# -*- coding: utf-8 -*-
"""
Basic processing procedures for time series (e.g., performing a z-score of a
signal, or filtering a signal).
.. autosummary::
:toctree: _toctree/signal_processing
zscore
cross_correlation_function
butter
wavelet_transform
hilbert
rauc
derivative
:copyright: Copyright 2014-2024 by the Elephant team, see `doc/authors.rst`.
:license: Modified BSD, see LICENSE.txt for details.
"""
from __future__ import division, print_function, unicode_literals
import neo
import numpy as np
import quantities as pq
import scipy.signal
from elephant.utils import check_same_units
__all__ = [
"zscore",
"cross_correlation_function",
"butter",
"wavelet_transform",
"hilbert",
"rauc",
"derivative"
]
[docs]
def zscore(signal, inplace=True):
r"""
Apply a z-score operation to one or several `neo.AnalogSignal` objects.
The z-score operation subtracts the mean :math:`\mu` of the signal, and
divides by its standard deviation :math:`\sigma`:
.. math::
Z(x(t)) = \frac{x(t)-\mu}{\sigma}
If a `neo.AnalogSignal` object containing multiple signals is provided,
the z-transform is always calculated for each signal individually.
If a list of `neo.AnalogSignal` objects is supplied, the mean and standard
deviation are calculated across all objects of the list. Thus, all list
elements are z-transformed by the same values of :math:`\\mu` and
:math:`\sigma`. For a `neo.AnalogSignal` that contains multiple signals,
each signal of the array is treated separately across list elements.
Therefore, the number of signals must be identical for each
`neo.AnalogSignal` object of the list.
Parameters
----------
signal : neo.AnalogSignal or list of neo.AnalogSignal
Signals for which to calculate the z-score.
inplace : bool, optional
If True, the contents of the input `signal` is replaced by the
z-transformed signal, if possible, i.e when the signal type is float.
If the signal type is not float, an error is raised.
If False, a copy of the original `signal` is returned.
Default: True
Returns
-------
signal_ztransformed : neo.AnalogSignal or list of neo.AnalogSignal
The output format matches the input format: for each input
`neo.AnalogSignal`, a corresponding `neo.AnalogSignal` is returned,
containing the z-transformed signal with dimensionless unit.
Raises
------
ValueError
If `inplace` is True and the type of `signal` is not float.
Notes
-----
You may supply a list of `neo.AnalogSignal` objects, where each object in
the list contains the data of one trial of the experiment, and each signal
of the `neo.AnalogSignal` corresponds to the recordings from one specific
electrode in a particular trial. In this scenario, you will z-transform
the signal of each electrode separately, but transform all trials of a
given electrode in the same way.
Examples
--------
Z-transform a single `neo.AnalogSignal`, containing only a single signal.
>>> import neo
>>> import numpy as np
>>> import quantities as pq
>>> from elephant.signal_processing import zscore
>>> a = neo.AnalogSignal(
... np.array([1, 2, 3, 4, 5, 6]).reshape(-1,1) * pq.mV,
... t_start=0*pq.s, sampling_rate=1000*pq.Hz)
>>> zscore(a).as_quantity()
array([[-1.46385011],
[-0.87831007],
[-0.29277002],
[ 0.29277002],
[ 0.87831007],
[ 1.46385011]]) * dimensionless
Z-transform a single `neo.AnalogSignal` containing multiple signals.
