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import numpy as np
from nitime.lazy import scipy
from nitime.lazy import scipy_signal as signal
from nitime.lazy import scipy_fftpack as fftpack
from nitime import descriptors as desc
from nitime import utils as tsu
from nitime import algorithms as tsa
from nitime import timeseries as ts
from .base import BaseAnalyzer
class SpectralAnalyzer(BaseAnalyzer):
""" Analyzer object for spectral analysis"""
def __init__(self, input=None, method=None, BW=None, adaptive=False,
low_bias=False):
"""
The initialization of the
Parameters
----------
input: time-series objects
method: dict (optional),
The method spec used in calculating 'psd' see
:func:`algorithms.get_spectra` for details.
BW: float (optional),
In 'spectrum_multi_taper' The bandwidth of the windowing function
will determine the number tapers to use. This parameters represents
trade-off between frequency resolution (lower main lobe BW for the
taper) and variance reduction (higher BW and number of averaged
estimates).
adaptive : {True/False}
In 'spectrum_multi_taper', use an adaptive weighting routine to
combine the PSD estimates of different tapers.
low_bias: {True/False}
In spectrum_multi_taper, use bias correction
Examples
--------
>>> np.set_printoptions(precision=4) # for doctesting
>>> t1 = ts.TimeSeries(data = np.arange(0,1024,1).reshape(2,512),
... sampling_rate=np.pi)
>>> s1 = SpectralAnalyzer(t1)
>>> s1.method['this_method']
'welch'
>>> s1.method['Fs'] # doctest: +ELLIPSIS
3.1415926535... Hz
>>> f,s = s1.psd
>>> f
array([ 0. , 0.0491, 0.0982, 0.1473, 0.1963, 0.2454, 0.2945,
0.3436, 0.3927, 0.4418, 0.4909, 0.54 , 0.589 , 0.6381,
0.6872, 0.7363, 0.7854, 0.8345, 0.8836, 0.9327, 0.9817,
1.0308, 1.0799, 1.129 , 1.1781, 1.2272, 1.2763, 1.3254,
1.3744, 1.4235, 1.4726, 1.5217, 1.5708])
>>> s[0,0] # doctest: +ELLIPSIS
1128276.92538360...
"""
BaseAnalyzer.__init__(self, input)
self.method = method
if self.method is None:
self.method = {'this_method': 'welch',
'Fs': self.input.sampling_rate}
self.BW = BW
self.adaptive = adaptive
self.low_bias = low_bias
@desc.setattr_on_read
def psd(self):
"""
The standard output for this analyzer is a tuple f,s, where: f is the
frequency bands associated with the discrete spectral components
and s is the PSD calculated using :func:`mlab.psd`.
"""
NFFT = self.method.get('NFFT', 64)
Fs = self.input.sampling_rate
detrend = self.method.get('detrend', tsa.mlab.detrend_none)
window = self.method.get('window', tsa.mlab.window_hanning)
n_overlap = self.method.get('n_overlap', int(np.ceil(NFFT / 2.0)))
if np.iscomplexobj(self.input.data):
psd_len = NFFT
dt = complex
else:
psd_len = NFFT / 2.0 + 1
dt = float
#If multi-channel data:
if len(self.input.data.shape) > 1:
psd_shape = (self.input.shape[:-1] + (psd_len,))
flat_data = np.reshape(self.input.data, (-1,
self.input.data.shape[-1]))
flat_psd = np.empty((flat_data.shape[0], psd_len), dtype=dt)
for i in range(flat_data.shape[0]):
#'f' are the center frequencies of the frequency bands
#represented in the psd. These are identical in each iteration
#of the loop, so they get reassigned into the same variable in
#each iteration:
temp, f = tsa.mlab.psd(flat_data[i],
NFFT=NFFT,
Fs=Fs,
detrend=detrend,
window=window,
noverlap=n_overlap)
flat_psd[i] = temp.squeeze()
psd = np.reshape(flat_psd, psd_shape).squeeze()
else:
psd, f = tsa.mlab.psd(self.input.data,
NFFT=NFFT,
Fs=Fs,
detrend=detrend,
window=window,
noverlap=n_overlap)
return f, psd
@desc.setattr_on_read
def cpsd(self):
"""
This outputs both the PSD and the CSD calculated using
:func:`algorithms.get_spectra`.
