def test_axis_reverse(self):
a = np.arange(12).reshape(3, 4)
r = axis_reverse(a, axis=0)
assert_array_equal(r, a[::-1, :])
r = axis_reverse(a, axis=1)
assert_array_equal(r, a[:, ::-1])
def test_axis_reverse(self):
a = np.arange(12).reshape(3, 4)
r = axis_reverse(a, axis=0)
assert_array_equal(r, a[::-1, :])
r = axis_reverse(a, axis=1)
assert_array_equal(r, a[:, ::-1])
def _sosfiltfilt(sos, x, axis=-1, padtype='odd', padlen=None, method='pad', irlen=None):
"""Filtfilt version using Second Order sections. Code is taken from scipy.signal.filtfilt and adapted to make it work with SOS.
Note that broadcasting does not work.
"""
from scipy.signal import sosfilt_zi
from scipy.signal._arraytools import odd_ext, axis_slice, axis_reverse
x = np.asarray(x)
if padlen is None:
edge = 0
else:
edge = padlen
# x's 'axis' dimension must be bigger than edge.
if x.shape[axis] <= edge:
raise ValueError("The length of the input vector x must be at least "
"padlen, which is %d." % edge)
if padtype is not None and edge > 0:
# Make an extension of length `edge` at each
# end of the input array.
if padtype == 'even':
ext = even_ext(x, edge, axis=axis)
elif padtype == 'odd':
ext = odd_ext(x, edge, axis=axis)
else:
ext = const_ext(x, edge, axis=axis)
else:
ext = x
# Get the steady state of the filter's step response.
zi = sosfilt_zi(sos)
# Reshape zi and create x0 so that zi*x0 broadcasts
# to the correct value for the 'zi' keyword argument
# to lfilter.
#zi_shape = [1] * x.ndim
#zi_shape[axis] = zi.size
#zi = np.reshape(zi, zi_shape)
x0 = axis_slice(ext, stop=1, axis=axis)
# Forward filter.
(y, zf) = sosfilt(sos, ext, axis=axis, zi=zi * x0)
# Backward filter.
# Create y0 so zi*y0 broadcasts appropriately.
y0 = axis_slice(y, start=-1, axis=axis)
(y, zf) = sosfilt(sos, axis_reverse(y, axis=axis), axis=axis, zi=zi * y0)
# Reverse y.
y = axis_reverse(y, axis=axis)
if edge > 0:
# Slice the actual signal from the extended signal.
y = axis_slice(y, start=edge, stop=-edge, axis=axis)
return y
def _sosfiltfilt(sos, x, axis=-1, padtype='odd', padlen=None, method='pad', irlen=None):
"""Filtfilt version using Second Order sections. Code is taken from scipy.signal.filtfilt and adapted to make it work with SOS.
Note that broadcasting does not work.
"""
from scipy.signal import sosfilt_zi
from scipy.signal._arraytools import odd_ext, axis_slice, axis_reverse
x = np.asarray(x)
if padlen is None:
edge = 0
else:
edge = padlen
# x's 'axis' dimension must be bigger than edge.
if x.shape[axis] <= edge:
raise ValueError("The length of the input vector x must be at least "
"padlen, which is %d." % edge)
if padtype is not None and edge > 0:
# Make an extension of length `edge` at each
# end of the input array.
if padtype == 'even':
ext = even_ext(x, edge, axis=axis)
elif padtype == 'odd':
ext = odd_ext(x, edge, axis=axis)
else:
ext = const_ext(x, edge, axis=axis)
else:
ext = x
# Get the steady state of the filter's step response.
zi = sosfilt_zi(sos)
# Reshape zi and create x0 so that zi*x0 broadcasts
# to the correct value for the 'zi' keyword argument
# to lfilter.
#zi_shape = [1] * x.ndim
#zi_shape[axis] = zi.size
#zi = np.reshape(zi, zi_shape)
x0 = axis_slice(ext, stop=1, axis=axis)
# Forward filter.
(y, zf) = sosfilt(sos, ext, axis=axis, zi=zi * x0)