>>> b = neo.AnalogSignal(
... np.transpose([[1, 2, 3, 4, 5, 6],
... [11, 12, 13, 14, 15, 16]]) * pq.mV,
... t_start=0*pq.s, sampling_rate=1000*pq.Hz)
>>> zscore(b, inplace=False).as_quantity()
array([[-1.46385011, -1.46385011],
[-0.87831007, -0.87831007],
[-0.29277002, -0.29277002],
[ 0.29277002, 0.29277002],
[ 0.87831007, 0.87831007],
[ 1.46385011, 1.46385011]]) * dimensionless
Z-transform a list of `neo.AnalogSignal`, each one containing more than
one signal:
>>> c = neo.AnalogSignal(
... np.transpose([[21, 22, 23, 24, 25, 26],
... [31, 32, 33, 34, 35, 36]]) * pq.mV,
... t_start=0*pq.s, sampling_rate=1000*pq.Hz)
>>> zscore([b, c]) # doctest: +SKIP
[<AnalogSignal(array([[-1.11669108, -1.08361877],
[-1.0672076 , -1.04878252],
[-1.01772411, -1.01394628],
[-0.96824063, -0.97911003],
[-0.91875714, -0.94427378],
[-0.86927366, -0.90943753]]) * dimensionless, [0.0 s, 0.006 s],
sampling rate: 1000.0 Hz)>,
<AnalogSignal(array([[ 0.78170952, 0.84779261],
[ 0.86621866, 0.90728682],
[ 0.9507278 , 0.96678104],
[ 1.03523694, 1.02627526],
[ 1.11974608, 1.08576948],
[ 1.20425521, 1.1452637 ]]) * dimensionless, [0.0 s, 0.006 s],
sampling rate: 1000.0 Hz)>]
"""
# Transform input to a list
if isinstance(signal, neo.AnalogSignal):
signal = [signal]
check_same_units(signal, object_type=neo.AnalogSignal)
# Calculate mean and standard deviation
signal_stacked = np.vstack(signal).magnitude
mean = signal_stacked.mean(axis=0)
std = signal_stacked.std(axis=0)
signal_ztransformed = []
for sig in signal:
# Perform inplace operation only if array is of dtype float.
# Otherwise, raise an error.
if inplace and not np.issubdtype(sig.dtype, np.floating):
raise ValueError(f"Cannot perform inplace operation as the "
f"signal dtype is not float. Source: {sig.name}")
sig_normalized = sig.magnitude.astype(mean.dtype, copy=not inplace)
sig_normalized -= mean
# items where std is zero are already zero
np.divide(sig_normalized, std, out=sig_normalized, where=std != 0)
if inplace:
# Replace unit in the original array by dimensionless
sig._dimensionality = pq.dimensionless.dimensionality
sig_dimless = sig
else:
# Create new object
sig_dimless = sig.duplicate_with_new_data(sig_normalized,
units=pq.dimensionless)
# todo use flag once is fixed
# https://github.com/NeuralEnsemble/python-neo/issues/752
sig_dimless.array_annotate(**sig.array_annotations)
signal_ztransformed.append(sig_dimless)
# Return single object, or list of objects
if len(signal_ztransformed) == 1:
signal_ztransformed = signal_ztransformed[0]
return signal_ztransformed
[docs]
def cross_correlation_function(signal, channel_pairs, hilbert_envelope=False,
n_lags=None, scaleopt='unbiased'):
r"""
Computes an estimator of the cross-correlation function
:cite:`signal-Stoica2005`.
.. math::
R(\tau) = \frac{1}{N-|k|} R'(\tau) \\
where :math:`R'(\tau) = \left<x(t)y(t+\tau)\right>` in a pairwise
manner, i.e.:
`signal[channel_pairs[0,0]]` vs `signal[channel_pairs[0,1]]`,
`signal[channel_pairs[1,0]]` vs `signal[channel_pairs[1,1]]`,
and so on.
The input time series are z-scored beforehand. `scaleopt` controls the
choice of :math:`R_{xy}(\tau)` normalizer. Alternatively, returns the
Hilbert envelope of :math:`R_{xy}(\tau)`, which is useful to determine the
correlation length of oscillatory signals.
Parameters
----------
signal : (nt, nch) neo.AnalogSignal
Signal with `nt` number of samples that contains `nch` LFP channels.
channel_pairs : list or (n, 2) np.ndarray
List with `n` channel pairs for which to compute cross-correlation.
Each element of the list must contain 2 channel indices.
If `np.ndarray`, the second axis must have dimension 2.
hilbert_envelope : bool, optional
If True, returns the Hilbert envelope of cross-correlation function
result.
Default: False
n_lags : int, optional
Defines the number of lags for cross-correlation function. If a `float`
is passed, it will be rounded to the nearest integer. Number of
samples of output is `2*n_lags+1`.
If None, the number of samples of the output is equal to the number of
samples of the input signal (namely `nt`).
Default: None
scaleopt : {'none', 'biased', 'unbiased', 'normalized', 'coeff'}, optional
Normalization option, equivalent to matlab `xcorr(..., scaleopt)`.
Specified as one of the following.
