def fftgram(timeseries, stride, pad=False):
"""
calculates fourier-gram with automatic
50% overlapping hann windowing.
Parameters
----------
timeseries : gwpy TimeSeries
time series to take fftgram of
stride : `int`
number of seconds in single PSD
Returns
-------
fftgram : gwpy spectrogram
a fourier-gram
"""
fftlength = stride
dt = stride
df = 1. / fftlength
# number of values in a step
stride *= timeseries.sample_rate.value
# number of steps
nsteps = 2 * int(timeseries.size // stride) - 1
# only get positive frequencies
if pad:
nfreqs = int(fftlength * timeseries.sample_rate.value)
df = df / 2
f0 = df
else:
nfreqs = int(fftlength * timeseries.sample_rate.value) / 2
dtype = np.complex
# initialize the spectrogram
out = Spectrogram(np.zeros((nsteps, nfreqs), dtype=dtype),
name=timeseries.name, epoch=timeseries.epoch,
f0=df, df=df, dt=dt, copy=True,
unit=1 / u.Hz**0.5, dtype=dtype)
# stride through TimeSeries, recording FFTs as columns of Spectrogram
for step in range(nsteps):
# indexes for this step
idx = (stride / 2) * step
idx_end = idx + stride
stepseries = timeseries[idx:idx_end]
# zeropad, window, fft, shift zero to center, normalize
# window
stepseries = np.multiply(stepseries,
np.hanning(stepseries.value.size))
# take fft
if pad:
stepseries = TimeSeries(np.hstack((stepseries, np.zeros(stepseries.size))),
name=stepseries.name, x0=stepseries.x0,
dx=timeseries.dx)
tempfft = stepseries.fft(stepseries.size)
else:
tempfft = stepseries.fft(stepseries.size)
tempfft.override_unit(out.unit)
out[step] = tempfft[1:]
return out
noise, then inject a loud, steady sinuosoid. We will do this in the
frequency domain because it is much easier to model a sinusoid there.
"""
__author__ = "Alex Urban <*****@*****.**>"
__currentmodule__ = 'gwpy.timeseries'
# First, we prepare one second of Gaussian noise:
from numpy import random
from gwpy.timeseries import TimeSeries
noise = TimeSeries(random.normal(scale=.1, size=1024), sample_rate=1024)
# To inject a signal in the frequency domain, we need to take an FFT:
noisefd = noise.fft()
# We can now easily inject a loud sinusoid of unit amplitude at, say,
# 30 Hz. To do this, we use :meth:`~gwpy.types.series.Series.inject`.
import numpy
from gwpy.frequencyseries import FrequencySeries
signal = FrequencySeries(numpy.array([1.]), f0=30, df=noisefd.df)
injfd = noisefd.inject(signal)
# We can then visualize the data before and after injection in the frequency
# domain:
from gwpy.plot import Plot
plot = Plot(numpy.abs(noisefd),
numpy.abs(injfd),
def test_ifft(self):
# construct a TimeSeries, then check that it is unchanged by
# the operation TimeSeries.fft().ifft()
ts = TimeSeries([1.0, 0.0, -1.0, 0.0], sample_rate=1.0)
assert ts.fft().ifft() == ts
utils.assert_allclose(ts.fft().ifft().value, ts.value)
noise, then inject a loud, steady sinuosoid. We will do this in the
frequency domain because it is much easier to model a sinusoid there.
"""
__author__ = "Alex Urban <*****@*****.**>"
__currentmodule__ = 'gwpy.timeseries'
# First, we prepare one second of Gaussian noise:
from numpy import random
from gwpy.timeseries import TimeSeries
noise = TimeSeries(random.normal(scale=.1, size=1024), sample_rate=1024)
# To inject a signal in the frequency domain, we need to take an FFT:
noisefd = noise.fft()
# We can now easily inject a loud sinusoid of unit amplitude at, say,
# 30 Hz. To do this, we use :meth:`~gwpy.types.series.Series.inject`.
import numpy
from gwpy.frequencyseries import FrequencySeries
signal = FrequencySeries(numpy.array([1.]), f0=30, df=noisefd.df)
injfd = noisefd.inject(signal)
# We can then visualize the data before and after injection in the frequency
# domain:
from gwpy.plot import Plot
plot = Plot(numpy.abs(noisefd), numpy.abs(injfd), separate=True,
sharex=True, sharey=True, xscale='log', yscale='log')
def fftgram(timeseries, stride, overlap=None, pad=False):
"""
calculates fourier-gram with auto 50% overlapping
segments and hann windowed
Parameters
----------
timeseries : gwpy TimeSeries
time series to take fftgram of
stride : `int`
number of seconds in single PSD
overalp : `int`
number of seconds of overlap
Returns
-------
fftgram : gwpy spectrogram
a fourier-gram
"""
fftlength = stride
if not overlap:
overlap = stride / 2.
