signal_processing  Signal processing¶
Basic processing procedures for analog signals (e.g., performing a zscore of a signal, or filtering a signal).

elephant.signal_processing.
butter
(signal, highpass_freq=None, lowpass_freq=None, order=4, filter_function='filtfilt', fs=1.0, axis=1)[source]¶ Butterworth filtering function for neo.AnalogSignal. Filter type is determined according to how values of highpass_freq and lowpass_freq are given (see Parameters section for details).
Parameters:  signal : AnalogSignal or Quantity array or NumPy ndarray
Time series data to be filtered. When given as Quantity array or NumPy ndarray, the sampling frequency should be given through the keyword argument fs.
 highpass_freq, lowpass_freq : Quantity or float
Highpass and lowpass cutoff frequencies, respectively. When given as float, the given value is taken as frequency in Hz. Filter type is determined depending on values of these arguments:
 highpass_freq only (lowpass_freq = None): highpass filter
 lowpass_freq only (highpass_freq = None): lowpass filter
 highpass_freq < lowpass_freq: bandpass filter
 highpass_freq > lowpass_freq: bandstop filter
 order : int
Order of Butterworth filter. Default is 4.
 filter_function : string
 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 issue https://github.com/NeuralEnsemble/elephant/issues/220). Default is ‘filtfilt’.
 fs : Quantity or float
The sampling frequency of the input time series. When given as float, its value is taken as frequency in Hz. When the input is given as neo AnalogSignal, its attribute is used to specify the sampling frequency and this parameter is ignored. Default is 1.0.
 axis : int
Axis along which filter is applied. Default is 1.
Returns:  filtered_signal : AnalogSignal or Quantity array or NumPy ndarray
Filtered input data. The shape and type is identical to those of the input.
Raises:  ValueError
If filter_function is not one of ‘lfilter’, ‘filtfilt’, or ‘sosfiltfilt’. When both highpass_freq and lowpass_freq are None.

elephant.signal_processing.
cross_correlation_function
(signal, ch_pairs, env=False, nlags=None)[source]¶ Computes unbiased estimator of the crosscorrelation function.
Calculates the unbiased estimator of the crosscorrelation function [1]
where in a pairwise manner, i.e. signal[ch_pairs[0,0]] vs signal2[ch_pairs[0,1]], signal[ch_pairs[1,0]] vs signal2[ch_pairs[1,1]], and so on. The crosscorrelation function is obtained by scipy.signal.fftconvolve. Time series in signal are zscored beforehand. Alternatively returns the Hilbert envelope of , which is useful to determine the correlation length of oscillatory signals.
Parameters:  signal : neo.AnalogSignal (nt x nch)
Signal with nt number of samples that contains nch LFP channels
 ch_pairs : list (or array with shape (n,2))
list with n channel pairs for which to compute crosscorrelation, each element of list must contain 2 channel indices
 env : bool
Return Hilbert envelope of crosscorrelation function Default: False
 nlags : int
Defines number of lags for crosscorrelation function. Float will be rounded to nearest integer. Number of samples of output is 2*nlags+1. If None, number of samples of output is equal to number of samples of input signal, namely nt Default: None
Returns:  cross_corr : neo.AnalogSignal (2*nlag+1 x n)
Pairwise crosscorrelation functions for channel pairs given by ch_pairs. If env=True, the output is the Hilbert envelope of the pairwise crosscorrelation function. This is helpful to compute the correlation length for oscillating crosscorrelation functions
Raises:  ValueError
If the input signal is not a neo.AnalogSignal.
 ValueError
If ch_pairs is not a list of channel pair indices with shape (n,2).
 KeyError
If keyword env is not a boolean.
 KeyError
If nlags is not an integer or float larger than 0.
References
[1] Hall & River (2009) “Spectral Analysis of Signals, Spectral Element Method in Structural Dynamics”, Eq. 2.2.3 Examples
>>> 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 >>> signal = neo.AnalogSignal(x, units='mV', t_start=0.*pq.ms, >>> sampling_rate=1/dt*pq.Hz, dtype=float) >>> rho = elephant.signal_processing.cross_correlation_function( >>> signal, [0,1], nlags=150) >>> env = elephant.signal_processing.cross_correlation_function( >>> signal, [0,1], nlags=150, env=True) >>> plt.plot(rho.times, rho) >>> plt.plot(env.times, env) # should be equal to one >>> plt.show()

elephant.signal_processing.
derivative
(signal)[source]¶ Calculate the derivative of an AnalogSignal.
Parameters:  signal : neo.AnalogSignal
The signal to differentiate. If signal contains more than one channel, each is differentiated separately.
Returns:  neo.AnalogSignal
The returned object is an 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 the input signal is not a neo.AnalogSignal.

elephant.signal_processing.
hilbert
(signal, N='nextpow')[source]¶ Apply a Hilbert transform to an 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) and absolute value (np.abs) of the complex analytic signal, respectively.
By default, the function will zeropad 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() will not terminate.
Parameters:  signal : neo.AnalogSignal
Signal(s) to transform
 N : string or int
 Defines whether the signal is zeropadded.
‘none’: no padding ‘nextpow’: zeropad to the next length that is a power of 2 int: directly specify the length to zeropad to (indicates the
number of Fourier components, see parameter N of scipy.signal.hilbert()).
Default: ‘nextpow’.
Returns:  neo.AnalogSignal
Contains the complex analytic signal(s) corresponding to the input signals. The unit of the analytic signal is dimensionless.