* 'none': raw, unscaled cross-correlation
.. math::
R_{xy}(\tau)
* 'biased': biased estimate of the cross-correlation:
.. math::
R_{xy,biased}(\tau) = \frac{1}{N} R_{xy}(\tau)
* 'unbiased': unbiased estimate of the cross-correlation:
.. math::
R_{xy,unbiased}(\tau) = \frac{1}{N-\tau} R_{xy}(\tau)
* 'normalized' or 'coeff': normalizes the sequence so that the
autocorrelations at zero lag equal 1:
.. math::
R_{xy,coeff}(\tau) = \frac{1}{\sqrt{R_{xx}(0) R_{yy}(0)}}
R_{xy}(\tau)
Default: 'unbiased'
Returns
-------
cross_corr : neo.AnalogSignal
Shape: `[2*n_lags+1, n]`
Pairwise cross-correlation functions for channel pairs given by
`channel_pairs`. If `hilbert_envelope` is True, the output is the
Hilbert envelope of the pairwise cross-correlation function. This is
helpful to compute the correlation length for oscillating
cross-correlation functions.
Raises
------
ValueError
If input `signal` is not a `neo.AnalogSignal`.
If `channel_pairs` is not a list of channel pair indices with shape
`(n,2)`.
If `hilbert_envelope` is not a boolean.
If `n_lags` is not a positive integer.
If `scaleopt` is not one of the predefined above keywords.
Examples
--------
.. plot::
:include-source:
import neo
import numpy as np
import quantities as pq
import matplotlib.pyplot as plt
from elephant.signal_processing import cross_correlation_function
dt = 0.02
N = 2018
f = 0.5
t = np.arange(N)*dt
x = np.zeros((N,2))
x[:,0] = 0.2 * np.sin(2.*np.pi*f*t)
x[:,1] = 5.3 * np.cos(2.*np.pi*f*t)
# Generate neo.AnalogSignals from x and find cross-correlation
signal = neo.AnalogSignal(x, units='mV', t_start=0.*pq.ms,
sampling_rate=1/dt*pq.Hz, dtype=float)
rho = cross_correlation_function(signal, [0,1], n_lags=150)
env = cross_correlation_function(signal, [0,1], n_lags=150,
hilbert_envelope=True)
plt.plot(rho.times, rho)
plt.plot(env.times, env) # should be equal to one
plt.show()
"""
# Make channel_pairs a 2D array
pairs = np.asarray(channel_pairs)
if pairs.ndim == 1:
pairs = np.expand_dims(pairs, axis=0)
# Check input
if not isinstance(signal, neo.AnalogSignal):
raise ValueError('Input signal must be of type neo.AnalogSignal')
if pairs.shape[1] != 2:
raise ValueError("'channel_pairs' is not a list of channel pair "
"indices. Cannot define pairs for cross-correlation.")
if not isinstance(hilbert_envelope, bool):
raise ValueError("'hilbert_envelope' must be a boolean value")
if n_lags is not None:
if not isinstance(n_lags, int) or n_lags <= 0:
raise ValueError('n_lags must be a non-negative integer')
# z-score analog signal and store channel time series in different arrays
# Cross-correlation will be calculated between xsig and ysig
z_transformed = signal.magnitude - signal.magnitude.mean(axis=0)
z_transformed = np.divide(z_transformed, signal.magnitude.std(axis=0),
out=z_transformed,
where=z_transformed != 0)
# transpose (nch, xy, nt) -> (xy, nt, nch)
xsig, ysig = np.transpose(z_transformed.T[pairs], (1, 2, 0))
# Define vector of lags tau
nt, nch = xsig.shape
tau = np.arange(nt) - nt // 2
# Calculate cross-correlation by taking Fourier transform of signal,
# multiply in Fourier space, and transform back. Correct for bias due
# to zero-padding
xcorr = scipy.signal.fftconvolve(xsig, ysig[::-1], mode='same', axes=0)
if scaleopt == 'biased':
xcorr /= nt
elif scaleopt == 'unbiased':
normalizer = np.expand_dims(nt - np.abs(tau), axis=1)
xcorr /= normalizer
elif scaleopt in ('normalized', 'coeff'):
normalizer = np.sqrt((xsig ** 2).sum(axis=0) * (ysig ** 2).sum(axis=0))
xcorr /= normalizer
elif scaleopt != 'none':
raise ValueError("Invalid scaleopt mode: '{}'".format(scaleopt))
