def average_err(x, window=5):
"""
Generate a moving (boxcar) average and variance of the time-series, x, using
the specified window size.
Parameters
----------
x: ndarray,
The time-series of data to bandpass filter.
cutoff: float,
The period at which the bandpass filter will apply the cutoff.
Units are same as the time-step of the signal provided (e.g., if the
data are provided every hour, then a cutoff=12 would be a 12 hour
cutoff.)
Returns
-------
x, variance: ndarray, ndarray
Returns the moving average of x with the moving variance of the
average window
Examples
--------
Create data every 30 minutes for 3 days with time in days:
>>> t = np.linspace(0, 3.0, 2 * 24 * 3.0, endpoint=False)
>>> x = 0.1 * np.sin(2 * np.pi / .008 * t)
>>> x += 0.2 * np.cos(2 * np.pi / 0.6 * t + 0.1)
>>> x += 0.2 * np.cos(2 * np.pi / 1.6 * t + .11)
>>> x += 1 * np.cos(2 * np.pi / 10 * t + 11)
Average the data over 6 hour period
>>> nx, err = average_err(x, window=12)
>>> plt.plot(t, x, 'k', t, nx, 'r', label=['Raw', 'Average'])
>>> plt.figure()
>>> plt.plot(t, err, 'g', label='Variance')
"""
x = np.atleast_1d(x).flatten()
nx = np.ma.masked_all(x.shape)
err = np.ma.masked_all(x.shape)
filt = np.ones(window) / window
padlen = window * 4
# Go over all contiguous regions
regions = seapy.contiguous(x)
for r in regions:
if ((r.stop - r.start) >= padlen):
nx[r] = scipy.signal.filtfilt(filt, [1.0],
x[r],
padlen=padlen,
axis=0)
err[r] = scipy.signal.filtfilt(filt, [1.0], (nx[r] - x[r])**2,
padlen=padlen,
axis=0)
return nx, err
def average_err(x, window=5):
"""
Generate a moving (boxcar) average and variance of the time-series, x, using
the specified window size.
Parameters
----------
x: ndarray,
The time-series of data to bandpass filter.
cutoff: float,
The period at which the bandpass filter will apply the cutoff.
Units are same as the time-step of the signal provided (e.g., if the
data are provided every hour, then a cutoff=12 would be a 12 hour
cutoff.)
Returns
-------
x, variance: ndarray, ndarray
Returns the moving average of x with the moving variance of the
average window
Examples
--------
Create data every 30 minutes for 3 days with time in days:
>>> t = np.linspace(0, 3.0, 2 * 24 * 3.0, endpoint=False)
>>> x = 0.1 * np.sin(2 * np.pi / .008 * t)
>>> x += 0.2 * np.cos(2 * np.pi / 0.6 * t + 0.1)
>>> x += 0.2 * np.cos(2 * np.pi / 1.6 * t + .11)
>>> x += 1 * np.cos(2 * np.pi / 10 * t + 11)
Average the data over 6 hour period
>>> nx, err = average_err(x, window=12)
>>> plt.plot(t, x, 'k', t, nx, 'r', label=['Raw', 'Average'])
>>> plt.figure()
>>> plt.plot(t, err, 'g', label='Variance')
"""
x = np.atleast_1d(x).flatten()
nx = np.ma.masked_all(x.shape)
err = np.ma.masked_all(x.shape)
filt = np.ones(window) / window
padlen = window * 4
# Go over all contiguous regions
regions = seapy.contiguous(x)
for r in regions:
if ((r.stop - r.start) >= padlen):
nx[r] = scipy.signal.filtfilt(
filt, [1.0], x[r], padlen=padlen, axis=0)
err[r] = scipy.signal.filtfilt(
filt, [1.0], (nx[r] - x[r])**2, padlen=padlen, axis=0)
return nx, err
def bandpass(x, dt, low_cutoff=None, hi_cutoff=None, order=7):
"""
Perform a bandpass filter at the cutoff period (same units as the
time-series step).
Parameters
----------
x : ndarray,
The time-series of data to bandpass filter.
dt : float,
The time-step between the values in x. Units must be consistent
with the cutoff period.
low_cutoff: float,
The period at which the bandpass filter will apply the lowpass filter.
Units are same as the time-step of the signal provided (e.g., if the
data are provided every hour, then a cutoff=12 would be a 12 hour
cutoff.) Everything that has a longer period will remain. If you only
want a hi-pass filter, this value should be None.
hi_cutoff: float,
The period at which the bandpass filter will apply the high-pass filter.
