def compute_fast_fourier_transform(time_series, segment_length,
window_function, detrend):
"""
# type: (TimeSeries, float, function, bool) -> FourierSpectrum
Calculate the FFT of time_series broken into segments of length
segment_length and filtered by window_function.
Parameters
__________
time_series : TimeSeries
The TimeSeries to which the FFT is to be applied.
segment_length : float
The segment length determines the frequency resolution of the resulting power spectra -- longer
windows produce finer frequency resolution
window_function : str
Windowing functions can be applied before the FFT is performed. Default is None, possibilities are: 'hamming';
'bartlett';'blackman'; and 'hanning'. See, numpy.<function_name>.
detrend : bool
Default is True, False means no detrending is performed on the time series.
"""
tpts = time_series.data.shape[0]
time_series_length = tpts * time_series.sample_period
# Segment time-series, overlapping if necessary
nseg = int(numpy.ceil(time_series_length / segment_length))
if nseg > 1:
seg_tpts = numpy.ceil(segment_length / time_series.sample_period)
overlap = (seg_tpts * nseg - tpts) / (nseg - 1.0)
starts = [max(seg * (seg_tpts - overlap), 0) for seg in range(nseg)]
segments = [
time_series.data[int(start):int(start) + int(seg_tpts)]
for start in starts
]
segments = [segment[:, :, :, :, numpy.newaxis] for segment in segments]
ts = numpy.concatenate(segments, axis=4)
else:
segment_length = time_series_length
ts = time_series.data[:, :, :, :, numpy.newaxis]
seg_tpts = ts.shape[0]
log.debug("Segment length being used is: %s" % segment_length)
# Base-line correct the segmented time-series
if detrend:
ts = scipy.signal.detrend(ts, axis=0)
log.debug("time_series " + narray_describe(ts))
# Apply windowing function
if window_function is not None:
wf = SUPPORTED_WINDOWING_FUNCTIONS[window_function]
window_mask = numpy.reshape(wf(int(seg_tpts)),
(int(seg_tpts), 1, 1, 1, 1))
ts = ts * window_mask
# Calculate the FFT
result = numpy.fft.fft(ts, axis=0)
nfreq = result.shape[0] // 2
result = result[1:nfreq + 1, :]
log.debug("result " + narray_describe(result))
spectra = FourierSpectrum(source=time_series,
segment_length=segment_length,
array_data=result,
windowing_function=window_function)
spectra.configure()
return spectra
def evaluate(self):
"""
Calculate the FFT of time_series broken into segments of length
segment_length and filtered by window_function.
"""
tpts = self.time_series.data.shape[0]
time_series_length = tpts * self.time_series.sample_period
# Segment time-series, overlapping if necessary
nseg = int(numpy.ceil(time_series_length / self.segment_length))
if nseg > 1:
seg_tpts = numpy.ceil(self.segment_length /
self.time_series.sample_period)
overlap = (seg_tpts * nseg - tpts) / (nseg - 1.0)
starts = [
max(seg * (seg_tpts - overlap), 0) for seg in range(nseg)
]
segments = [
self.time_series.data[int(start):int(start) + int(seg_tpts)]
for start in starts
]
segments = [
segment[:, :, :, :, numpy.newaxis] for segment in segments
]
time_series = numpy.concatenate(segments, axis=4)
else:
self.segment_length = time_series_length
time_series = self.time_series.data[:, :, :, :, numpy.newaxis]
seg_tpts = time_series.shape[0]
self.log.debug("Segment length being used is: %s" %
self.segment_length)
# Base-line correct the segmented time-series
if self.detrend:
time_series = scipy.signal.detrend(time_series, axis=0)
self.log.debug("time_series " + narray_describe(time_series))
# Apply windowing function
if self.window_function is not None:
window_function = SUPPORTED_WINDOWING_FUNCTIONS[
self.window_function]
window_mask = numpy.reshape(window_function(int(seg_tpts)),
(int(seg_tpts), 1, 1, 1, 1))
time_series = time_series * window_mask
# Calculate the FFT
result = numpy.fft.fft(time_series, axis=0)
nfreq = result.shape[0] // 2
result = result[1:nfreq + 1, :]
self.log.debug("result " + narray_describe(result))
spectra = FourierSpectrum(source=self.time_series,
segment_length=self.segment_length,
array_data=result,
windowing_function=self.window_function)
spectra.configure()
return spectra