# Calculate envelope of cross-correlation function with Hilbert transform.
# This is useful for transient oscillatory signals.
if hilbert_envelope:
xcorr = np.abs(scipy.signal.hilbert(xcorr, axis=0))
# Cut off lags outside the desired range
if n_lags is not None:
tau0 = np.argwhere(tau == 0).item()
xcorr = xcorr[tau0 - n_lags: tau0 + n_lags + 1, :]
# Return neo.AnalogSignal
cross_corr = neo.AnalogSignal(xcorr,
units='',
t_start=tau[0] * signal.sampling_period,
t_stop=tau[-1] * signal.sampling_period,
sampling_rate=signal.sampling_rate,
dtype=float)
return cross_corr
[docs]
def butter(signal, highpass_frequency=None, lowpass_frequency=None, order=4,
filter_function='filtfilt', sampling_frequency=1.0, axis=-1):
"""
Butterworth filtering function for `neo.AnalogSignal`.
Filter type is determined according to how values of `highpass_frequency`
and `lowpass_frequency` are given (see "Parameters" section for details).
Parameters
----------
signal : neo.AnalogSignal or pq.Quantity or np.ndarray
Time series data to be filtered.
If `pq.Quantity` or `np.ndarray`, the sampling frequency should be
given through the keyword argument `fs`.
highpass_frequency : pq.Quantity of float, optional
High-pass cut-off frequency. If `float`, the given value is taken as
frequency in Hz.
Default: None
lowpass_frequency : pq.Quantity or float, optional
Low-pass cut-off frequency. If `float`, the given value is taken as
frequency in Hz.
Filter type is determined depending on the values of
`lowpass_frequency` and `highpass_frequency`:
* `highpass_frequency` only (`lowpass_frequency` is None):
highpass filter
* `lowpass_frequency` only (`highpass_frequency` is None):
lowpass filter
* `highpass_frequency` < `lowpass_frequency`: bandpass filter
* `highpass_frequency` > `lowpass_frequency`: bandstop filter
Default: None
order : int, optional
Order of the Butterworth filter.
Default: 4
filter_function : {'filtfilt', 'lfilter', 'sosfiltfilt'}, optional
Filtering function to be used. Available filters:
* 'filtfilt': `scipy.signal.filtfilt`;
* 'lfilter': `scipy.signal.lfilter`;
* 'sosfiltfilt': `scipy.signal.sosfiltfilt`.
In most applications 'filtfilt' should be used, because it doesn't
bring about phase shift due to filtering. For numerically stable
filtering, in particular higher order filters, use 'sosfiltfilt'
(see https://github.com/NeuralEnsemble/elephant/issues/220).
Default: 'filtfilt'
sampling_frequency : pq.Quantity or float, optional
The sampling frequency of the input time series. When given as
`float`, its value is taken as frequency in Hz. When `signal` is given
as `neo.AnalogSignal`, its attribute is used to specify the sampling
frequency and this parameter is ignored.
Default: 1.0
axis : int, optional
Axis along which filter is applied.
Default: last axis (-1)
Returns
-------
filtered_signal : neo.AnalogSignal or pq.Quantity or np.ndarray
Filtered input data. The shape and type is identical to those of the
input `signal`.
Raises
------
ValueError
If `filter_function` is not one of 'lfilter', 'filtfilt',
or 'sosfiltfilt'.
If both `highpass_frequency` and `lowpass_frequency` are None.
Examples
--------
>>> import neo
>>> import numpy as np
>>> import quantities as pq
>>> from elephant.signal_processing import butter
>>> np.random.seed(0)
>>> noise = neo.AnalogSignal(np.random.normal(size=5000),
... sampling_rate=1000 * pq.Hz, units='mV')
>>> filtered_noise = butter(noise, highpass_frequency=250.0 * pq.Hz)
>>> filtered_noise
<AnalogSignal(array([[-2.70236218e-05],
[-3.44299631e-01],
[-1.36890122e-01],
...,
[ 1.12088277e-01],
[-3.11053132e-01],
[ 2.63563988e-03]]) * mV, [0.0 s, 5.0 s], sampling rate: 1000.0 Hz)>
Let's check that the normal noise power spectrum at zero frequency is close
to zero.
