def butter(signal,
highpass_freq=None,
lowpass_freq=None,
order=4,
filter_function='filtfilt',
fs=1.0,
axis=-1):
"""
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
High-pass and low-pass cut-off 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.
"""
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'):
fs = signal.sampling_rate.rescale(pq.Hz).magnitude
if isinstance(highpass_freq, pq.quantity.Quantity):
highpass_freq = highpass_freq.rescale(pq.Hz).magnitude
if isinstance(lowpass_freq, pq.quantity.Quantity):
lowpass_freq = lowpass_freq.rescale(pq.Hz).magnitude
Fn = fs / 2.
# filter type is determined according to the values of cut-off
# frequencies
if lowpass_freq and highpass_freq:
if highpass_freq < lowpass_freq:
Wn = (highpass_freq / Fn, lowpass_freq / Fn)
btype = 'bandpass'
else:
Wn = (lowpass_freq / Fn, highpass_freq / Fn)
btype = 'bandstop'
elif lowpass_freq:
Wn = lowpass_freq / Fn
btype = 'lowpass'
elif highpass_freq:
Wn = highpass_freq / Fn
btype = 'highpass'
else:
raise ValueError("Either highpass_freq or lowpass_freq 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)
return signal.duplicate_with_new_data(filtered_data)
elif isinstance(signal, pq.quantity.Quantity):
return filtered_data * signal.units
else:
return filtered_data
def hilbert(signal, N='nextpow'):
'''
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 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() will not terminate.
Parameters
-----------
signal : neo.AnalogSignal
Signal(s) to transform
N : string or int
Defines whether the signal is zero-padded.
'none': no padding
'nextpow': zero-pad to the next length that is a power of 2
int: directly specify the length to zero-pad 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.
Example
-------
Create a sine signal at 5 Hz with increasing amplitude and calculate the
instantaneous phases
>>> t = np.arange(0, 5000) * ms
>>> f = 5. * Hz
>>> a = neo.AnalogSignal(
... np.array(
... (1 + t.magnitude / t[-1].magnitude) * np.sin(
... 2. * np.pi * f * t.rescale(s))).reshape((-1,1))*mV,
... t_start=0*s, sampling_rate=1000*Hz)
>>> analytic_signal = hilbert(a, N='nextpow')
>>> angles = np.angle(analytic_signal)
>>> amplitudes = np.abs(analytic_signal)
>>> print angles
[[-1.57079633]
[-1.51334228]
[-1.46047675]
...,
[-1.73112977]
[-1.68211683]
[-1.62879501]]
>>> plt.plot(t,angles)
'''
# Length of input signals
n_org = signal.shape[0]
# Right-pad signal to desired length using the signal itself
if type(N) == int:
# User defined padding
n = N
elif N == '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 N == 'none':
# No padding
n = n_org
else:
raise ValueError("'{}' is an unknown N.".format(N))
output = signal.duplicate_with_new_data(
scipy.signal.hilbert(signal.magnitude, N=n, axis=0)[:n_org])
return output / output.units
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:
>>> 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)
>>> print(angles)
[[-1.57079633]
[-1.51334228]
[-1.46047675]
...,
[-1.73112977]
[-1.68211683]
[-1.62879501]]
>>> 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
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
>>> 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 with 1 channels of length 5000; units mV; datatype float64
sampling rate: 1000.0 Hz
time: 0.0 s to 5.0 s
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]
(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
elif isinstance(signal, pq.quantity.Quantity):
return filtered_data * signal.units
else:
return filtered_data
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 [1]_).
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.
References
----------
.. [1] https://github.com/NeuralEnsemble/elephant/issues/220
"""
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
elif isinstance(signal, pq.quantity.Quantity):
return filtered_data * signal.units
else:
return filtered_data
def hilbert(signal, N='nextpow'):
'''
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 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() will not terminate.
