def compute_continuous_wavelet_transform(time_series, frequencies,
sample_period, q_ratio, normalisation,
mother):
"""
# type: (TimeSeries, Range, float, float, str, str) -> WaveletCoefficients
Calculate the continuous wavelet transform of time_series.
Parameters
__________
time_series : TimeSeries
The timeseries to which the wavelet is to be applied.
frequencies : Range
The frequency resolution and range returned. Requested frequencies
are converted internally into appropriate scales.
sample_period : float
The sampling period of the computed wavelet spectrum.
q_ratio : float
NFC. Must be greater than 5. Ratios of the center frequencies to bandwidths.
normalisation : str
The type of normalisation for the resulting wavet spectrum. Default is 'energy', options are: 'energy'; 'gabor'.
mother : str
The mother wavelet function used in the transform.
"""
ts_shape = time_series.data.shape
if frequencies.step == 0:
log.warning("Frequency step can't be 0! Trying default step, 2e-3.")
frequencies.step = 0.002
freqs = numpy.arange(frequencies.lo, frequencies.hi, frequencies.step)
if (freqs.size == 0) or any(freqs <= 0.0):
# TODO: Maybe should limit number of freqs... ~100 is probably a reasonable upper bound.
log.warning("Invalid frequency range! Falling back to default.")
log.debug("freqs")
log.debug(narray_describe(freqs))
frequencies = Range(lo=0.008, hi=0.060, step=0.002)
freqs = numpy.arange(frequencies.lo, frequencies.hi, frequencies.step)
log.debug("freqs")
log.debug(narray_describe(freqs))
sample_rate = time_series.sample_rate
# Duke: code below is as given by Andreas Spiegler, I've just wrapped
# some of the original argument names
nf = len(freqs)
temporal_step = max(
(1,
ReferenceBackend.iround(sample_period / time_series.sample_period)))
nt = int(numpy.ceil(ts_shape[0] / temporal_step))
if not isinstance(q_ratio, numpy.ndarray):
new_q_ratio = q_ratio * numpy.ones((1, nf))
if numpy.nanmin(new_q_ratio) < 5:
msg = "q_ratio must be not lower than 5 !"
log.error(msg)
raise Exception(msg)
if numpy.nanmax(freqs) > sample_rate / 2.0:
msg = "Sampling rate is too low for the requested frequency range !"
log.error(msg)
raise Exception(msg)
# TODO: This isn't used, but min frequency seems like it should be important... Check with A.S.
# fmin = 3.0 * numpy.nanmin(q_ratio) * sample_rate / numpy.pi / nt
sigma_f = freqs / new_q_ratio
sigma_t = 1.0 / (2.0 * numpy.pi * sigma_f)
if normalisation == 'energy':
Amp = 1.0 / numpy.sqrt(sample_rate * numpy.sqrt(numpy.pi) * sigma_t)
elif normalisation == 'gabor':
Amp = numpy.sqrt(2.0 / numpy.pi) / sample_rate / sigma_t
coef_shape = (nf, nt, ts_shape[1], ts_shape[2], ts_shape[3])
coef = numpy.zeros(coef_shape, dtype=numpy.complex128)
log.debug("coef")
log.debug(narray_describe(coef))
scales = numpy.arange(0, nf, 1)
for i in scales:
f0 = freqs[i]
SDt = sigma_t[(0, i)]
A = Amp[(0, i)]
x = numpy.arange(0, 4.0 * SDt * sample_rate, 1) / sample_rate
wvlt = A * numpy.exp(-x**2 / (2.0 * SDt**2)) * numpy.exp(
2j * numpy.pi * f0 * x)
wvlt = numpy.hstack((numpy.conjugate(wvlt[-1:0:-1]), wvlt))
# util.self.log_debug_array(self.log, wvlt, "wvlt")
for var in range(ts_shape[1]):
for node in range(ts_shape[2]):
for mode in range(ts_shape[3]):
data = time_series.data[:, var, node, mode]
wt = signal.convolve(data, wvlt, 'same')
# util.self.log_debug_array(self.log, wt, "wt")
res = wt[0::temporal_step]