Returns
-------
(f,s): tuple
f: Frequency bands over which the psd/csd are calculated and
s: the n by n by len(f) matrix of PSD (on the main diagonal) and CSD
(off diagonal)
"""
self.welch_method = self.method
self.welch_method['this_method'] = 'welch'
self.welch_method['Fs'] = self.input.sampling_rate
f, spectrum_welch = tsa.get_spectra(self.input.data,
method=self.welch_method)
return f, spectrum_welch
@desc.setattr_on_read
def periodogram(self):
"""
This is the spectrum estimated as the FFT of the time-series
Returns
-------
(f,spectrum): f is an array with the frequencies and spectrum is the
complex-valued FFT.
"""
return tsa.periodogram(self.input.data,
Fs=self.input.sampling_rate)
@desc.setattr_on_read
def spectrum_fourier(self):
"""
This is the spectrum estimated as the FFT of the time-series
Returns
-------
(f,spectrum): f is an array with the frequencies and spectrum is the
complex-valued FFT.
"""
data = self.input.data
sampling_rate = self.input.sampling_rate
fft = fftpack.fft
if np.any(np.iscomplex(data)):
# Get negative frequencies, as well as positive:
f = np.linspace(-sampling_rate/2., sampling_rate/2., data.shape[-1])
spectrum_fourier = np.fft.fftshift(fft(data))
else:
f = tsu.get_freqs(sampling_rate, data.shape[-1])
spectrum_fourier = fft(data)[..., :f.shape[0]]
return f, spectrum_fourier
@desc.setattr_on_read
def spectrum_multi_taper(self):
"""
The spectrum and cross-spectra, computed using
:func:`multi_taper_csd'
"""
if np.iscomplexobj(self.input.data):
psd_len = self.input.shape[-1]
dt = complex
else:
psd_len = self.input.shape[-1] / 2 + 1
dt = float
#Initialize the output
spectrum_multi_taper = np.empty((self.input.shape[:-1] + (psd_len,)),
dtype=dt)
#If multi-channel data:
if len(self.input.data.shape) > 1:
for i in range(self.input.data.shape[0]):
# 'f' are the center frequencies of the frequency bands
# represented in the MT psd. These are identical in each
# iteration of the loop, so they get reassigned into the same
# variable in each iteration:
f, spectrum_multi_taper[i], _ = tsa.multi_taper_psd(
self.input.data[i],
Fs=self.input.sampling_rate,
BW=self.BW,
adaptive=self.adaptive,
low_bias=self.low_bias)
else:
f, spectrum_multi_taper, _ = tsa.multi_taper_psd(self.input.data,
Fs=self.input.sampling_rate,
BW=self.BW,
adaptive=self.adaptive,
low_bias=self.low_bias)
return f, spectrum_multi_taper
class FilterAnalyzer(desc.ResetMixin):
""" A class for performing filtering operations on time-series and
producing the filtered versions of the time-series
Parameters
----------
time_series: A nitime TimeSeries object.
lb,ub: float (optional)
Lower and upper band of a pass-band into which the data will be
filtered. Default: 0, Nyquist
boxcar_iterations: int (optional)
For box-car filtering, how many times to iterate over the data while
convolving with a box-car function. Default: 2
gpass: float (optional)
For iir filtering, the pass-band maximal ripple loss (default: 1)
gstop: float (optional)
For iir filtering, the stop-band minimal attenuation (default: 60).
filt_order: int (optional)
For iir/fir filtering, the order of the filter. Note for fir filtering,
this needs to be an even number. Default: 64
iir_ftype: str (optional)
The type of filter to be used in iir filtering (see
scipy.signal.iirdesign for details). Default 'ellip'
fir_win: str
The window to be used in fir filtering (see scipy.signal.firwin for
details). Default: 'hamming'
Note
----
All filtering methods used here keep the original DC component of the
signal.