# Backward filter.
# Create y0 so zi*y0 broadcasts appropriately.
y0 = axis_slice(y, start=-1, axis=axis)
(y, zf) = sosfilt(sos, axis_reverse(y, axis=axis), axis=axis, zi=zi * y0)
# Reverse y.
y = axis_reverse(y, axis=axis)
if edge > 0:
# Slice the actual signal from the extended signal.
y = axis_slice(y, start=edge, stop=-edge, axis=axis)
return y
def butter_bandpass_sosfiltfilt(self,
lowcut=None,
highcut=None,
accel_axis="z",
order=5,
axis=-1,
padtype="odd",
padlen=None,
method='pad',
irlen=None):
'''Filtfilt version using Second Order sections. Code is taken from scipy.signal.filtfilt and adapted to make it work with
sos. Note that broadcasting does not work'''
data = np.asarray(getattr(self.df, accel_axis[:]))
sos = self.butter_bandpass(lowcut, highcut, order)
if padlen is None:
edge = 0
else:
edge = padlen
if data.shape[axis] <= edge:
raise ValueError(
"The length of the input vector x must be at least padlen, which is %d."
% edge)
if padtype is not None and edge > 0:
if padtype == "even":
ext = even_ext(data, edge, axis=axis)
elif padtype == "odd":
ext = odd_ext(data, edge, axis=axis)
else:
ext = const_ext(data, edge, axis=axis)
else:
ext = data
# Get the steady state of the filter's first step resopnse
zi = sosfilt_zi(sos)
# Reshape zi and create x0 so that zi*x0 broadcasts to the correct value for the zi keyword argument to lfilter
x0 = axis_slice(ext, stop=1, axis=axis)
# Forward filter
(y, zf) = sosfilt(sos, ext, axis=axis, zi=zi * x0)
y0 = axis_slice(y, start=-1, axis=axis)
# Backward filter
(y, zf) = sosfilt(sos,
axis_reverse(y, axis=axis),
axis=axis,
zi=zi * y0)
y = axis_reverse(y, axis=axis)
if edge > 0:
y = axis_slice(y, start=edge, stop=-edge, axis=axis)
return y
def sosfiltfilt(sos, x, axis=-1, padtype="odd", padlen=0):
x = asarray(x)
# `method` is "pad"
if padtype not in ["even", "odd", "constant", None]:
raise ValueError(
("Unknown value '%s' given to padtype. padtype " "must be 'even', 'odd', 'constant', or None.") % padtype
)
if padtype is None:
padlen = 0
if padlen is None:
edge = sos.shape[0] * 6
else:
edge = padlen
# x's 'axis' dimension must be bigger than edge.
if x.shape[axis] <= edge:
raise ValueError("The length of the input vector x must be at least " "padlen, which is %d." % edge)
if padtype is not None and edge > 0:
# Make an extension of length `edge` at each
# end of the input array.
if padtype == "even":
ext = even_ext(x, edge, axis=axis)
elif padtype == "odd":
ext = odd_ext(x, edge, axis=axis)
else:
ext = const_ext(x, edge, axis=axis)
else:
ext = x
# Get the steady state of the filter's step response.
zi = sosfilt_zi(sos)
# Reshape zi and create x0 so that zi*x0 broadcasts
# to the correct value for the 'zi' keyword argument
# to lfilter.
zi_shape = [1] * x.ndim
zi_shape[axis] = zi.size
zi = reshape(zi, zi_shape)
x0 = axis_slice(ext, stop=1, axis=axis)
zix0 = reshape(zi * x0, (sos.shape[0], 2))
# Forward filter
(y, zf) = sosfilt(sos, ext, axis=axis, zi=zix0)
# Backward filter
# Create y0 so zi*y0 broadcasts appropriately.
y0 = axis_slice(y, start=-1, axis=axis)
ziy0 = reshape(zi * y0, (sos.shape[0], 2))
(y, zf) = sosfilt(sos, axis_reverse(y, axis=axis), axis=axis, zi=ziy0)
# Reverse y
y = axis_reverse(y, axis=axis)
if edge > 0:
# Slice the actual signal from the extended signal.
y = axis_slice(y, start=edge, stop=-edge, axis=axis)
return y
def sosfiltfilt(sos, x, axis=-1, padtype='odd', padlen=0):
x = asarray(x)
# `method` is "pad"
if padtype not in ['even', 'odd', 'constant', None]:
raise ValueError(("Unknown value '%s' given to padtype. padtype "
"must be 'even', 'odd', 'constant', or None.") %
padtype)
if padtype is None:
padlen = 0
if padlen is None:
edge = sos.shape[0] * 6
else:
