Returns
-------
powers : numpy 2D array
RP value for each band, epoch and channel. [n_bands, n_epochs,
n_channels]
"""
# To numpy arrays
psd = np.array(psd)
# Check errors
if len(psd.shape) != 3:
raise Exception('Parameter psd must have shape [n_epochs x n_samples x '
'n_channels]')
# Calculate freqs array
freqs = np.linspace(0, fs/2, psd.shape[1])
# Compute power
psd_target_samp = \
np.logical_and(freqs >= target_band[0], freqs <= target_band[1])
band_power = np.sum(psd[:, psd_target_samp, :], axis=1) * \
(fs / (2 * freqs.shape[0]))
return band_power
[docs]def relative_band_power(psd, fs, target_band, baseline_band=None):
"""This method computes the relative band power of the signal in the given
band using the power spectral density (PSD). Do not use this method on PSDs
that are already normalized! In this case, use absolute_band_power function.
Parameters
----------
psd : numpy array
PSD with shape [n_epochs, n_samples, n_channels]. Some of these
dimensions may not exist in advance. In these case, create new axis
using np.newaxis. E.g., non-epoched single-channel psd with shape
[n_samples] can be passed to this function with psd[numpy.newaxis, ...,
numpy.newaxis]. Afterwards, you may use numpy.squeeze to eliminate
those axes.
fs : int
Sampling frequency of the signal
target_band : numpy nd array
Frequency band where to calculate the power in Hz. E.g., [8, 13]
baseline_band: numpy nd array or None
Frequency band where used as baseline in Hz. Leave to None to normalize
by the whole spectrum, which is preferred in most cases
Returns
-------
powers : numpy 2D array
RP value for each band, epoch and channel. [n_bands, n_epochs,
n_channels]
"""
# To numpy arrays
psd = np.array(psd)
# Check errors
if len(psd.shape) != 3:
raise Exception('Parameter psd must have shape [n_epochs x n_samples x '
'n_channels]')
# Calculate freqs array
freqs = np.linspace(0, fs/2, psd.shape[1])
# Compute power
psd_target_samp = \
np.logical_and(freqs >= target_band[0], freqs <= target_band[1])
psd_baseline_samp = \
np.logical_and(freqs >= baseline_band[0], freqs <= baseline_band[1]) \
if baseline_band is not None else np.ones_like(freqs).astype(int)
band_power = np.sum(psd[:, psd_target_samp, :], axis=1) * \
(fs / (2 * freqs.shape[0]))
baseline_power = np.sum(psd[:, psd_baseline_samp, :], axis=1) * \
(fs / (2 * freqs.shape[0]))
return band_power / baseline_power
[docs]def shannon_spectral_entropy(psd, fs, target_band=(1, 70)):
"""Computes the Shannon spectral entropy of the power spectral density (PSD)
in the given band.
Parameters
----------
psd : numpy array
PSD of the signal with shape [n_epochs, n_samples, n_channels]. Some
of these dimensions may not exist in advance. In these case, create new
axis using np.newaxis. E.g., non-epoched single-channel psd with
shape [n_samples] can be passed to this function with psd[numpy.newaxis,
..., numpy.newaxis]. Afterwards, you may use numpy.squeeze to eliminate
those axes.
fs : int
Sampling frequency of the signal
target_band : numpy array
Frequency band where the SE will be computed. [b1_start, b1_end].
Default [1, 70]
Returns
-------
sample_entropy : numpy 2D array
SE value for each epoch and channel with shape [n_epochs x n_channels].
"""
# To numpy arrays
psd = np.array(psd)
target_band = np.array(target_band)
# Check errors
if len(psd.shape) != 3:
raise ValueError('Parameter psd does not have correct dimensions. '
'Check the documentation for more information.')
if len(target_band.shape) != 1 and target_band.shape[0] != 2:
raise Exception('Parameter band must be an array with the desired '
'band. E.g., Delta: [0, 4]')
# Calculate freqs array
freqs = np.linspace(0, fs/2, psd.shape[1])
# Compute shannon entropy
idx = np.logical_and(freqs >= target_band[0], freqs < target_band[1])
# Calculate total power
total_power = np.sum(psd[:, idx, :], axis=1, keepdims=True)
# Calculate the probability density function
pdf = np.abs(psd[:, idx, :]) / total_power
# Calculate shannon entropy
se = -np.sum(pdf * np.log(pdf), axis=1) / np.log(pdf.shape[1])
return se