# NOTE: this is a horrible horrible quick hack (alas, a solution) to avoid broadcasting errors
# when using dt and sample periods which are not powers of 2.
coef[i, :, var, node,
mode] = res if len(res) == nt else res[:coef.shape[1]]
log.debug("coef")
log.debug(narray_describe(coef))
spectra = spectral.WaveletCoefficients(source=time_series,
mother=mother,
sample_period=sample_period,
frequencies=frequencies.to_array(),
normalisation=normalisation,
q_ratio=q_ratio,
array_data=coef)
return spectra
def test_range():
ra = Range(0, 10, 5)
assert 1 in ra
numpy.testing.assert_allclose(ra.to_array(), [0, 5])
repr(ra)
class ContinuousWaveletTransform(HasTraits):
"""
A class for calculating the wavelet transform of a TimeSeries object of TVB
and returning a WaveletSpectrum object. The sampling period and frequency
range of the result can be specified. The mother wavelet can also be
specified... (So far, only Morlet.)
References:
.. [TBetal_1996] C. Tallon-Baudry et al, *Stimulus Specificity of
Phase-Locked and Non-Phase-Locked 40 Hz Visual Responses in Human.*,
J Neurosci 16(13):4240-4249, 1996.
.. [Mallat_1999] S. Mallat, *A wavelet tour of signal processing.*,
book, Academic Press, 1999.
"""
time_series = Attr(
field_type=time_series.TimeSeries,
label="Time Series",
doc="""The timeseries to which the wavelet is to be applied.""")
mother = Attr(
field_type=str,
label="Wavelet function",
default="morlet",
doc="""The mother wavelet function used in the transform. Default is
'morlet', possibilities are: 'morlet'...""")
sample_period = Float(
label="Sample period of result (ms)",
default=7.8125, #7.8125 => 128 Hz
doc="""The sampling period of the computed wavelet spectrum. NOTE:
This should be an integral multiple of the of the sampling period
of the source time series, otherwise the actual resulting sample
period will be the first correct value below that requested.""")
frequencies = Attr(
field_type=Range,
label="Frequency range of result (kHz).",
default=Range(lo=0.008, hi=0.060, step=0.002),
doc="""The frequency resolution and range returned. Requested
frequencies are converted internally into appropriate scales.""")
normalisation = Attr(
field_type=str,
label="Normalisation",
default="energy",
doc="""The type of normalisation for the resulting wavet spectrum.
Default is 'energy', options are: 'energy'; 'gabor'.""")
q_ratio = Float(
label="Q-ratio",
default=5.0,
doc="""NFC. Must be greater than 5. Ratios of the center frequencies to bandwidths.""")
def evaluate(self):
"""
Calculate the continuous wavelet transform of time_series.
"""
ts_shape = self.time_series.data.shape
if self.frequencies.step == 0:
self.log.warning("Frequency step can't be 0! Trying default step, 2e-3.")
self.frequencies.step = 0.002
freqs = numpy.arange(self.frequencies.lo, self.frequencies.hi,
self.frequencies.step)
if (freqs.size == 0) or any(freqs <= 0.0):
# TODO: Maybe should limit number of freqs... ~100 is probably a reasonable upper bound.
self.log.warning("Invalid frequency range! Falling back to default.")
self.log.debug("freqs")
self.log.debug(narray_describe(freqs))
self.frequencies = Range(lo=0.008, hi=0.060, step=0.002)
freqs = numpy.arange(self.frequencies.lo, self.frequencies.hi,
self.frequencies.step)
self.log.debug("freqs")
self.log.debug(narray_describe(freqs))
sample_rate = self.time_series.sample_rate
# Duke: code below is as given by Andreas Spiegler, I've just wrapped
# some of the original argument names
nf = len(freqs)
temporal_step = max((1, iround(self.sample_period / self.time_series.sample_period)))
nt = int(numpy.ceil(ts_shape[0] / temporal_step))
if not isinstance(self.q_ratio, numpy.ndarray):
q_ratio = self.q_ratio * numpy.ones((1, nf))
if numpy.nanmin(q_ratio) < 5:
msg = "q_ratio must be not lower than 5 !"
