# Source code for pycbc.filter.zpk

```
# Copyright (C) 2014 Christopher M. Biwer
#
# 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 numpy as np
from scipy.signal import zpk2sos, sosfilt
from pycbc.types import TimeSeries
[docs]def filter_zpk(timeseries, z, p, k):
"""Return a new timeseries that was filtered with a zero-pole-gain filter.
The transfer function in the s-domain looks like:
.. math::
\\frac{H(s) = (s - s_1) * (s - s_3) * ... * (s - s_n)}{(s - s_2) * (s - s_4) * ... * (s - s_m)}, m >= n
The zeroes, and poles entered in Hz are converted to angular frequency,
along the imaginary axis in the s-domain s=i*omega. Then the zeroes, and
poles are bilinearly transformed via:
.. math::
z(s) = \\frac{(1 + s*T/2)}{(1 - s*T/2)}
Where z is the z-domain value, s is the s-domain value, and T is the
sampling period. After the poles and zeroes have been bilinearly
transformed, then the second-order sections are found and filter the data
using scipy.
Parameters
----------
timeseries: TimeSeries
The TimeSeries instance to be filtered.
z: array
Array of zeros to include in zero-pole-gain filter design.
In units of Hz.
p: array
Array of poles to include in zero-pole-gain filter design.
In units of Hz.
k: float
Gain to include in zero-pole-gain filter design. This gain is a
constant multiplied to the transfer function.
Returns
-------
Time Series: TimeSeries
A new TimeSeries that has been filtered.
Examples
--------
To apply a 5 zeroes at 100Hz, 5 poles at 1Hz, and a gain of 1e-10 filter
to a TimeSeries instance, do:
>>> filtered_data = zpk_filter(timeseries, [100]*5, [1]*5, 1e-10)
"""
# sanity check type
if not isinstance(timeseries, TimeSeries):
raise TypeError("Can only filter TimeSeries instances.")
# sanity check casual filter
degree = len(p) - len(z)
if degree < 0:
raise TypeError("May not have more zeroes than poles. \
Filter is not casual.")
# cast zeroes and poles as arrays and gain as a float
z = np.array(z)
p = np.array(p)
k = float(k)
# put zeroes and poles in the s-domain
# convert from frequency to angular frequency
z *= -2 * np.pi
p *= -2 * np.pi
# get denominator of bilinear transform
fs = 2.0 * timeseries.sample_rate
# zeroes in the z-domain
z_zd = (1 + z/fs) / (1 - z/fs)
# any zeros that were at infinity are moved to the Nyquist frequency
z_zd = z_zd[np.isfinite(z_zd)]
z_zd = np.append(z_zd, -np.ones(degree))
# poles in the z-domain
p_zd = (1 + p/fs) / (1 - p/fs)
# gain change in z-domain
k_zd = k * np.prod(fs - z) / np.prod(fs - p)
# get second-order sections
sos = zpk2sos(z_zd, p_zd, k_zd)
# filter
filtered_data = sosfilt(sos, timeseries.numpy())
return TimeSeries(filtered_data, delta_t = timeseries.delta_t,
dtype=timeseries.dtype,
epoch=timeseries._epoch)
```