elephant.signal_processing.
rauc
(signal, baseline=None, bin_duration=None, t_start=None, t_stop=None)[source]¶ Calculate the rectified area under the curve (RAUC) for an 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. If the number of bins is 1 (default), a single value is returned for each channel in the input signal. Otherwise, an AnalogSignal containing the values for each bin is returned along with the times of the centers of the bins.
Parameters:  signal : neo.AnalogSignal
The signal to integrate. If signal contains more than one channel, each is integrated separately.
 bin_duration : quantities.Quantity
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
 baseline : string or quantities.Quantity
A factor to subtract from the signal before rectification. If ‘mean’ or ‘median’, the mean or median value of the entire signal is subtracted on a channelbychannel basis. Default: None
 t_start, t_stop : quantities.Quantity
Times to start and end the algorithm. 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:  quantities.Quantity or neo.AnalogSignal
If the number of bins is 1, the returned object is a scalar or vector Quantity containing a single RAUC value for each channel. Otherwise, the returned object is an 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:  TypeError
If the input signal is not a neo.AnalogSignal.
 TypeError
If bin_duration is not None or a Quantity.
 TypeError
If baseline is not None, ‘mean’, ‘median’, or a Quantity.

elephant.signal_processing.
wavelet_transform
(signal, freq, nco=6.0, fs=1.0, zero_padding=True)[source]¶ Compute the wavelet transform of a given signal with Morlet mother wavelet. The parametrization of the wavelet is based on [1].
Parameters:  signal : neo.AnalogSignal or array_like
Time series data to be wavelettransformed. When multidimensional array_like is given, the time axis must be the last dimension of the array_like.
 freq : float or list of floats
Center frequency of the Morlet wavelet in Hz. Multiple center frequencies can be given as a list, in which case the function computes the wavelet transforms for all the given frequencies at once.
 nco : float (optional)
Size of the mother wavelet (approximate number of oscillation cycles within a wavelet; related to the wavelet number w as w ~ 2 pi nco / 6), as defined in [1]. A larger nco value leads to a higher frequency resolution and a lower temporal resolution, and vice versa. Typically used values are in a range of 3  8, but one should be cautious when using a value smaller than ~ 6, in which case the admissibility of the wavelet is not ensured (cf. [2]). Default value is 6.0.
 fs : float (optional)
Sampling rate of the input data in Hz. When signal is given as an AnalogSignal, the sampling frequency is taken from its attribute and this parameter is ignored. Default value is 1.0.
 zero_padding : bool (optional)
Specifies whether the data length is extended to the least power of 2 greater than the original length, by padding zeros to the tail, for speeding up the computation. In the case of True, the extended part is cut out from the final result before returned, so that the output has the same length as the input. Default is True.
Returns:  signal_wt: complex array
Wavelet transform of the input data. When freq was given as a list, the way how the wavelet transforms for different frequencies are returned depends on the input type. When the input was an AnalogSignal of shape (Nt, Nch), where Nt and Nch are the numbers of time points and channels, respectively, the returned array has a shape (Nt, Nch, Nf), where Nf = len(freq), such that the last dimension indexes the frequencies. When the input was an array_like of shape (a, b, …, c, Nt), the returned array has a shape (a, b, …, c, Nf, Nt), such that the second last dimension indexes the frequencies. To summarize, signal_wt.ndim = signal.ndim + 1, with the additional dimension in the last axis (for AnalogSignal input) or the second last axis (for array_like input) indexing the frequencies.
Raises:  ValueError
If freq (or one of the values in freq when it is a list) is greater than the half of fs, or nco is not positive.
References
 Le van Quyen et al. J Neurosci Meth 111:8398 (2001)
 Farge, Annu Rev Fluid Mech 24:395458 (1992)

elephant.signal_processing.
zscore
(signal, inplace=True)[source]¶ Apply a zscore operation to one or several AnalogSignal objects.
The zscore operation subtracts the mean of the signal, and divides by its standard deviation :
If an AnalogSignal containing multiple signals is provided, the ztransform is always calculated for each signal individually.
If a list of AnalogSignal objects is supplied, the mean and standard deviation are calculated across all objects of the list. Thus, all list elements are ztransformed by the same values of and . For AnalogSignals, each signal of the array is treated separately across list elements. Therefore, the number of signals must be identical for each AnalogSignal of the list.
Parameters:  signal : neo.AnalogSignal or list of neo.AnalogSignal
Signals for which to calculate the zscore.
 inplace : bool
If True, the contents of the input signal(s) is replaced by the ztransformed signal. Otherwise, a copy of the original AnalogSignal(s) is returned. Default: True
Returns:  neo.AnalogSignal or list of neo.AnalogSignal
The output format matches the input format: for each supplied AnalogSignal object a corresponding object is returned containing the ztransformed signal with the unit dimensionless.
Examples
>>> a = neo.AnalogSignal( ... np.array([1, 2, 3, 4, 5, 6]).reshape(1,1)*mV, ... t_start=0*s, sampling_rate=1000*Hz)
>>> b = neo.AnalogSignal( ... np.transpose([[1, 2, 3, 4, 5, 6], [11, 12, 13, 14, 15, 16]])*mV, ... t_start=0*s, sampling_rate=1000*Hz)
>>> c = neo.AnalogSignal( ... np.transpose([[21, 22, 23, 24, 25, 26], [31, 32, 33, 34, 35, 36]])*mV, ... t_start=0*s, sampling_rate=1000*Hz)
>>> print zscore(a) [[1.46385011] [0.87831007] [0.29277002] [ 0.29277002] [ 0.87831007] [ 1.46385011]] dimensionless
>>> print zscore(b) [[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
>>> print zscore([b,c]) [<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)>]