Units are same as the time-step of the signal provided (e.g., if the
data are provided every hour, then a cutoff=12 would be a 12 hour
cutoff.) Everything that has a shorter period will remain. If you only
want a low-pass filter, this value should be None.
order: int optional,
The order of the filter to apply
Returns
-------
x : ndarray
The bandpass filtered time-series
Examples
--------
Create data every 30 minutes for 3 days with time in days:
>>> t = np.linspace(0, 3.0, 2 * 24 * 3.0, endpoint=False)
>>> x = 0.1 * np.sin(2 * np.pi / .008 * t)
>>> x += 0.2 * np.cos(2 * np.pi / 0.6 * t + 0.1)
>>> x += 0.2 * np.cos(2 * np.pi / 1.6 * t + .11)
>>> x += 1 * np.cos(2 * np.pi / 10 * t + 11)
Filter the data to low-pass everything longer than the 1 day period
>>> nx = bandpass(x, dt=0.5, low_cutoff=24 )
>>> plt.plot(t, x, 'k', t, nx, 'r', label=['Raw', 'Filter'])
Filter the data to low-pass everything longer the 2 day period
>>> nx = bandpass(x, dt=0.5, low_cutoff=48 )
>>> plt.plot(t, x, 'k', t, nx, 'r', label=['Raw', 'Filter'])
Filter the data to band-pass everything shorter the 2 day period
and longer the 1 hour period
>>> nx = bandpass(x, dt=0.5, low_cutoff=48, hi_cutoff=1 )
>>> plt.plot(t, x, 'k', t, nx, 'r', label=['Raw', 'Filter'])
"""
x = np.ma.array(np.atleast_1d(x).flatten(), copy=False)
nx = np.ma.masked_all(x.shape)
if low_cutoff and hi_cutoff:
freq = 2.0 * dt / np.array([hi_cutoff, low_cutoff])
btype = 'bandpass'
elif low_cutoff:
freq = 2.0 * dt / low_cutoff
btype = 'lowpass'
elif hi_cutoff:
freq = 2.0 * dt / hi_cutoff
btype = 'highpass'
else:
raise AttributeError("You must specify either low or hi cutoff.")
b, a = scipy.signal.butter(order, freq, btype=btype)
padlen = max(len(a), len(b))
# Go over all contiguous regions
regions = seapy.contiguous(x)
for r in regions:
if ((r.stop - r.start) >= padlen):
nx[r] = scipy.signal.filtfilt(
b, a, x[r], padlen=5 * padlen, axis=0)
return nx
def bandpass(x, dt, low_cutoff=None, hi_cutoff=None, order=7):
"""
Perform a bandpass filter at the cutoff period (same units as the
time-series step).
Parameters
----------
x : ndarray,
The time-series of data to bandpass filter.
dt : float,
The time-step between the values in x. Units must be consistent
with the cutoff period.
low_cutoff: float,
The period at which the bandpass filter will apply the lowpass filter.
Units are same as the time-step of the signal provided (e.g., if the
data are provided every hour, then a cutoff=12 would be a 12 hour
cutoff.) Everything that has a longer period will remain. If you only
want a hi-pass filter, this value should be None.
hi_cutoff: float,
The period at which the bandpass filter will apply the high-pass filter.
Units are same as the time-step of the signal provided (e.g., if the
data are provided every hour, then a cutoff=12 would be a 12 hour
cutoff.) Everything that has a shorter period will remain. If you only
want a low-pass filter, this value should be None.
order: int optional,
The order of the filter to apply
Returns
-------
x : ndarray
The bandpass filtered time-series
Examples
--------
Create data every 30 minutes for 3 days with time in days:
>>> t = np.linspace(0, 3.0, 2 * 24 * 3.0, endpoint=False)
>>> x = 0.1 * np.sin(2 * np.pi / .008 * t)
>>> x += 0.2 * np.cos(2 * np.pi / 0.6 * t + 0.1)
>>> x += 0.2 * np.cos(2 * np.pi / 1.6 * t + .11)
>>> x += 1 * np.cos(2 * np.pi / 10 * t + 11)
Filter the data to low-pass everything longer than the 1 day period
>>> nx = bandpass(x, dt=0.5, low_cutoff=24 )
>>> plt.plot(t, x, 'k', t, nx, 'r', label=['Raw', 'Filter'])
Filter the data to low-pass everything longer the 2 day period
>>> nx = bandpass(x, dt=0.5, low_cutoff=48 )
>>> plt.plot(t, x, 'k', t, nx, 'r', label=['Raw', 'Filter'])
Filter the data to band-pass everything shorter the 2 day period
and longer the 1 hour period
>>> nx = bandpass(x, dt=0.5, low_cutoff=48, hi_cutoff=1 )
>>> plt.plot(t, x, 'k', t, nx, 'r', label=['Raw', 'Filter'])
"""
x = np.ma.array(np.atleast_1d(x).flatten(), copy=False)
nx = np.ma.masked_all(x.shape)
if low_cutoff and hi_cutoff:
freq = 2.0 * dt / np.array([hi_cutoff, low_cutoff])
btype = 'bandpass'
elif low_cutoff:
freq = 2.0 * dt / low_cutoff
btype = 'lowpass'
elif hi_cutoff:
freq = 2.0 * dt / hi_cutoff
btype = 'highpass'
else:
raise AttributeError("You must specify either low or hi cutoff.")
b, a = scipy.signal.butter(order, freq, btype=btype)
padlen = max(len(a), len(b))
# Go over all contiguous regions
regions = seapy.contiguous(x)
for r in regions:
if ((r.stop - r.start) >= padlen):
nx[r] = scipy.signal.filtfilt(b,
a,
x[r],
padlen=5 * padlen,
axis=0)
return nx