>>> from elephant.spectral import welch_psd
>>> freq, psd = welch_psd(filtered_noise, fs=1000.0)
>>> psd.shape
(1, 556)
>>> freq[0], psd[0, 0] # doctest: +SKIP
(array(0.) * Hz, array(7.21464674e-08) * mV**2/Hz)
"""
available_filters = 'lfilter', 'filtfilt', 'sosfiltfilt'
if filter_function not in available_filters:
raise ValueError("Invalid `filter_function`: {filter_function}. "
"Available filters: {available_filters}".format(
filter_function=filter_function,
available_filters=available_filters))
# design filter
if hasattr(signal, 'sampling_rate'):
sampling_frequency = signal.sampling_rate.rescale(pq.Hz).magnitude
if isinstance(highpass_frequency, pq.quantity.Quantity):
highpass_frequency = highpass_frequency.rescale(pq.Hz).magnitude
if isinstance(lowpass_frequency, pq.quantity.Quantity):
lowpass_frequency = lowpass_frequency.rescale(pq.Hz).magnitude
Fn = sampling_frequency / 2.
# filter type is determined according to the values of cut-off
# frequencies
if lowpass_frequency and highpass_frequency:
if highpass_frequency < lowpass_frequency:
Wn = (highpass_frequency / Fn, lowpass_frequency / Fn)
btype = 'bandpass'
else:
Wn = (lowpass_frequency / Fn, highpass_frequency / Fn)
btype = 'bandstop'
elif lowpass_frequency:
Wn = lowpass_frequency / Fn
btype = 'lowpass'
elif highpass_frequency:
Wn = highpass_frequency / Fn
btype = 'highpass'
else:
raise ValueError(
"Either highpass_frequency or lowpass_frequency must be given"
)
if filter_function == 'sosfiltfilt':
output = 'sos'
else:
output = 'ba'
designed_filter = scipy.signal.butter(order, Wn, btype=btype,
output=output)
# When the input is AnalogSignal, the axis for time index (i.e. the
# first axis) needs to be rolled to the last
data = np.asarray(signal)
if isinstance(signal, neo.AnalogSignal):
data = np.rollaxis(data, 0, len(data.shape))
# apply filter
if filter_function == 'lfilter':
b, a = designed_filter
filtered_data = scipy.signal.lfilter(b=b, a=a, x=data, axis=axis)
elif filter_function == 'filtfilt':
b, a = designed_filter
filtered_data = scipy.signal.filtfilt(b=b, a=a, x=data, axis=axis)
else:
filtered_data = scipy.signal.sosfiltfilt(sos=designed_filter,
x=data, axis=axis)
if isinstance(signal, neo.AnalogSignal):
filtered_data = np.rollaxis(filtered_data, -1, 0)
signal_out = signal.duplicate_with_new_data(filtered_data)
# todo use flag once is fixed
# https://github.com/NeuralEnsemble/python-neo/issues/752
signal_out.array_annotate(**signal.array_annotations)
return signal_out
if isinstance(signal, pq.quantity.Quantity):
return filtered_data * signal.units
return filtered_data
[docs]
def hilbert(signal, padding='nextpow'):
"""
Apply a Hilbert transform to a `neo.AnalogSignal` object in order to
obtain its (complex) analytic signal.
The time series of the instantaneous angle and amplitude can be obtained
as the angle (`np.angle` function) and absolute value (`np.abs` function)
of the complex analytic signal, respectively.
By default, the function will zero-pad the signal to a length
corresponding to the next higher power of 2. This will provide higher
computational efficiency at the expense of memory. In addition, this
circumvents a situation where, for some specific choices of the length of
the input, `scipy.signal.hilbert` function will not terminate.
Parameters
----------
signal : neo.AnalogSignal
Signal(s) to transform.
padding : int, {'none', 'nextpow'}, or None, optional
Defines whether the signal is zero-padded.
The `padding` argument corresponds to `N` in
`scipy.signal.hilbert(signal, N=padding)` function.
If 'none' or None, no padding.
If 'nextpow', zero-pad to the next length that is a power of 2.
If it is an `int`, directly specify the length to zero-pad to
(indicates the number of Fourier components).