"""
def __init__(self, time_series, lb=0, ub=None, boxcar_iterations=2,
filt_order=64, gpass=1, gstop=60, iir_ftype='ellip',
fir_win='hamming'):
#Initialize all the local variables you will need for all the different
#filtering methods:
self.data = time_series.data
self.sampling_rate = time_series.sampling_rate
self.ub = ub
self.lb = lb
self.time_unit = time_series.time_unit
self._boxcar_iterations = boxcar_iterations
self._gstop = gstop
self._gpass = gpass
self._filt_order = filt_order
self._ftype = iir_ftype
self._win = fir_win
def filtfilt(self, b, a, in_ts=None):
"""
Zero-phase delay filtering (either iir or fir).
Parameters
----------
a,b: filter coefficients
in_ts: time-series object.
This allows to replace the input. Instead of analyzing this
analyzers input data, analyze some other time-series object
Note
----
This is a wrapper around scipy.signal.filtfilt
"""
# Switch in the new in_ts:
if in_ts is not None:
data = in_ts.data
Fs = in_ts.sampling_rate
else:
data = self.data
Fs = self.sampling_rate
#filtfilt only operates channel-by-channel, so we need to loop over the
#channels, if the data is multi-channel data:
if len(data.shape) > 1:
out_data = np.empty(data.shape, dtype=data.dtype)
for i in range(data.shape[0]):
out_data[i] = signal.filtfilt(b, a, data[i])
#Make sure to preserve the DC:
dc = np.mean(data[i])
out_data[i] -= np.mean(out_data[i])
out_data[i] += dc
else:
out_data = signal.filtfilt(b, a, data)
#Make sure to preserve the DC:
dc = np.mean(data)
out_data -= np.mean(out_data)
out_data += dc
return ts.TimeSeries(out_data,
sampling_rate=Fs,
time_unit=self.time_unit)
@desc.setattr_on_read
def fir(self):
"""
Filter the time-series using an FIR digital filter. Filtering is done
back and forth (using scipy.signal.filtfilt) to achieve zero phase
delay
"""
#Passband and stop-band are expressed as fraction of the Nyquist
#frequency:
if self.ub is not None:
ub_frac = self.ub / (self.sampling_rate / 2.)
else:
ub_frac = 1.0
lb_frac = self.lb / (self.sampling_rate / 2.)
if lb_frac < 0 or ub_frac > 1:
e_s = "The lower-bound or upper bound used to filter"
e_s += " are beyond the range 0-Nyquist. You asked for"
e_s += " a filter between"
e_s += "%s and %s percent of" % (lb_frac * 100, ub_frac * 100)
e_s += "the Nyquist frequency"
raise ValueError(e_s)
n_taps = self._filt_order + 1
#This means the filter order you chose was too large (needs to be
#shorter than a 1/3 of your time-series )
if n_taps > self.data.shape[-1] * 3:
e_s = "The filter order chosen is too large for this time-series"
raise ValueError(e_s)
# a is always 1:
a = [1]
sig = ts.TimeSeries(data=self.data, sampling_rate=self.sampling_rate)
#Lowpass:
if ub_frac < 1:
b = signal.firwin(n_taps, ub_frac, window=self._win)
sig = self.filtfilt(b, a, sig)
#High-pass
if lb_frac > 0:
#Includes a spectral inversion:
b = -1 * signal.firwin(n_taps, lb_frac, window=self._win)
b[n_taps / 2] = b[n_taps / 2] + 1
sig = self.filtfilt(b, a, sig)
return sig
@desc.setattr_on_read
def iir(self):
"""
Filter the time-series using an IIR filter. Filtering is done back and
forth (using scipy.signal.filtfilt) to achieve zero phase delay
"""
#Passband and stop-band are expressed as fraction of the Nyquist
#frequency:
if self.ub is not None:
ub_frac = self.ub / (self.sampling_rate / 2.)
else:
ub_frac = 1.0
lb_frac = self.lb / (self.sampling_rate / 2.)