edge = padlen
# x's 'axis' dimension must be bigger than edge.
if x.shape[axis] <= edge:
raise ValueError("The length of the input vector x must be at least "
"padlen, which is %d." % edge)
if padtype is not None and edge > 0:
# Make an extension of length `edge` at each
# end of the input array.
if padtype == 'even':
ext = even_ext(x, edge, axis=axis)
elif padtype == 'odd':
ext = odd_ext(x, edge, axis=axis)
else:
ext = const_ext(x, edge, axis=axis)
else:
ext = x
# Get the steady state of the filter's step response.
zi = sosfilt_zi(sos)
# Reshape zi and create x0 so that zi*x0 broadcasts
# to the correct value for the 'zi' keyword argument
# to lfilter.
zi_shape = [1] * x.ndim
zi_shape[axis] = zi.size
zi = reshape(zi, zi_shape)
x0 = axis_slice(ext, stop=1, axis=axis)
zix0 = reshape(zi * x0, (sos.shape[0], 2))
# Forward filter
(y, zf) = sosfilt(sos, ext, axis=axis, zi=zix0)
# Backward filter
# Create y0 so zi*y0 broadcasts appropriately.
y0 = axis_slice(y, start=-1, axis=axis)
ziy0 = reshape(zi * y0, (sos.shape[0], 2))
(y, zf) = sosfilt(sos, axis_reverse(y, axis=axis), axis=axis, zi=ziy0)
# Reverse y
y = axis_reverse(y, axis=axis)
if edge > 0:
# Slice the actual signal from the extended signal.
y = axis_slice(y, start=edge, stop=-edge, axis=axis)
return y
def filtfilt(b, a, x, axis=-1, padtype='odd', padlen=None):
"""
A forward-backward filter.
This function applies a linear filter twice, once forward
and once backwards. The combined filter has linear phase.
Before applying the filter, the function can pad the data along the
given axis in one of three ways: odd, even or constant. The odd
and even extensions have the corresponding symmetry about the end point
of the data. The constant extension extends the data with the values
at end points. On both the forward and backwards passes, the
initial condition of the filter is found by using `lfilter_zi` and
scaling it by the end point of the extended data.
Parameters
----------
b : (N,) array_like
The numerator coefficient vector of the filter.
a : (N,) array_like
The denominator coefficient vector of the filter. If a[0]
is not 1, then both a and b are normalized by a[0].
x : array_like
The array of data to be filtered.
axis : int, optional
The axis of `x` to which the filter is applied.
Default is -1.
padtype : str or None, optional
Must be 'odd', 'even', 'constant', or None. This determines the
type of extension to use for the padded signal to which the filter
is applied. If `padtype` is None, no padding is used. The default
is 'odd'.
padlen : int or None, optional
The number of elements by which to extend `x` at both ends of
`axis` before applying the filter. This value must be less than
`x.shape[axis]-1`. `padlen=0` implies no padding.
The default value is 3*max(len(a),len(b)).
Returns
-------
y : ndarray
The filtered output, an array of type numpy.float64 with the same
shape as `x`.
See Also
--------
lfilter_zi, lfilter
Examples
--------
First we create a one second signal that is the sum of two pure sine
waves, with frequencies 5 Hz and 250 Hz, sampled at 2000 Hz.
>>> t = np.linspace(0, 1.0, 2001)
>>> xlow = np.sin(2 * np.pi * 5 * t)
>>> xhigh = np.sin(2 * np.pi * 250 * t)
>>> x = xlow + xhigh
Now create a lowpass Butterworth filter with a cutoff of 0.125 times
the Nyquist rate, or 125 Hz, and apply it to x with filtfilt. The
result should be approximately xlow, with no phase shift.
>>> from scipy import signal
>>> b, a = signal.butter(8, 0.125)
>>> y = filtfilt(b, a, x, padlen=150)
>>> print('%.5g' % np.abs(y - xlow).max())
9.1086e-06
We get a fairly clean result for this artificial example because
the odd extension is exact, and with the moderately long padding,
the filter's transients have dissipated by the time the actual data
is reached. In general, transient effects at the edges are
unavoidable.
