# Source code for pycbc.psd.variation

```
""" PSD Variation """
import numpy
from numpy.fft import rfft, irfft
import scipy.signal as sig
from scipy.interpolate import interp1d
import pycbc.psd
from pycbc.types import TimeSeries
[docs]def create_full_filt(freqs, filt, plong, srate, psd_duration):
"""Create a filter to convolve with strain data to find PSD variation.
Parameters
----------
freqs : numpy.ndarray
Array of sample frequencies of the PSD.
filt : numpy.ndarray
A bandpass filter.
plong : numpy.ndarray
The estimated PSD.
srate : float
The sample rate of the data.
psd_duration : float
The duration of the estimated PSD.
Returns
-------
full_filt : numpy.ndarray
The full filter used to calculate PSD variation.
"""
# Make the weighting filter - bandpass, which weight by f^-7/6,
# and whiten. The normalization is chosen so that the variance
# will be one if this filter is applied to white noise which
# already has a variance of one.
fweight = freqs ** (-7./6.) * filt / numpy.sqrt(plong)
fweight[0] = 0.
norm = (sum(abs(fweight) ** 2) / (len(fweight) - 1.)) ** -0.5
fweight = norm * fweight
fwhiten = numpy.sqrt(2. / srate) / numpy.sqrt(plong)
fwhiten[0] = 0.
full_filt = sig.windows.hann(int(psd_duration * srate)) * numpy.roll(
irfft(fwhiten * fweight), int(psd_duration / 2) * srate)
return full_filt
[docs]def mean_square(data, delta_t, srate, short_stride, stride):
""" Calculate mean square of given time series once per stride
First of all this function calculate the mean square of given time
series once per short_stride. This is used to find and remove
outliers due to short glitches. Here an outlier is defined as any
element which is greater than two times the average of its closest
neighbours. Every outlier is substituted with the average of the
corresponding adjacent elements.
Then, every second the function compute the mean square of the
smoothed time series, within the stride.
Parameters
----------
data : numpy.ndarray
delta_t : float
Duration of the time series
srate : int
Sample rate of the data were it given as a TimeSeries
short_stride : float
Stride duration for outlier removal
stride ; float
Stride duration
Returns
-------
m_s: List
Mean square of given time series
"""
# Calculate mean square of data once per short stride and replace
# outliers
short_ms = numpy.mean(data.reshape(-1, int(srate * short_stride)) ** 2,
axis=1)
# Define an array of averages that is used to substitute outliers
ave = 0.5 * (short_ms[2:] + short_ms[:-2])
outliers = short_ms[1:-1] > (2. * ave)
short_ms[1:-1][outliers] = ave[outliers]
# Calculate mean square of data every step within a window equal to
# stride seconds
m_s = []
inv_time = int(1. / short_stride)
for index in range(int(delta_t - stride + 1)):
m_s.append(numpy.mean(short_ms[inv_time * index:inv_time *
int(index+stride)]))
return m_s
[docs]def calc_filt_psd_variation(strain, segment, short_segment, psd_long_segment,
psd_duration, psd_stride, psd_avg_method, low_freq,
high_freq):
""" Calculates time series of PSD variability
This function first splits the segment up into 512 second chunks. It
then calculates the PSD over this 512 second. The PSD is used to
to create a filter that is the composition of three filters:
1. Bandpass filter between f_low and f_high.
2. Weighting filter which gives the rough response of a CBC template.
3. Whitening filter.
Next it makes the convolution of this filter with the stretch of data.
This new time series is given to the "mean_square" function, which
computes the mean square of the timeseries within an 8 seconds window,
once per second.
The result, which is the variance of the S/N in that stride for the
Parseval theorem, is then stored in a timeseries.
Parameters
----------
strain : TimeSeries
Input strain time series to estimate PSDs
segment : {float, 8}
Duration of the segments for the mean square estimation in seconds.
short_segment : {float, 0.25}
Duration of the short segments for the outliers removal.
psd_long_segment : {float, 512}
Duration of the long segments for PSD estimation in seconds.
psd_duration : {float, 8}
Duration of FFT segments for long term PSD estimation, in seconds.
psd_stride : {float, 4}
Separation between FFT segments for long term PSD estimation, in
seconds.
psd_avg_method : {string, 'median'}
Method for averaging PSD estimation segments.
low_freq : {float, 20}
Minimum frequency to consider the comparison between PSDs.
high_freq : {float, 480}
Maximum frequency to consider the comparison between PSDs.