# For the band-pass:
if lb_frac > 0 and ub_frac < 1:
wp = [lb_frac, ub_frac]
ws = [np.max([lb_frac - 0.1, 0]),
np.min([ub_frac + 0.1, 1.0])]
# For the lowpass:
elif lb_frac == 0:
wp = ub_frac
ws = np.min([ub_frac + 0.1, 0.9])
# For the highpass:
elif ub_frac == 1:
wp = lb_frac
ws = np.max([lb_frac - 0.1, 0.1])
b, a = signal.iirdesign(wp, ws, self._gpass, self._gstop,
ftype=self._ftype)
return self.filtfilt(b, a)
@desc.setattr_on_read
def filtered_fourier(self):
"""
Filter the time-series by passing it to the Fourier domain and null
out the frequency bands outside of the range [lb,ub]
"""
freqs = tsu.get_freqs(self.sampling_rate, self.data.shape[-1])
if self.ub is None:
self.ub = freqs[-1]
power = fftpack.fft(self.data)
idx_0 = np.hstack([np.where(freqs < self.lb)[0],
np.where(freqs > self.ub)[0]])
#Make sure that you keep the DC component:
keep_dc = np.copy(power[..., 0])
power[..., idx_0] = 0
power[..., -1 * idx_0] = 0 # Take care of the negative frequencies
power[..., 0] = keep_dc # And put the DC back in when you're done:
data_out = fftpack.ifft(power)
data_out = np.real(data_out) # In order to make sure that you are not
# left with float-precision residual
# complex parts
return ts.TimeSeries(data=data_out,
sampling_rate=self.sampling_rate,
time_unit=self.time_unit)
@desc.setattr_on_read
def filtered_boxcar(self):
"""
Filter the time-series by a boxcar filter.
The low pass filter is implemented by convolving with a boxcar function
of the right length and amplitude and the high-pass filter is
implemented by subtracting a low-pass version (as above) from the
signal
"""
if self.ub is not None:
ub = self.ub / self.sampling_rate
else:
ub = 1.0
lb = self.lb / self.sampling_rate
data_out = tsa.boxcar_filter(np.copy(self.data),
lb=lb, ub=ub,
n_iterations=self._boxcar_iterations)
return ts.TimeSeries(data=data_out,
sampling_rate=self.sampling_rate,
time_unit=self.time_unit)
class HilbertAnalyzer(BaseAnalyzer):
"""Analyzer class for extracting the Hilbert transform """
def __init__(self, input=None):
"""Constructor function for the Hilbert analyzer class.
Parameters
----------
input: TimeSeries
"""
BaseAnalyzer.__init__(self, input)
@desc.setattr_on_read
def analytic(self):
"""The natural output for this analyzer is the analytic signal """
data = self.input.data
sampling_rate = self.input.sampling_rate
#If you have scipy with the fixed scipy.signal.hilbert (r6205 and
#later)
if scipy.__version__ >= '0.9':
hilbert = signal.hilbert
else:
hilbert = tsu.hilbert_from_new_scipy
return ts.TimeSeries(data=hilbert(data),
sampling_rate=sampling_rate)
@desc.setattr_on_read
def amplitude(self):
return ts.TimeSeries(data=np.abs(self.analytic.data),
sampling_rate=self.analytic.sampling_rate)
@desc.setattr_on_read
def phase(self):
return ts.TimeSeries(data=np.angle(self.analytic.data),
sampling_rate=self.analytic.sampling_rate)
@desc.setattr_on_read
def real(self):
return ts.TimeSeries(data=self.analytic.data.real,
sampling_rate=self.analytic.sampling_rate)
@desc.setattr_on_read
def imag(self):
return ts.TimeSeries(data=self.analytic.data.imag,
sampling_rate=self.analytic.sampling_rate)
class MorletWaveletAnalyzer(BaseAnalyzer):
"""Analyzer class for extracting the (complex) Morlet wavelet transform """
def __init__(self, input=None, freqs=None, sd_rel=.2, sd=None, f_min=None,
f_max=None, nfreqs=None, log_spacing=False, log_morlet=False):
"""Constructor function for the Wavelet analyzer class.
