# Source code for pycbc.filter.resample

```
# Copyright (C) 2012 Alex Nitz
# This program is free software; you can redistribute it and/or modify it
# under the terms of the GNU General Public License as published by the
# Free Software Foundation; either version 3 of the License, or (at your
# option) any later version.
#
# This program is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
# Public License for more details.
#
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
#
# =============================================================================
#
# Preamble
#
# =============================================================================
#
import functools
import lal
import numpy
import scipy.signal
from pycbc.types import TimeSeries, Array, zeros, FrequencySeries, real_same_precision_as
from pycbc.types import complex_same_precision_as
from pycbc.fft import ifft, fft
_resample_func = {numpy.dtype('float32'): lal.ResampleREAL4TimeSeries,
numpy.dtype('float64'): lal.ResampleREAL8TimeSeries}
@functools.lru_cache(maxsize=20)
def cached_firwin(*args, **kwargs):
"""Cache the FIR filter coefficients.
This is mostly done for PyCBC Live, which rapidly and repeatedly resamples data.
"""
return scipy.signal.firwin(*args, **kwargs)
# Change to True in front-end if you want this function to use caching
# This is a mostly-hidden optimization option that most users will not want
# to use. It is used in PyCBC Live
USE_CACHING_FOR_LFILTER = False
# If using caching we want output to be unique if called at different places
# (and if called from different modules/functions), these unique IDs acheive
# that. The numbers are not significant, only that they are unique.
LFILTER_UNIQUE_ID_1 = 651273657
LFILTER_UNIQUE_ID_2 = 154687641
LFILTER_UNIQUE_ID_3 = 548946442
def lfilter(coefficients, timeseries):
""" Apply filter coefficients to a time series
Parameters
----------
coefficients: numpy.ndarray
Filter coefficients to apply
timeseries: numpy.ndarray
Time series to be filtered.
Returns
-------
tseries: numpy.ndarray
filtered array
"""
from pycbc.filter import correlate
fillen = len(coefficients)
# If there aren't many points just use the default scipy method
if len(timeseries) < 2**7:
series = scipy.signal.lfilter(coefficients, 1.0, timeseries)
return TimeSeries(series,
epoch=timeseries.start_time,
delta_t=timeseries.delta_t)
elif (len(timeseries) < fillen * 10) or (len(timeseries) < 2**18):
from pycbc.strain.strain import create_memory_and_engine_for_class_based_fft
from pycbc.strain.strain import execute_cached_fft
cseries = (Array(coefficients[::-1] * 1)).astype(timeseries.dtype)
cseries.resize(len(timeseries))
cseries.roll(len(timeseries) - fillen + 1)
flen = len(cseries) // 2 + 1
ftype = complex_same_precision_as(timeseries)
if not USE_CACHING_FOR_LFILTER:
cfreq = zeros(flen, dtype=ftype)
tfreq = zeros(flen, dtype=ftype)
fft(Array(cseries), cfreq)
fft(Array(timeseries), tfreq)
cout = zeros(flen, ftype)
correlate(cfreq, tfreq, cout)
out = zeros(len(timeseries), dtype=timeseries)
ifft(cout, out)
else:
npoints = len(cseries)
# NOTE: This function is cached!
ifftouts = create_memory_and_engine_for_class_based_fft(
npoints,
timeseries.dtype,
ifft=True,
uid=LFILTER_UNIQUE_ID_1
)
# FFT contents of cseries into cfreq
cfreq = execute_cached_fft(cseries, uid=LFILTER_UNIQUE_ID_2,
copy_output=False,
normalize_by_rate=False)
# FFT contents of timeseries into tfreq
tfreq = execute_cached_fft(timeseries, uid=LFILTER_UNIQUE_ID_3,
copy_output=False,
normalize_by_rate=False)
cout, out, fft_class = ifftouts
# Correlate cfreq and tfreq
correlate(cfreq, tfreq, cout)
# IFFT correlation output into out
fft_class.execute()
return TimeSeries(out.numpy() / len(out), epoch=timeseries.start_time,
delta_t=timeseries.delta_t)
else:
# recursively perform which saves a bit on memory usage
# but must keep within recursion limit
chunksize = max(fillen * 5, len(timeseries) // 128)
part1 = lfilter(coefficients, timeseries[0:chunksize])
part2 = lfilter(coefficients, timeseries[chunksize - fillen:])
out = timeseries.copy()
out[:len(part1)] = part1
out[len(part1):] = part2[fillen:]
return out
[docs]def fir_zero_filter(coeff, timeseries):
"""Filter the timeseries with a set of FIR coefficients
Parameters
----------
coeff: numpy.ndarray
FIR coefficients. Should be and odd length and symmetric.
timeseries: pycbc.types.TimeSeries
Time series to be filtered.
