def colored_noise(psd,
start_time,
end_time,
seed=0,
sample_rate=16384,
low_frequency_cutoff=1.0,
filter_duration=128):
""" Create noise from a PSD
Return noise from the chosen PSD. Note that if unique noise is desired
a unique seed should be provided.
Parameters
----------
psd : pycbc.types.FrequencySeries
PSD to color the noise
start_time : int
Start time in GPS seconds to generate noise
end_time : int
End time in GPS seconds to generate nosie
seed : {None, int}
The seed to generate the noise.
sample_rate: {16384, float}
The sample rate of the output data. Keep constant if you want to
ensure continuity between disjoint time spans.
low_frequency_cutof : {1.0, float}
The low frequency cutoff to pass to the PSD generation.
filter_duration : {128, float}
The duration in seconds of the coloring filter
Returns
--------
noise : TimeSeries
A TimeSeries containing gaussian noise colored by the given psd.
"""
psd = psd.copy()
flen = int(sample_rate / psd.delta_f) // 2 + 1
oldlen = len(psd)
psd.resize(flen)
# Want to avoid zeroes in PSD.
max_val = psd.max()
for i in range(len(psd)):
if i >= (oldlen - 1):
psd.data[i] = psd[oldlen - 2]
if psd[i] == 0:
psd.data[i] = max_val
fil_len = int(filter_duration * sample_rate)
wn_dur = int(end_time - start_time) + 2 * filter_duration
if psd.delta_f >= 1. / (2. * filter_duration):
# If the PSD is short enough, this method is less memory intensive than
# resizing and then calling inverse_spectrum_truncation
psd = pycbc.psd.interpolate(psd, 1.0 / (2. * filter_duration))
# inverse_spectrum_truncation truncates the inverted PSD. To truncate
# the non-inverted PSD we give it the inverted PSD to truncate and then
# invert the output.
psd = 1. / pycbc.psd.inverse_spectrum_truncation(
1. / psd,
fil_len,
low_frequency_cutoff=low_frequency_cutoff,
trunc_method='hann')
psd = psd.astype(complex_same_precision_as(psd))
# Zero-pad the time-domain PSD to desired length. Zeroes must be added
# in the middle, so some rolling between a resize is used.
psd = psd.to_timeseries()
psd.roll(fil_len)
psd.resize(int(wn_dur * sample_rate))
psd.roll(-fil_len)
# As time series is still mirrored the complex frequency components are
# 0. But convert to real by using abs as in inverse_spectrum_truncate
psd = psd.to_frequencyseries()
else:
psd = pycbc.psd.interpolate(psd, 1.0 / wn_dur)
psd = 1. / pycbc.psd.inverse_spectrum_truncation(
1. / psd,
fil_len,
low_frequency_cutoff=low_frequency_cutoff,
trunc_method='hann')
kmin = int(low_frequency_cutoff / psd.delta_f)
psd[:kmin].clear()
asd = (psd.squared_norm())**0.25
del psd
white_noise = normal(start_time - filter_duration,
end_time + filter_duration,
seed=seed,
sample_rate=sample_rate)
white_noise = white_noise.to_frequencyseries()
# Here we color. Do not want to duplicate memory here though so use '*='
white_noise *= asd
del asd
colored = white_noise.to_timeseries(delta_t=1.0 / sample_rate)
del white_noise
return colored.time_slice(start_time, end_time)
def colored_noise(psd, start_time, end_time, seed=0, low_frequency_cutoff=1.0):
""" Create noise from a PSD
Return noise from the chosen PSD. Note that if unique noise is desired
a unique seed should be provided.
Parameters
----------
psd : pycbc.types.FrequencySeries
PSD to color the noise
start_time : int
Start time in GPS seconds to generate noise
end_time : int
End time in GPS seconds to generate nosie
seed : {None, int}
The seed to generate the noise.
low_frequency_cutof : {1.0, float}
The low frequency cutoff to pass to the PSD generation.
Returns
--------
noise : TimeSeries
A TimeSeries containing gaussian noise colored by the given psd.
"""
psd = psd.copy()
flen = int(SAMPLE_RATE / psd.delta_f) / 2 + 1
oldlen = len(psd)
psd.resize(flen)
# Want to avoid zeroes in PSD.
max_val = psd.max()
for i in xrange(len(psd)):
if i >= (oldlen-1):
psd.data[i] = psd[oldlen - 2]
if psd[i] == 0:
psd.data[i] = max_val
wn_dur = int(end_time - start_time) + 2*FILTER_LENGTH
if psd.delta_f >= 1. / (2.*FILTER_LENGTH):
# If the PSD is short enough, this method is less memory intensive than
# resizing and then calling inverse_spectrum_truncation
psd = pycbc.psd.interpolate(psd, 1.0 / (2.*FILTER_LENGTH))