"""
if padtype not in ['even', 'odd', 'constant', None]:
raise ValueError(("Unknown value '%s' given to padtype. padtype must "
"be 'even', 'odd', 'constant', or None.") %
padtype)
b = np.asarray(b)
a = np.asarray(a)
x = np.asarray(x)
ntaps = max(len(a), len(b))
if padtype is None:
padlen = 0
if padlen is None:
# Original padding; preserved for backwards compatibility.
edge = ntaps * 3
else:
edge = padlen
# x's 'axis' dimension must be bigger than edge.
if x.shape[axis] <= edge:
raise ValueError("The length of the input vector x must be at least "
"padlen, which is %d." % edge)
if padtype is not None and edge > 0:
# Make an extension of length `edge` at each
# end of the input array.
if padtype == 'even':
ext = even_ext(x, edge, axis=axis)
elif padtype == 'odd':
ext = odd_ext(x, edge, axis=axis)
else:
ext = const_ext(x, edge, axis=axis)
else:
ext = x
# Get the steady state of the filter's step response.
zi = lfilter_zi(b, a)
# Reshape zi and create x0 so that zi*x0 broadcasts
# to the correct value for the 'zi' keyword argument
# to lfilter.
zi_shape = [1] * x.ndim
zi_shape[axis] = zi.size
zi = np.reshape(zi, zi_shape)
x0 = axis_slice(ext, stop=1, axis=axis)
# Forward filter.
(y, zf) = lfilter(b, a, ext, axis=axis, zi=zi * x0)
# Backward filter.
# Create y0 so zi*y0 broadcasts appropriately.
y0 = axis_slice(y, start=-1, axis=axis)
(y, zf) = lfilter(b, a, axis_reverse(y, axis=axis), axis=axis, zi=zi * y0)
# Reverse y.
y = axis_reverse(y, axis=axis)
if edge > 0:
# Slice the actual signal from the extended signal.
y = axis_slice(y, start=edge, stop=-edge, axis=axis)
return y
def filtfilt(b, a, x, axis=-1, padtype='odd', padlen=None):
"""
A forward-backward filter.
This function applies a linear filter twice, once forward
and once backwards. The combined filter has linear phase.
Before applying the filter, the function can pad the data along the
given axis in one of three ways: odd, even or constant. The odd
and even extensions have the corresponding symmetry about the end point
of the data. The constant extension extends the data with the values
at end points. On both the forward and backwards passes, the
initial condition of the filter is found by using `lfilter_zi` and
scaling it by the end point of the extended data.
Parameters
----------
b : (N,) array_like
The numerator coefficient vector of the filter.
a : (N,) array_like
The denominator coefficient vector of the filter. If a[0]
is not 1, then both a and b are normalized by a[0].
x : array_like
The array of data to be filtered.
axis : int, optional
The axis of `x` to which the filter is applied.
Default is -1.
padtype : str or None, optional
Must be 'odd', 'even', 'constant', or None. This determines the
type of extension to use for the padded signal to which the filter
is applied. If `padtype` is None, no padding is used. The default
is 'odd'.
padlen : int or None, optional
The number of elements by which to extend `x` at both ends of
`axis` before applying the filter. This value must be less than
`x.shape[axis]-1`. `padlen=0` implies no padding.
The default value is 3*max(len(a),len(b)).
Returns
-------
y : ndarray
The filtered output, an array of type numpy.float64 with the same
shape as `x`.
See Also
--------
lfilter_zi, lfilter
Examples
--------
First we create a one second signal that is the sum of two pure sine
waves, with frequencies 5 Hz and 250 Hz, sampled at 2000 Hz.
>>> t = np.linspace(0, 1.0, 2001)
>>> xlow = np.sin(2 * np.pi * 5 * t)
>>> xhigh = np.sin(2 * np.pi * 250 * t)
>>> x = xlow + xhigh
Now create a lowpass Butterworth filter with a cutoff of 0.125 times
the Nyquist rate, or 125 Hz, and apply it to x with filtfilt. The
result should be approximately xlow, with no phase shift.
>>> from scipy import signal
>>> b, a = signal.butter(8, 0.125)
>>> y = filtfilt(b, a, x, padlen=150)
>>> print('%.5g' % np.abs(y - xlow).max())
9.1086e-06
We get a fairly clean result for this artificial example because
the odd extension is exact, and with the moderately long padding,
the filter's transients have dissipated by the time the actual data
is reached. In general, transient effects at the edges are
unavoidable.