Default: 'nextpow'
Returns
-------
neo.AnalogSignal
Contains the complex analytic signal(s) corresponding to the input
`signal`. The unit of the returned `neo.AnalogSignal` is
dimensionless.
Raises
------
ValueError:
If `padding` is not an integer or neither 'nextpow' nor 'none' (None).
Examples
--------
Create a sine signal at 5 Hz with increasing amplitude and calculate the
instantaneous phases:
.. plot::
:include-source:
import neo
import numpy as np
import quantities as pq
import matplotlib.pyplot as plt
from elephant.signal_processing import hilbert
t = np.arange(0, 5000) * pq.ms
f = 5. * pq.Hz
a = neo.AnalogSignal(
np.array(
(1 + t.magnitude / t[-1].magnitude) * np.sin(
2. * np.pi * f * t.rescale(pq.s))).reshape(
(-1,1)) * pq.mV,
t_start=0*pq.s,
sampling_rate=1000*pq.Hz)
analytic_signal = hilbert(a, padding='nextpow')
angles = np.angle(analytic_signal)
amplitudes = np.abs(analytic_signal)
plt.plot(t, angles)
"""
# Length of input signals
n_org = signal.shape[0]
# Right-pad signal to desired length using the signal itself
if isinstance(padding, int):
# User defined padding
n = padding
elif padding == 'nextpow':
# To speed up calculation of the Hilbert transform, make sure we change
# the signal to be of a length that is a power of two. Failure to do so
# results in computations of certain signal lengths to not finish (or
# finish in absurd time). This might be a bug in scipy (0.16), e.g.,
# the following code will not terminate for this value of k:
#
# import numpy
# import scipy.signal
# k=679346
# t = np.arange(0, k) / 1000.
# a = (1 + t / t[-1]) * np.sin(2 * np.pi * 5 * t)
# analytic_signal = scipy.signal.hilbert(a)
#
# For this reason, nextpow is the default setting for now.
n = 2 ** (int(np.log2(n_org - 1)) + 1)
elif padding == 'none' or padding is None:
# No padding
n = n_org
else:
raise ValueError("Invalid padding '{}'.".format(padding))
output = signal.duplicate_with_new_data(
scipy.signal.hilbert(signal.magnitude, N=n, axis=0)[:n_org])
# todo use flag once is fixed
# https://github.com/NeuralEnsemble/python-neo/issues/752
output.array_annotate(**signal.array_annotations)
return output / output.units
[docs]
def rauc(signal, baseline=None, bin_duration=None, t_start=None, t_stop=None):
"""
Calculate the rectified area under the curve (RAUC) for a
`neo.AnalogSignal`.
The signal is optionally divided into bins with duration `bin_duration`,
and the rectified signal (absolute value) is integrated within each bin to
find the area under the curve. The mean or median of the signal or an
arbitrary baseline may optionally be subtracted before rectification.
Parameters
----------
signal : neo.AnalogSignal
The signal to integrate. If `signal` contains more than one channel,
each is integrated separately.
baseline : pq.Quantity or {'mean', 'median'}, optional
A factor to subtract from the signal before rectification.
If 'mean', the mean value of the entire `signal` is subtracted on a
channel-by-channel basis.
If 'median', the median value of the entire `signal` is subtracted on
a channel-by-channel basis.
Default: None
bin_duration : pq.Quantity, optional
The length of time that each integration should span.
If None, there will be only one bin spanning the entire signal
duration.
If `bin_duration` does not divide evenly into the signal duration, the
end of the signal is padded with zeros to accomodate the final,
overextending bin.
Default: None
t_start : pq.Quantity, optional
Time to start the algorithm.
If None, starts at the beginning of `signal`.
Default: None
t_stop : pq.Quantity, optional
Time to end the algorithm.
If None, ends at the last time of `signal`.
The signal is cropped using `signal.time_slice(t_start, t_stop)` after
baseline removal. Useful if you want the RAUC for a short section of
the signal but want the mean or median calculation (`baseline` ='mean'
or `baseline` ='median') to use the entire signal for better baseline
estimation.
Default: None
Returns
-------
pq.Quantity or neo.AnalogSignal
If the number of bins is 1, the returned object is a scalar or
vector `pq.Quantity` containing a single RAUC value for each channel.