Returns
-------
filtered_series: pycbc.types.TimeSeries
Return the filtered timeseries, which has been properly shifted to account
for the FIR filter delay and the corrupted regions zeroed out.
"""
# apply the filter
series = lfilter(coeff, timeseries)
# reverse the time shift caused by the filter,
# corruption regions contain zeros
# If the number of filter coefficients is odd, the central point *should*
# be included in the output so we only zero out a region of len(coeff) - 1
series[:(len(coeff) // 2) * 2] = 0
series.roll(-len(coeff)//2)
return series
[docs]def resample_to_delta_t(timeseries, delta_t, method='butterworth'):
"""Resmple the time_series to delta_t
Resamples the TimeSeries instance time_series to the given time step,
delta_t. Only powers of two and real valued time series are supported
at this time. Additional restrictions may apply to particular filter
methods.
Parameters
----------
time_series: TimeSeries
The time series to be resampled
delta_t: float
The desired time step
Returns
-------
Time Series: TimeSeries
A TimeSeries that has been resampled to delta_t.
Raises
------
TypeError:
time_series is not an instance of TimeSeries.
TypeError:
time_series is not real valued
Examples
--------
>>> h_plus_sampled = resample_to_delta_t(h_plus, 1.0/2048)
"""
if not isinstance(timeseries,TimeSeries):
raise TypeError("Can only resample time series")
if timeseries.kind != 'real':
raise TypeError("Time series must be real")
if timeseries.sample_rate_close(1.0 / delta_t):
return timeseries * 1
if method == 'butterworth':
lal_data = timeseries.lal()
_resample_func[timeseries.dtype](lal_data, delta_t)
data = lal_data.data.data
elif method == 'ldas':
factor = int(round(delta_t / timeseries.delta_t))
numtaps = factor * 20 + 1
# The kaiser window has been testing using the LDAS implementation
# and is in the same configuration as used in the original lalinspiral
filter_coefficients = cached_firwin(numtaps, 1.0 / factor,
window=('kaiser', 5))
# apply the filter and decimate
data = fir_zero_filter(filter_coefficients, timeseries)[::factor]
else:
raise ValueError('Invalid resampling method: %s' % method)
ts = TimeSeries(data, delta_t = delta_t,
dtype=timeseries.dtype,
epoch=timeseries._epoch)
# From the construction of the LDAS FIR filter there will be 10 corrupted samples
# explanation here http://software.ligo.org/docs/lalsuite/lal/group___resample_time_series__c.html
ts.corrupted_samples = 10
return ts
_highpass_func = {numpy.dtype('float32'): lal.HighPassREAL4TimeSeries,
numpy.dtype('float64'): lal.HighPassREAL8TimeSeries}
_lowpass_func = {numpy.dtype('float32'): lal.LowPassREAL4TimeSeries,
numpy.dtype('float64'): lal.LowPassREAL8TimeSeries}
[docs]def notch_fir(timeseries, f1, f2, order, beta=5.0):
""" notch filter the time series using an FIR filtered generated from
the ideal response passed through a time-domain kaiser window (beta = 5.0)
The suppression of the notch filter is related to the bandwidth and
the number of samples in the filter length. For a few Hz bandwidth,
a length corresponding to a few seconds is typically
required to create significant suppression in the notched band.
To achieve frequency resolution df at sampling frequency fs,
order should be at least fs/df.
Parameters
----------
Time Series: TimeSeries
The time series to be notched.
f1: float
The start of the frequency suppression.
f2: float
The end of the frequency suppression.
order: int
Number of corrupted samples on each side of the time series
(Extent of the filter on either side of zero)
beta: float
Beta parameter of the kaiser window that sets the side lobe attenuation.
"""
k1 = f1 / float((int(1.0 / timeseries.delta_t) / 2))
k2 = f2 / float((int(1.0 / timeseries.delta_t) / 2))
coeff = cached_firwin(order * 2 + 1, [k1, k2], window=('kaiser', beta))
return fir_zero_filter(coeff, timeseries)
[docs]def lowpass_fir(timeseries, frequency, order, beta=5.0):
""" Lowpass filter the time series using an FIR filtered generated from
the ideal response passed through a kaiser window (beta = 5.0)
Parameters
----------
Time Series: TimeSeries
The time series to be low-passed.
frequency: float
The frequency below which is suppressed.
order: int
Number of corrupted samples on each side of the time series
beta: float
Beta parameter of the kaiser window that sets the side lobe attenuation.