dt = stride - overlap
df = 1. / fftlength
# number of values in a step
stride *= timeseries.sample_rate.value
overlap *= timeseries.sample_rate.value
step = stride - overlap
# number of steps
nsteps = int(timeseries.size // step) - 1
# only get positive frequencies
if pad:
nfreqs = int(fftlength * timeseries.sample_rate.value)
df = df / 2
f0 = df
else:
nfreqs = int(fftlength * timeseries.sample_rate.value) / 2
dtype = np.complex
# initialize the spectrogram
out = Spectrogram(np.zeros((nsteps, nfreqs), dtype=dtype),
name=timeseries.name, epoch=timeseries.epoch,
f0=df, df=df, dt=dt, copy=True,
unit=1 / u.Hz**0.5, dtype=dtype)
# stride through TimeSeries, recording FFTs as columns of Spectrogram
if (timeseries.sample_rate.value * stride) % 1:
raise ValueError('1 / stride must evenly divide sample rate of channel')
for step in range(nsteps):
# indexes for this step
idx = (stride / 2) * step
idx_end = idx + stride
stepseries = timeseries[idx:idx_end]
# zeropad, window, fft
stepseries = np.multiply(stepseries,
np.hanning(stepseries.value.size))
# hann windowing normalization
norm = np.sum(np.hanning(stepseries.value.size))
if pad:
stepseries = TimeSeries(np.hstack((stepseries, np.zeros(stepseries.size))),
name=stepseries.name, x0=stepseries.x0,
dx=timeseries.dx)
tempfft = stepseries.fft(stepseries.size)
else:
tempfft = stepseries.fft(stepseries.size)
# reset proper unit
tempfft.override_unit(out.unit)
# normalize
out[step] = tempfft[1:] / norm
return out
def test_ifft(self):
# construct a TimeSeries, then check that it is unchanged by
# the operation TimeSeries.fft().ifft()
ts = TimeSeries([1.0, 0.0, -1.0, 0.0], sample_rate=1.0)
assert ts.fft().ifft() == ts
utils.assert_allclose(ts.fft().ifft().value, ts.value)
def fftgram(timeseries, stride, pad=False):
"""
calculates fourier-gram with automatic
50% overlapping hann windowing.
Parameters
----------
timeseries : gwpy TimeSeries
time series to take fftgram of
stride : `int`
number of seconds in single PSD
Returns
-------
fftgram : gwpy spectrogram
a fourier-gram
"""
fftlength = stride
dt = stride
df = 1. / fftlength
# number of values in a step
stride *= timeseries.sample_rate.value
# number of steps
nsteps = 2 * int(timeseries.size // stride) - 1
# only get positive frequencies
if pad:
nfreqs = int(fftlength * timeseries.sample_rate.value)
df = df / 2
f0 = df
else:
nfreqs = int(fftlength * timeseries.sample_rate.value) / 2
dtype = np.complex
# initialize the spectrogram
out = Spectrogram(np.zeros((nsteps, nfreqs), dtype=dtype),
name=timeseries.name,
epoch=timeseries.epoch,
f0=df,
df=df,
dt=dt,
copy=True,
unit=1 / u.Hz**0.5,
dtype=dtype)
# stride through TimeSeries, recording FFTs as columns of Spectrogram
for step in range(nsteps):
# indexes for this step
idx = (stride / 2) * step
idx_end = idx + stride
stepseries = timeseries[idx:idx_end]
# zeropad, window, fft, shift zero to center, normalize
# window
stepseries = np.multiply(stepseries, np.hanning(stepseries.value.size))
# take fft
if pad:
stepseries = TimeSeries(np.hstack(
(stepseries, np.zeros(stepseries.size))),
name=stepseries.name,
x0=stepseries.x0,
dx=timeseries.dx)
tempfft = stepseries.fft(stepseries.size)
else:
tempfft = stepseries.fft(stepseries.size)
tempfft.override_unit(out.unit)
out[step] = tempfft[1:]
return out
def fftgram(timeseries, stride, overlap=None, pad=False):
"""
calculates fourier-gram with auto 50% overlapping
segments and hann windowed
Parameters
----------
timeseries : :py:mod:`gwpy.timeseries.TimeSeries`
time series to take fftgram of
stride : `int`
number of seconds in single PSD
overalp : `int`
number of seconds of overlap. Defaults to half of stride.
Returns
-------
fftgram : :py:mod:`gwpy.spectrogram.Spectrogram`
a fourier-gram
"""
fftlength = stride
if overlap is None:
overlap = stride / 2.
dt = stride - overlap
df = 1. / fftlength
# number of values in a step
stride *= timeseries.sample_rate.value
overlap *= timeseries.sample_rate.value
step = stride - overlap
# number of steps
nsteps = int(timeseries.size // step) - 1
# only get positive frequencies
if pad:
nfreqs = int(fftlength * timeseries.sample_rate.value)
df = df / 2
f0 = df
else:
nfreqs = int(fftlength * timeseries.sample_rate.value) / 2
dtype = np.complex
# initialize the spectrogram
out = Spectrogram(np.zeros((nsteps, nfreqs), dtype=dtype),
name=timeseries.name,
epoch=timeseries.epoch,
f0=df,
df=df,
dt=dt,
copy=True,
unit=u.Hz**(-0.5),
dtype=dtype)
# stride through TimeSeries, recording FFTs as columns of Spectrogram
if (timeseries.sample_rate.value * stride) % 1:
raise ValueError('1/stride must evenly divide sample rate of channel')
for step in range(nsteps):
# indexes for this step
idx = int((stride / 2) * step)
idx_end = int(idx + stride)
stepseries = timeseries[idx:idx_end]
# zeropad, window, fft
stepseries = np.multiply(stepseries, np.hanning(stepseries.value.size))
# hann windowing normalization
norm = np.sum(np.hanning(stepseries.value.size))
if pad:
stepseries = TimeSeries(np.hstack(
(stepseries, np.zeros(stepseries.size))),
name=stepseries.name,
x0=stepseries.x0,
dx=timeseries.dx)
tempfft = stepseries.fft(stepseries.size)
else:
tempfft = stepseries.fft(stepseries.size)
# reset proper unit
tempfft.override_unit(out.unit)
# normalize
out[step] = tempfft[1:] / norm
return out