Returns
-------
psd_var : TimeSeries
Time series of the variability in the PSD estimation
"""
# Calculate strain precision
if strain.precision == 'single':
fs_dtype = numpy.float32
elif strain.precision == 'double':
fs_dtype = numpy.float64
# Convert start and end times immediately to floats
start_time = float(strain.start_time)
end_time = float(strain.end_time)
srate = int(strain.sample_rate)
# Fix the step for the PSD estimation and the time to remove at the
# edge of the time series.
step = 1.0
strain_crop = 8.0
# Find the times of the long segments
times_long = numpy.arange(start_time, end_time,
psd_long_segment - 2 * strain_crop
- segment + step)
# Create a bandpass filter between low_freq and high_freq
filt = sig.firwin(4 * srate, [low_freq, high_freq], pass_zero=False,
window='hann', nyq=srate / 2)
filt.resize(int(psd_duration * srate))
# Fourier transform the filter and take the absolute value to get
# rid of the phase.
filt = abs(rfft(filt))
psd_var_list = []
for tlong in times_long:
# Calculate PSD for long segment
if tlong + psd_long_segment <= float(end_time):
astrain = strain.time_slice(tlong, tlong + psd_long_segment)
plong = pycbc.psd.welch(
astrain,
seg_len=int(psd_duration * strain.sample_rate),
seg_stride=int(psd_stride * strain.sample_rate),
avg_method=psd_avg_method)
else:
astrain = strain.time_slice(tlong, end_time)
plong = pycbc.psd.welch(
strain.time_slice(end_time - psd_long_segment,
end_time),
seg_len=int(psd_duration * strain.sample_rate),
seg_stride=int(psd_stride * strain.sample_rate),
avg_method=psd_avg_method)
astrain = astrain.numpy()
freqs = numpy.array(plong.sample_frequencies, dtype=fs_dtype)
plong = plong.numpy()
full_filt = create_full_filt(freqs, filt, plong, srate, psd_duration)
# Convolve the filter with long segment of data
wstrain = sig.fftconvolve(astrain, full_filt, mode='same')
wstrain = wstrain[int(strain_crop * srate):-int(strain_crop * srate)]
# compute the mean square of the chunk of data
delta_t = len(wstrain) * strain.delta_t
variation = mean_square(wstrain, delta_t, srate, short_segment, segment)
psd_var_list.append(numpy.array(variation, dtype=wstrain.dtype))
# Package up the time series to return
psd_var = TimeSeries(numpy.concatenate(psd_var_list), delta_t=step,
epoch=start_time + strain_crop + segment)
return psd_var
[docs]def find_trigger_value(psd_var, idx, start, sample_rate):
""" Find the PSD variation value at a particular time with the filter
method. If the time is outside the timeseries bound, 1. is given.
Parameters
----------
psd_var : TimeSeries
Time series of the varaibility in the PSD estimation
idx : numpy.ndarray
Time indices of the triggers
start : float
GPS start time
sample_rate : float
Sample rate defined in ini file
Returns
-------
vals : Array
PSD variation value at a particular time
"""
# Find gps time of the trigger
time = start + idx / sample_rate
# Extract the PSD variation at trigger time through linear
# interpolation
if not hasattr(psd_var, 'cached_psd_var_interpolant'):
psd_var.cached_psd_var_interpolant = \
interp1d(psd_var.sample_times.numpy(),
psd_var.numpy(),
fill_value=1.0,
bounds_error=False)
vals = psd_var.cached_psd_var_interpolant(time)
return vals
[docs]def live_create_filter(psd_estimated,
psd_duration,
sample_rate,
low_freq=20,
high_freq=480):
"""
Create a filter to be used in the calculation of the psd variation for the
PyCBC Live search. This filter combines a bandpass between a lower and
upper frequency and an estimated signal response so that the variance
will be 1 when the filter is applied to white noise.
Within the PyCBC Live search this filter needs to be recreated every time
the estimated psd is updated and needs to be unique for each detector.
Parameters
----------
psd_estimated : pycbc.frequencyseries
The current PyCBC Live PSD: variations are measured relative to this
estimate.
psd_duration : float
The duration of the estimation of the psd, in seconds.
sample_rate : int
The sample rate of the strain data being search over.
low_freq : int (default = 20)
The lower frequency to apply in the bandpass filter.
high_freq : int (default = 480)
The upper frequency to apply in the bandpass filter.
