def qtransform(fseries, Q, f0):
"""Calculate the energy 'TimeSeries' for the given fseries
Parameters
----------
fseries: 'pycbc FrequencySeries'
frequency-series data set
Q:
q value
f0:
central frequency
Returns
-------
norm_energy: '~pycbc.types.aligned.ArrayWithAligned'
A 'TimeSeries' of the normalized energy from the Q-transform of
this tile against the data.
cenergy: '~pycbc.types.aligned.ArrayWithAligned'
A 'TimeSeries' of the complex energy from the Q-transform of
this tile against the data.
"""
# q-transform data for each (Q, frequency) tile
# initialize parameters
qprime = Q / 11**(1 / 2.) # ... self.qprime
dur = 1.0 / fseries.delta_f
# check for sampling rate
sampling = (len(fseries) - 1) * 2 * fseries.delta_f
# choice of output sampling rate
output_sampling = sampling # Can lower this to highest bandwidth
output_samples = int(dur * output_sampling)
# window fft
window_size = 2 * int(f0 / qprime * dur) + 1
# get start and end indices
start = int((f0 - (f0 / qprime)) * dur)
end = int(start + window_size)
# apply window to fft
# normalize and generate bi-square window
norm = np.sqrt(315. * qprime / (128. * f0))
windowed = fseries[start:end].numpy() * (bisquare(window_size) * norm)
# pad data, move negative frequencies to the end, and IFFT
padded = np.pad(windowed,
padding(window_size, output_samples),
mode='constant')
wenergy = npfft.ifftshift(padded)
# return a 'TimeSeries'
wenergy = FrequencySeries(wenergy, delta_f=1. / dur)
cenergy = TimeSeries(zeros(output_samples, dtype=np.complex128),
delta_t=1. / sampling)
ifft(wenergy, cenergy)
energy = cenergy.squared_norm()
medianenergy = np.median(energy.numpy())
norm_energy = energy / float(medianenergy)
return norm_energy, cenergy
def qseries(fseries, Q, f0, return_complex=False):
"""Calculate the energy 'TimeSeries' for the given fseries
Parameters
----------
fseries: 'pycbc FrequencySeries'
frequency-series data set
Q:
q value
f0:
central frequency
return_complex: {False, bool}
Return the raw complex series instead of the normalized power.
Returns
-------
energy: '~pycbc.types.TimeSeries'
A 'TimeSeries' of the normalized energy from the Q-transform of
this tile against the data.
"""
# normalize and generate bi-square window
qprime = Q / 11**(1 / 2.)
norm = numpy.sqrt(315. * qprime / (128. * f0))
window_size = 2 * int(f0 / qprime * fseries.duration) + 1
xfrequencies = numpy.linspace(-1., 1., window_size)
start = int((f0 - (f0 / qprime)) * fseries.duration)
end = int(start + window_size)
center = (start + end) / 2
windowed = fseries[start:end] * (1 - xfrequencies**2)**2 * norm
tlen = (len(fseries) - 1) * 2
windowed.resize(tlen)
windowed = numpy.roll(windowed, -center)
# calculate the time series for this q -value
windowed = FrequencySeries(windowed,
delta_f=fseries.delta_f,
epoch=fseries.start_time)
ctseries = TimeSeries(zeros(tlen, dtype=numpy.complex128),
delta_t=fseries.delta_t)
ifft(windowed, ctseries)
if return_complex:
return ctseries
else:
energy = ctseries.squared_norm()
medianenergy = numpy.median(energy.numpy())
return energy / float(medianenergy)
def qseries(fseries, Q, f0, return_complex=False):
"""Calculate the energy 'TimeSeries' for the given fseries
Parameters
----------
fseries: 'pycbc FrequencySeries'
frequency-series data set
Q:
q value
f0:
central frequency
return_complex: {False, bool}
Return the raw complex series instead of the normalized power.
Returns
-------
energy: '~pycbc.types.TimeSeries'
A 'TimeSeries' of the normalized energy from the Q-transform of
this tile against the data.
"""
# normalize and generate bi-square window
qprime = Q / 11**(1/2.)
norm = numpy.sqrt(315. * qprime / (128. * f0))
window_size = 2 * int(f0 / qprime * fseries.duration) + 1
xfrequencies = numpy.linspace(-1., 1., window_size)
start = int((f0 - (f0 / qprime)) * fseries.duration)
end = int(start + window_size)
center = (start + end) / 2
windowed = fseries[start:end] * (1 - xfrequencies ** 2) ** 2 * norm
tlen = (len(fseries)-1) * 2
windowed.resize(tlen)
windowed = numpy.roll(windowed, -center)
# calculate the time series for this q -value
windowed = FrequencySeries(windowed, delta_f=fseries.delta_f,
epoch=fseries.start_time)
ctseries = TimeSeries(zeros(tlen, dtype=numpy.complex128),
delta_t=fseries.delta_t)
ifft(windowed, ctseries)
if return_complex:
return ctseries
else:
energy = ctseries.squared_norm()
medianenergy = numpy.median(energy.numpy())
return energy / float(medianenergy)
def qtransform(fseries, Q, f0):
"""Calculate the energy 'TimeSeries' for the given fseries
Parameters
----------
fseries: 'pycbc FrequencySeries'
frequency-series data set
Q:
q value
f0:
central frequency
Returns
-------
norm_energy: '~pycbc.types.aligned.ArrayWithAligned'
A 'TimeSeries' of the normalized energy from the Q-transform of
this tile against the data.
cenergy: '~pycbc.types.aligned.ArrayWithAligned'
A 'TimeSeries' of the complex energy from the Q-transform of
this tile against the data.
"""
# q-transform data for each (Q, frequency) tile
# initialize parameters
qprime = Q / 11**(1/2.) # ... self.qprime
dur = fseries.duration
# check for sampling rate
sampling = fseries.sample_rate
# window fft
window_size = 2 * int(f0 / qprime * dur) + 1
# get start and end indices
start = int((f0 - (f0 / qprime)) * dur)
end = int(start + window_size)
# apply window to fft
# normalize and generate bi-square window
norm = np.sqrt(315. * qprime / (128. * f0))
windowed = fseries[start:end].numpy() * bisquare(window_size) * norm
# choice of output sampling rate
output_sampling = sampling # Can lower this to highest bandwidth
output_samples = int(dur * output_sampling)
# pad data, move negative frequencies to the end, and IFFT
padded = np.pad(windowed, padding(window_size, output_samples), mode='constant')
wenergy = npfft.ifftshift(padded)
# return a 'TimeSeries'
wenergy = FrequencySeries(wenergy, delta_f=1./dur)
cenergy = TimeSeries(zeros(output_samples, dtype=np.complex128),
delta_t=1./sampling)
ifft(wenergy, cenergy)
energy = cenergy.squared_norm()
medianenergy = np.median(energy.numpy())
norm_energy = energy / float(medianenergy)
return norm_energy, cenergy