# inverse_spectrum_truncation truncates the inverted PSD. To truncate
# the non-inverted PSD we give it the inverted PSD to truncate and then
# invert the output.
psd = 1. / pycbc.psd.inverse_spectrum_truncation(1./psd,
FILTER_LENGTH * SAMPLE_RATE,
low_frequency_cutoff=low_frequency_cutoff,
trunc_method='hann')
psd = psd.astype(complex_same_precision_as(psd))
# Zero-pad the time-domain PSD to desired length. Zeroes must be added
# in the middle, so some rolling between a resize is used.
psd = psd.to_timeseries()
psd.roll(SAMPLE_RATE * FILTER_LENGTH)
psd.resize(wn_dur * SAMPLE_RATE)
psd.roll(-SAMPLE_RATE * FILTER_LENGTH)
# As time series is still mirrored the complex frequency components are
# 0. But convert to real by using abs as in inverse_spectrum_truncate
psd = psd.to_frequencyseries()
else:
psd = pycbc.psd.interpolate(psd, 1.0 / wn_dur)
psd = 1. / pycbc.psd.inverse_spectrum_truncation(1./psd,
FILTER_LENGTH * SAMPLE_RATE,
low_frequency_cutoff=low_frequency_cutoff,
trunc_method='hann')
kmin = int(low_frequency_cutoff / psd.delta_f)
psd[:kmin].clear()
asd = (psd.real())**0.5
del psd
white_noise = normal(start_time - FILTER_LENGTH, end_time + FILTER_LENGTH,
seed=seed)
white_noise = white_noise.to_frequencyseries()
# Here we color. Do not want to duplicate memory here though so use '*='
white_noise *= asd
del asd
colored = white_noise.to_timeseries()
del white_noise
return colored.time_slice(start_time, end_time)
def colored_noise(psd, start_time, end_time, seed=0, low_frequency_cutoff=1.0):
""" Create noise from a PSD
Return noise from the chosen PSD. Note that if unique noise is desired
a unique seed should be provided.
Parameters
----------
psd : pycbc.types.FrequencySeries
PSD to color the noise
start_time : int
Start time in GPS seconds to generate noise
end_time : int
End time in GPS seconds to generate nosie
seed : {None, int}
The seed to generate the noise.
low_frequency_cutof : {1.0, float}
The low frequency cutoff to pass to the PSD generation.
Returns
--------
noise : TimeSeries
A TimeSeries containing gaussian noise colored by the given psd.
"""
psd = psd.copy()
flen = int(SAMPLE_RATE / psd.delta_f) / 2 + 1
oldlen = len(psd)
psd.resize(flen)
# Want to avoid zeroes in PSD.
max_val = psd.max()
for i in xrange(len(psd)):
if i >= (oldlen - 1):
psd.data[i] = psd[oldlen - 2]
if psd[i] == 0:
psd.data[i] = max_val
wn_dur = int(end_time - start_time) + 2 * FILTER_LENGTH
if psd.delta_f >= 1. / (2. * FILTER_LENGTH):
# If the PSD is short enough, this method is less memory intensive than
# resizing and then calling inverse_spectrum_truncation
psd = pycbc.psd.interpolate(psd, 1.0 / (2. * FILTER_LENGTH))
# inverse_spectrum_truncation truncates the inverted PSD. To truncate
# the non-inverted PSD we give it the inverted PSD to truncate and then
# invert the output.
psd = 1. / pycbc.psd.inverse_spectrum_truncation(
1. / psd,
FILTER_LENGTH * SAMPLE_RATE,
low_frequency_cutoff=low_frequency_cutoff,
trunc_method='hann')
psd = psd.astype(complex_same_precision_as(psd))
# Zero-pad the time-domain PSD to desired length. Zeroes must be added
# in the middle, so some rolling between a resize is used.
psd = psd.to_timeseries()
psd.roll(SAMPLE_RATE * FILTER_LENGTH)
psd.resize(wn_dur * SAMPLE_RATE)
psd.roll(-SAMPLE_RATE * FILTER_LENGTH)
# As time series is still mirrored the complex frequency components are
# 0. But convert to real by using abs as in inverse_spectrum_truncate
psd = psd.to_frequencyseries()
else:
psd = pycbc.psd.interpolate(psd, 1.0 / wn_dur)
psd = 1. / pycbc.psd.inverse_spectrum_truncation(
1. / psd,
FILTER_LENGTH * SAMPLE_RATE,
low_frequency_cutoff=low_frequency_cutoff,
trunc_method='hann')
kmin = int(low_frequency_cutoff / psd.delta_f)
psd[:kmin].clear()
asd = (psd.real())**0.5
del psd
white_noise = normal(start_time - FILTER_LENGTH,
end_time + FILTER_LENGTH,
seed=seed)
white_noise = white_noise.to_frequencyseries()
# Here we color. Do not want to duplicate memory here though so use '*='
white_noise *= asd
del asd
colored = white_noise.to_timeseries()
del white_noise
return colored.time_slice(start_time, end_time)