Parameters
-----------
signal : neo.AnalogSignal
Signal(s) to transform
N : string or int
Defines whether the signal is zero-padded.
'none': no padding
'nextpow': zero-pad to the next length that is a power of 2
int: directly specify the length to zero-pad 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.
Example
-------
Create a sine signal at 5 Hz with increasing amplitude and calculate the
instantaneous phases
>>> t = np.arange(0, 5000) * ms
>>> f = 5. * Hz
>>> a = neo.AnalogSignal(
... np.array(
... (1 + t.magnitude / t[-1].magnitude) * np.sin(
... 2. * np.pi * f * t.rescale(s))).reshape((-1,1))*mV,
... t_start=0*s, sampling_rate=1000*Hz)
>>> analytic_signal = hilbert(a, N='nextpow')
>>> angles = np.angle(analytic_signal)
>>> amplitudes = np.abs(analytic_signal)
>>> print angles
[[-1.57079633]
[-1.51334228]
[-1.46047675]
...,
[-1.73112977]
[-1.68211683]
[-1.62879501]]
>>> plt.plot(t,angles)
'''
# Length of input signals
n_org = signal.shape[0]
# Right-pad signal to desired length using the signal itself
if type(N) == int:
# User defined padding
n = N
elif N == '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 N == 'none':
# No padding
n = n_org
else:
raise ValueError("'{}' is an unknown N.".format(N))
output = signal.duplicate_with_new_data(
scipy.signal.hilbert(signal.magnitude, N=n, axis=0)[:n_org])
return output / output.units
def butter(signal, highpass_freq=None, lowpass_freq=None, order=4,
filter_function='filtfilt', fs=1.0, axis=-1):
"""
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
High-pass and low-pass cut-off 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. Either 'filtfilt'
(`scipy.signal.filtfilt()`) or 'lfilter' (`scipy.signal.lfilter()`). In
most applications 'filtfilt' should be used, because it doesn't bring
about phase shift due to filtering. 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.
"""
def _design_butterworth_filter(Fs, hpfreq=None, lpfreq=None, order=4):
# set parameters for filter design
Fn = Fs / 2.
# - filter type is determined according to the values of cut-off
# frequencies
if lpfreq and hpfreq:
if hpfreq < lpfreq:
Wn = (hpfreq / Fn, lpfreq / Fn)
btype = 'bandpass'
else:
Wn = (lpfreq / Fn, hpfreq / Fn)
btype = 'bandstop'
elif lpfreq:
Wn = lpfreq / Fn
btype = 'lowpass'
elif hpfreq:
Wn = hpfreq / Fn
btype = 'highpass'
else:
raise ValueError(
"Either highpass_freq or lowpass_freq must be given"
)
# return filter coefficients
return scipy.signal.butter(order, Wn, btype=btype)
# design filter
Fs = signal.sampling_rate.rescale(pq.Hz).magnitude \
if hasattr(signal, 'sampling_rate') else fs
Fh = highpass_freq.rescale(pq.Hz).magnitude \
if isinstance(highpass_freq, pq.quantity.Quantity) else highpass_freq
Fl = lowpass_freq.rescale(pq.Hz).magnitude \
if isinstance(lowpass_freq, pq.quantity.Quantity) else lowpass_freq
b, a = _design_butterworth_filter(Fs, Fh, Fl, order)
# 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 is 'lfilter':
filtered_data = scipy.signal.lfilter(b, a, data, axis=axis)
elif filter_function is 'filtfilt':
filtered_data = scipy.signal.filtfilt(b, a, data, axis=axis)
else:
raise ValueError(
"filter_func must to be either 'filtfilt' or 'lfilter'"
)
if isinstance(signal, neo.AnalogSignal):
return signal.duplicate_with_new_data(np.rollaxis(filtered_data, -1, 0))
elif isinstance(signal, pq.quantity.Quantity):
return filtered_data * signal.units
else:
return filtered_data