"""
if padtype not in ['even', 'odd', 'constant', None]:
raise ValueError(
("Unknown value '%s' given to padtype. padtype must "
"be 'even', 'odd', 'constant', or None.") % padtype)
b = np.asarray(b)
a = np.asarray(a)
x = np.asarray(x)
ntaps = max(len(a), len(b))
if padtype is None:
padlen = 0
if padlen is None:
# Original padding; preserved for backwards compatibility.
edge = ntaps * 3
else:
edge = padlen
# x's 'axis' dimension must be bigger than edge.
if x.shape[axis] <= edge:
raise ValueError(
"The length of the input vector x must be at least "
"padlen, which is %d." % edge)
if padtype is not None and edge > 0:
# Make an extension of length `edge` at each
# end of the input array.
if padtype == 'even':
ext = even_ext(x, edge, axis=axis)
elif padtype == 'odd':
ext = odd_ext(x, edge, axis=axis)
else:
ext = const_ext(x, edge, axis=axis)
else:
ext = x
# Get the steady state of the filter's step response.
zi = lfilter_zi(b, a)
# Reshape zi and create x0 so that zi*x0 broadcasts
# to the correct value for the 'zi' keyword argument
# to lfilter.
zi_shape = [1] * x.ndim
zi_shape[axis] = zi.size
zi = np.reshape(zi, zi_shape)
x0 = axis_slice(ext, stop=1, axis=axis)
# Forward filter.
(y, zf) = lfilter(b, a, ext, axis=axis, zi=zi * x0)
# Backward filter.
# Create y0 so zi*y0 broadcasts appropriately.
y0 = axis_slice(y, start=-1, axis=axis)
(y, zf) = lfilter(b,
a,
axis_reverse(y, axis=axis),
axis=axis,
zi=zi * y0)
# Reverse y.
y = axis_reverse(y, axis=axis)
if edge > 0:
# Slice the actual signal from the extended signal.
y = axis_slice(y, start=edge, stop=-edge, axis=axis)
return y
def sosfiltfilt(sos, x, axis=-1, padtype='odd', padlen=None):
"""
A forward-backward filter using cascaded second-order sections.
See `filtfilt` for more complete information about this method.
Parameters
----------
sos : array_like
Array of second-order filter coefficients, must have shape
``(n_sections, 6)``. Each row corresponds to a second-order
section, with the first three columns providing the numerator
coefficients and the last three providing the denominator
coefficients.
x : array_like
The array of data to be filtered.
axis : int, optional
The axis of `x` to which the filter is applied.
Default is -1.
padtype : str or None, optional
Must be 'odd', 'even', 'constant', or None. This determines the
type of extension to use for the padded signal to which the filter
is applied. If `padtype` is None, no padding is used. The default
is 'odd'.
padlen : int or None, optional
The number of elements by which to extend `x` at both ends of
`axis` before applying the filter. This value must be less than
``x.shape[axis] - 1``. ``padlen=0`` implies no padding.
The default value is::
3 * (2 * len(sos) + 1 - min((sos[:, 2] == 0).sum(),
(sos[:, 5] == 0).sum()))
The extra subtraction at the end attempts to compensate for poles
and zeros at the origin (e.g. for odd-order filters) to yield
equivalent estimates of `padlen` to those of `filtfilt` for
second-order section filters built with `scipy.signal` functions.
Returns
-------
y : ndarray
The filtered output with the same shape as `x`.
See Also
--------
filtfilt, sosfilt, sosfilt_zi
Notes
-----
.. versionadded:: 0.18.0
"""
sos, n_sections = _validate_sos(sos)
# `method` is "pad"...
ntaps = 2 * n_sections + 1
ntaps -= min((sos[:, 2] == 0).sum(), (sos[:, 5] == 0).sum())
edge, ext = _validate_pad(padtype, padlen, x, axis, ntaps=ntaps)
# These steps follow the same form as filtfilt with modifications
zi = sosfilt_zi(sos) # shape (n_sections, 2) --> (n_sections, ..., 2, ...)
zi_shape = [1] * x.ndim
zi_shape[axis] = 2
zi.shape = [n_sections] + zi_shape
x_0 = axis_slice(ext, stop=1, axis=axis)
(y, zf) = sosfilt(sos, ext, axis=axis, zi=zi * x_0)
y_0 = axis_slice(y, start=-1, axis=axis)
(y, zf) = sosfilt(sos, axis_reverse(y, axis=axis), axis=axis, zi=zi * y_0)
y = axis_reverse(y, axis=axis)
if edge > 0:
y = axis_slice(y, start=edge, stop=-edge, axis=axis)
return y