Otherwise, the returned object is a `neo.AnalogSignal` containing the
RAUC(s) for each bin stored as a sample, with times corresponding to
the center of each bin. The output signal will have the same number
of channels as the input signal.
Raises
------
ValueError
If `signal` is not `neo.AnalogSignal`.
If `bin_duration` is not None or `pq.Quantity`.
If `baseline` is not None, 'mean', 'median', or `pq.Quantity`.
See Also
--------
neo.AnalogSignal.time_slice : how `t_start` and `t_stop` are used
Examples
--------
>>> import neo
>>> import numpy as np
>>> import quantities as pq
>>> from elephant.signal_processing import rauc
>>> signal = neo.AnalogSignal(np.arange(10), sampling_rate=20 * pq.Hz,
... units='mV')
>>> rauc(signal)
array(2.025) * mV/Hz
"""
if not isinstance(signal, neo.AnalogSignal):
raise ValueError('Input signal is not a neo.AnalogSignal!')
if baseline is None:
pass
elif baseline == 'mean':
# subtract mean from each channel
signal = signal - signal.mean(axis=0)
elif baseline == 'median':
# subtract median from each channel
signal = signal - np.median(signal.as_quantity(), axis=0)
elif isinstance(baseline, pq.Quantity):
# subtract arbitrary baseline
signal = signal - baseline
else:
raise ValueError("baseline must be either None, 'mean', 'median', or "
"a Quantity. Got {}".format(baseline))
# slice the signal after subtracting baseline
signal = signal.time_slice(t_start, t_stop)
if bin_duration is not None:
# from bin duration, determine samples per bin and number of bins
if isinstance(bin_duration, pq.Quantity):
samples_per_bin = int(
np.round(
bin_duration.rescale('s') /
signal.sampling_period.rescale('s')))
n_bins = int(np.ceil(signal.shape[0] / samples_per_bin))
else:
raise ValueError("bin_duration must be a Quantity. Got {}".format(
bin_duration))
else:
# all samples in one bin
samples_per_bin = signal.shape[0]
n_bins = 1
# store the actual bin duration
bin_duration = samples_per_bin * signal.sampling_period
# reshape into equal size bins, padding the end with zeros if necessary
n_channels = signal.shape[1]
sig_binned = signal.as_quantity().copy()
sig_binned.resize(n_bins * samples_per_bin, n_channels, refcheck=False)
sig_binned = sig_binned.reshape(n_bins, samples_per_bin, n_channels)
# rectify and integrate over each bin
rauc = np.trapz(np.abs(sig_binned), dx=signal.sampling_period, axis=1)
if n_bins == 1:
# return a single value for each channel
return rauc.squeeze()
# return an AnalogSignal with times corresponding to center of each bin
t_start = signal.t_start.rescale(bin_duration.units) + bin_duration / 2
rauc_sig = neo.AnalogSignal(rauc, t_start=t_start,
sampling_period=bin_duration)
return rauc_sig
[docs]
def derivative(signal):
"""
Calculate the derivative of a `neo.AnalogSignal`.
Parameters
----------
signal : neo.AnalogSignal
The signal to differentiate. If `signal` contains more than one
channel, each is differentiated separately.
Returns
-------
derivative_sig : neo.AnalogSignal
The returned object is a `neo.AnalogSignal` containing the differences
between each successive sample value of the input signal divided by
the sampling period. Times are centered between the successive samples
of the input. The output signal will have the same number of channels
as the input signal.
Raises
------
TypeError
If `signal` is not a `neo.AnalogSignal`.
Examples
--------
>>> import neo
>>> import numpy as np
>>> import quantities as pq
>>> from elephant.signal_processing import derivative
>>> signal = neo.AnalogSignal([0, 3, 4, 11, -1], sampling_rate=1 * pq.Hz,
... units='mV')
>>> print(derivative(signal))
[[ 3.]
[ 1.]
[ 7.]
[-12.]] mV*Hz
"""
if not isinstance(signal, neo.AnalogSignal):
raise TypeError('Input signal is not a neo.AnalogSignal!')
derivative_sig = neo.AnalogSignal(
np.diff(signal.as_quantity(), axis=0) / signal.sampling_period,
t_start=signal.t_start + signal.sampling_period / 2,
sampling_period=signal.sampling_period)
return derivative_sig