self.log.error(msg)
raise Exception(msg)
if numpy.nanmax(freqs) > sample_rate / 2.0:
msg = "Sampling rate is too low for the requested frequency range !"
self.log.error(msg)
raise Exception(msg)
# TODO: This isn't used, but min frequency seems like it should be important... Check with A.S.
# fmin = 3.0 * numpy.nanmin(q_ratio) * sample_rate / numpy.pi / nt
sigma_f = freqs / q_ratio
sigma_t = 1.0 / (2.0 * numpy.pi * sigma_f)
if self.normalisation == 'energy':
Amp = 1.0 / numpy.sqrt(sample_rate * numpy.sqrt(numpy.pi) * sigma_t)
elif self.normalisation == 'gabor':
Amp = numpy.sqrt(2.0 / numpy.pi) / sample_rate / sigma_t
coef_shape = (nf, nt, ts_shape[1], ts_shape[2], ts_shape[3])
coef = numpy.zeros(coef_shape, dtype = numpy.complex128)
self.log.debug("coef")
self.log.debug(narray_describe(coef))
scales = numpy.arange(0, nf, 1)
for i in scales:
f0 = freqs[i]
SDt = sigma_t[(0, i)]
A = Amp[(0, i)]
x = numpy.arange(0, 4.0 * SDt * sample_rate, 1) / sample_rate
wvlt = A * numpy.exp(-x**2 / (2.0 * SDt**2) ) * numpy.exp(2j * numpy.pi * f0 * x )
wvlt = numpy.hstack((numpy.conjugate(wvlt[-1:0:-1]), wvlt))
#util.self.log_debug_array(self.log, wvlt, "wvlt")
for var in range(ts_shape[1]):
for node in range(ts_shape[2]):
for mode in range(ts_shape[3]):
data = self.time_series.data[:, var, node, mode]
wt = signal.convolve(data, wvlt, 'same')
#util.self.log_debug_array(self.log, wt, "wt")
res = wt[0::temporal_step]
# NOTE: this is a horrible horrible quick hack (alas, a solution) to avoid broadcasting errors
# when using dt and sample periods which are not powers of 2.
coef[i, :, var, node, mode] = res if len(res) == nt else res[:coef.shape[1]]
self.log.debug("coef")
self.log.debug(narray_describe(coef))
spectra = spectral.WaveletCoefficients(
source=self.time_series,
mother=self.mother,
sample_period=self.sample_period,
frequencies=self.frequencies.to_array(),
normalisation=self.normalisation,
q_ratio=self.q_ratio,
array_data=coef)
return spectra
def result_shape(self, input_shape, input_sample_period):
"""
Returns the shape of the main result (complex array) of the continuous
wavelet transform.
"""
freq_len = int((self.frequencies.hi - self.frequencies.lo) / self.frequencies.step)
temporal_step = max((1, self.sample_period / input_sample_period))
nt = int(round(input_shape[0] / temporal_step))
result_shape = (freq_len, nt, ) + input_shape[1:]
return result_shape
def result_size(self, input_shape, input_sample_period):
"""
Returns the storage size in Bytes of the main result (complex array) of
the continuous wavelet transform.
"""
result_size = numpy.prod(self.result_shape(input_shape, input_sample_period)) * 2.0 * 8.0 #complex*Bytes
return result_size
def extended_result_size(self, input_shape, input_sample_period):
"""
Returns the storage size in Bytes of the extended result of the
continuous wavelet transform. That is, it includes storage of the
evaluated WaveletCoefficients attributes such as power, phase,
amplitude, etc.
"""
result_shape = self.result_shape(input_shape, input_sample_period)
result_size = self.result_size(input_shape, input_sample_period)
extend_size = result_size #Main array
extend_size = extend_size + 0.5 * result_size #Amplitude
extend_size = extend_size + 0.5 * result_size #Phase
extend_size = extend_size + 0.5 * result_size #Power
extend_size = extend_size + result_shape[0] * 8.0 #Frequency
return extend_size