Returns
-------
full_filt : numpy.ndarray
The complete filter to be convolved with the strain data to
find the psd variation value.
"""
# Create a bandpass filter between low_freq and high_freq once
filt = sig.firwin(4 * sample_rate,
[low_freq, high_freq],
pass_zero=False,
window='hann',
nyq=sample_rate / 2)
filt.resize(int(psd_duration * sample_rate))
# Fourier transform the filter and take the absolute value to get
# rid of the phase.
filt = abs(rfft(filt))
# Extract the psd frequencies to create a representative filter.
freqs = numpy.array(psd_estimated.sample_frequencies, dtype=numpy.float32)
plong = psd_estimated.numpy()
full_filt = create_full_filt(freqs, filt, plong, sample_rate, psd_duration)
return full_filt
[docs]def live_calc_psd_variation(strain,
full_filt,
increment,
data_trim=2.0,
short_stride=0.25):
"""
Calculate the psd variation in the PyCBC Live search.
The Live strain data is convolved with the filter to produce a timeseries
containing the PSD variation values for each sample. The mean square of
the timeseries is calculated over the short_stride to find outliers caused
by short duration glitches. Outliers are replaced with the average of
adjacent elements in the array. This array is then further averaged every
second to produce the PSD variation timeseries.
Parameters
----------
strain : pycbc.timeseries
Live data being searched through by the PyCBC Live search.
full_filt : numpy.ndarray
A filter created by `live_create_filter`.
increment : float
The number of seconds in each increment in the PyCBC Live search.
data_trim : float
The number of seconds to be trimmed from either end of the convolved
timeseries to prevent artefacts.
short_stride : float
The number of seconds to average the PSD variation timeseries over to
remove the effects of short duration glitches.
Returns
-------
psd_var : pycbc.timeseries
A timeseries containing the PSD variation values.
"""
sample_rate = int(strain.sample_rate)
# Grab the last increments worth of data, plus padding for edge effects.
astrain = strain.time_slice(strain.end_time - increment - (data_trim * 3),
strain.end_time)
# Convolve the data and the filter to produce the PSD variation timeseries,
# then trim the beginning and end of the data to prevent edge effects.
wstrain = sig.fftconvolve(astrain, full_filt, mode='same')
wstrain = wstrain[int(data_trim * sample_rate):-int(data_trim * sample_rate)]
# Create a PSD variation array by taking the mean square of the PSD
# variation timeseries every short_stride
short_ms = numpy.mean(
wstrain.reshape(-1, int(sample_rate * short_stride)) ** 2, axis=1)
# Define an array of averages that is used to substitute outliers
ave = 0.5 * (short_ms[2:] + short_ms[:-2])
outliers = short_ms[1:-1] > (2. * ave)
short_ms[1:-1][outliers] = ave[outliers]
# Calculate the PSD variation every second by a moving window average
# containing (1/short_stride) short_ms samples.
m_s = []
samples_per_second = 1 / short_stride
for idx in range(int(len(short_ms) / samples_per_second)):
start = int(samples_per_second * idx)
end = int(samples_per_second * (idx + 1))
m_s.append(numpy.mean(short_ms[start:end]))
m_s = numpy.array(m_s, dtype=wstrain.dtype)
psd_var = TimeSeries(m_s,
delta_t=1.0,
epoch=strain.end_time - increment - (data_trim * 2))
return psd_var
[docs]def live_find_var_value(triggers,
psd_var_timeseries):
"""
Extract the PSD variation values at trigger times by linear interpolation.
Parameters
----------
triggers : dict
Dictionary containing input trigger times.
psd_var_timeseries : pycbc.timeseries
A timeseries containing the PSD variation value for each second of the
latest increment in PyCBC Live.
Returns
-------
psd_var_vals : numpy.ndarray
Array of interpolated PSD variation values at trigger times.
"""
# Create the interpolator
interpolator = interp1d(psd_var_timeseries.sample_times.numpy(),
psd_var_timeseries.numpy(),
fill_value=1.0,
bounds_error=False)
# Evaluate at the trigger times
psd_var_vals = interpolator(triggers['end_time'])
return psd_var_vals
```