"""
k = frequency / float((int(1.0 / timeseries.delta_t) / 2))
coeff = cached_firwin(order * 2 + 1, k, window=('kaiser', beta))
return fir_zero_filter(coeff, timeseries)
[docs]def highpass_fir(timeseries, frequency, order, beta=5.0):
""" Highpass filter the time series using an FIR filtered generated from
the ideal response passed through a kaiser window (beta = 5.0)
Parameters
----------
Time Series: TimeSeries
The time series to be high-passed.
frequency: float
The frequency below which is suppressed.
order: int
Number of corrupted samples on each side of the time series
beta: float
Beta parameter of the kaiser window that sets the side lobe attenuation.
"""
k = frequency / float((int(1.0 / timeseries.delta_t) / 2))
coeff = cached_firwin(order * 2 + 1, k, window=('kaiser', beta), pass_zero=False)
return fir_zero_filter(coeff, timeseries)
[docs]def highpass(timeseries, frequency, filter_order=8, attenuation=0.1):
"""Return a new timeseries that is highpassed.
Return a new time series that is highpassed above the `frequency`.
Parameters
----------
Time Series: TimeSeries
The time series to be high-passed.
frequency: float
The frequency below which is suppressed.
filter_order: {8, int}, optional
The order of the filter to use when high-passing the time series.
attenuation: {0.1, float}, optional
The attenuation of the filter.
Returns
-------
Time Series: TimeSeries
A new TimeSeries that has been high-passed.
Raises
------
TypeError:
time_series is not an instance of TimeSeries.
TypeError:
time_series is not real valued
"""
if not isinstance(timeseries, TimeSeries):
raise TypeError("Can only resample time series")
if timeseries.kind != 'real':
raise TypeError("Time series must be real")
lal_data = timeseries.lal()
_highpass_func[timeseries.dtype](lal_data, frequency,
1-attenuation, filter_order)
return TimeSeries(lal_data.data.data, delta_t = lal_data.deltaT,
dtype=timeseries.dtype, epoch=timeseries._epoch)
[docs]def lowpass(timeseries, frequency, filter_order=8, attenuation=0.1):
"""Return a new timeseries that is lowpassed.
Return a new time series that is lowpassed below the `frequency`.
Parameters
----------
Time Series: TimeSeries
The time series to be low-passed.
frequency: float
The frequency above which is suppressed.
filter_order: {8, int}, optional
The order of the filter to use when low-passing the time series.
attenuation: {0.1, float}, optional
The attenuation of the filter.
Returns
-------
Time Series: TimeSeries
A new TimeSeries that has been low-passed.
Raises
------
TypeError:
time_series is not an instance of TimeSeries.
TypeError:
time_series is not real valued
"""
if not isinstance(timeseries, TimeSeries):
raise TypeError("Can only resample time series")
if timeseries.kind != 'real':
raise TypeError("Time series must be real")
lal_data = timeseries.lal()
_lowpass_func[timeseries.dtype](lal_data, frequency,
1-attenuation, filter_order)
return TimeSeries(lal_data.data.data, delta_t = lal_data.deltaT,
dtype=timeseries.dtype, epoch=timeseries._epoch)
[docs]def interpolate_complex_frequency(series, delta_f, zeros_offset=0, side='right'):
"""Interpolate complex frequency series to desired delta_f.
Return a new complex frequency series that has been interpolated to the
desired delta_f.
Parameters
----------
series : FrequencySeries
Frequency series to be interpolated.
delta_f : float
The desired delta_f of the output
zeros_offset : optional, {0, int}
Number of sample to delay the start of the zero padding
side : optional, {'right', str}
The side of the vector to zero pad
Returns
-------
interpolated series : FrequencySeries
A new FrequencySeries that has been interpolated.
"""
new_n = int( (len(series)-1) * series.delta_f / delta_f + 1)
old_N = int( (len(series)-1) * 2 )
new_N = int( (new_n - 1) * 2 )
time_series = TimeSeries(zeros(old_N), delta_t =1.0/(series.delta_f*old_N),
dtype=real_same_precision_as(series))
ifft(series, time_series)
time_series.roll(-zeros_offset)
time_series.resize(new_N)
if side == 'left':
time_series.roll(zeros_offset + new_N - old_N)
elif side == 'right':
time_series.roll(zeros_offset)
out_series = FrequencySeries(zeros(new_n), epoch=series.epoch,
delta_f=delta_f, dtype=series.dtype)
fft(time_series, out_series)
return out_series
__all__ = ['resample_to_delta_t', 'highpass', 'lowpass',
'interpolate_complex_frequency', 'highpass_fir',
'lowpass_fir', 'notch_fir', 'fir_zero_filter']
```