Parameters
----------
freqs: list or float
List of center frequencies for the wavelet transform, or a scalar
for a single band-passed signal.
sd: list or float
List of filter bandwidths, given as standard-deviation of center
frequencies. Alternatively sd_rel can be specified.
sd_rel: float
Filter bandwidth, given as a fraction of the center frequencies.
f_min: float
Minimal frequency.
f_max: float
Maximal frequency.
nfreqs: int
Number of frequencies.
log_spacing: bool
If true, frequencies will be evenly spaced on a log-scale.
Default: False
log_morlet: bool
If True, a log-Morlet wavelet is used, if False, a regular Morlet
wavelet is used. Default: False
"""
BaseAnalyzer.__init__(self, input)
self.freqs = freqs
self.sd_rel = sd_rel
self.sd = sd
self.f_min = f_min
self.f_max = f_max
self.nfreqs = nfreqs
self.log_spacing = log_spacing
self.log_morlet = log_morlet
if log_morlet:
self.wavelet = tsa.wlogmorlet
else:
self.wavelet = tsa.wmorlet
if freqs is not None:
self.freqs = np.array(freqs)
elif f_min is not None and f_max is not None and nfreqs is not None:
if log_spacing:
self.freqs = np.logspace(np.log10(f_min), np.log10(f_max),
num=nfreqs, endpoint=True)
else:
self.freqs = np.linspace(f_min, f_max, num=nfreqs,
endpoint=True)
else:
raise NotImplementedError
if sd is None:
self.sd = self.freqs * self.sd_rel
@desc.setattr_on_read
def analytic(self):
"""The natural output for this analyzer is the analytic signal"""
data = self.input.data
sampling_rate = self.input.sampling_rate
a_signal =\
ts.TimeSeries(data=np.zeros(self.freqs.shape + data.shape,
dtype='D'), sampling_rate=sampling_rate)
if self.freqs.ndim == 0:
w = self.wavelet(self.freqs, self.sd,
sampling_rate=sampling_rate, ns=5,
normed='area')
# nd = (w.shape[0] - 1) / 2
a_signal.data[...] = (np.convolve(data, np.real(w), mode='same') +
1j * np.convolve(data, np.imag(w), mode='same'))
else:
for i, (f, sd) in enumerate(zip(self.freqs, self.sd)):
w = self.wavelet(f, sd, sampling_rate=sampling_rate,
ns=5, normed='area')
# nd = (w.shape[0] - 1) / 2
a_signal.data[i, ...] = (
np.convolve(data, np.real(w), mode='same') +
1j * np.convolve(data, np.imag(w), mode='same'))
return a_signal
@desc.setattr_on_read
def amplitude(self):
return ts.TimeSeries(data=np.abs(self.analytic.data),
sampling_rate=self.analytic.sampling_rate)
@desc.setattr_on_read
def phase(self):
return ts.TimeSeries(data=np.angle(self.analytic.data),
sampling_rate=self.analytic.sampling_rate)
@desc.setattr_on_read
def real(self):
return ts.TimeSeries(data=self.analytic.data.real,
sampling_rate=self.analytic.sampling_rate)
@desc.setattr_on_read
def imag(self):
return ts.TimeSeries(data=self.analytic.data.imag,
sampling_rate=self.analytic.sampling_rate)
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