def spectrum_multi_taper(self):
"""
The spectrum and cross-spectra, computed using
:func:`multi_taper_csd'
"""
#Initialize the output
spectrum_multi_taper = np.empty(
(self.input.shape[0], self.input.shape[-1] / 2 + 1))
#If multi-channel data:
if len(self.input.data.shape) > 1:
for i in xrange(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
def spectrum_multi_taper(self):
"""
The spectrum and cross-spectra, computed using
:func:`multi_taper_csd'
"""
#Initialize the output
spectrum_multi_taper = np.empty((self.input.shape[0],
self.input.shape[-1] / 2 + 1))
#If multi-channel data:
if len(self.input.data.shape) > 1:
for i in xrange(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
def test_multitaper_spectral_normalization():
"""
Check that the spectral estimators are normalized in the
correct Watts/Hz fashion
"""
x = np.random.randn(1024)
f1, Xp1, _ = tsa.multi_taper_psd(x)
f2, Xp2, _ = tsa.multi_taper_psd(x, Fs=100)
f3, Xp3, _ = tsa.multi_taper_psd(x, NFFT=2**12)
p1 = np.sum(Xp1) * 2 * np.pi / 2**10
p2 = np.sum(Xp2) * 100 / 2**10
p3 = np.sum(Xp3) * 2 * np.pi / 2**12
npt.assert_( np.abs(p1 - p2) < 1e-14,
'Inconsistent frequency normalization in MTM PSD (1)' )
npt.assert_( np.abs(p3 - p2) < 1e-8,
'Inconsistent frequency normalization in MTM PSD (2)' )
td_var = np.var(x)
# assure that the estimators are at least in the same
# order of magnitude as the time-domain variance
npt.assert_( np.abs(np.log10(p1/td_var)) < 1,
'Incorrect frequency normalization in MTM PSD' )
# check the freq vector while we're here
npt.assert_( f2.max() == 50, 'MTM PSD returns wrong frequency bins' )
def fakequakes_allpsd(home,project_name,run_name):
'''
Compute PSDs for either all the synthetics fo a aprticular run or all the data
'''
from numpy import savez
from obspy import read
import nitime.algorithms as tsa
from glob import glob
from os import path,makedirs
#Decide what I'm going to work on
paths=glob(home+run_name+'/output/waveforms/'+run_name+'.*')
for k in range(len(paths)):
waveforms=glob(paths[k]+'/*.sac')
print 'Working on '+paths[k]
outpath=home+project_name+'/analysis/frequency/'+paths[k].split('/')[-1]
if not path.exists(outpath):
makedirs(outpath)
for ksta in range(len(waveforms)):
sta=waveforms[ksta].split('/')[-1].split('.')[0]
n=read(paths[k]+'/'+sta+'.LYN.sac')
e=read(paths[k]+'/'+sta+'.LYE.sac')
u=read(paths[k]+'/'+sta+'.LYZ.sac')
outname=sta+'.psd'
#Compute spectra
fn, npsd, nu = tsa.multi_taper_psd(n[0].data,Fs=1./n[0].stats.delta,adaptive=True,jackknife=False,low_bias=True,NFFT=512)
fe, epsd, nu = tsa.multi_taper_psd(e[0].data,Fs=1./e[0].stats.delta,adaptive=True,jackknife=False,low_bias=True,NFFT=512)
fu, upsd, nu = tsa.multi_taper_psd(u[0].data,Fs=1./u[0].stats.delta,adaptive=True,jackknife=False,low_bias=True,NFFT=512)
#Write to file
savez(outpath+'/'+outname,fn=fn,fe=fe,fu=fu,npsd=npsd,epsd=epsd,upsd=upsd)
def test_multitaper_spectral_normalization():
"""
Check that the spectral estimators are normalized in the
correct Watts/Hz fashion
"""
x = np.random.randn(1024)
f1, Xp1, _ = tsa.multi_taper_psd(x)
f2, Xp2, _ = tsa.multi_taper_psd(x, Fs=100)
f3, Xp3, _ = tsa.multi_taper_psd(x, NFFT=2**12)
p1 = np.sum(Xp1) * 2 * np.pi / 2**10
p2 = np.sum(Xp2) * 100 / 2**10
p3 = np.sum(Xp3) * 2 * np.pi / 2**12
nt.assert_true(
np.abs(p1 - p2) < 1e-14,
'Inconsistent frequency normalization in MTM PSD (1)')
nt.assert_true(
np.abs(p3 - p2) < 1e-8,
'Inconsistent frequency normalization in MTM PSD (2)')
td_var = np.var(x)
# assure that the estimators are at least in the same
# order of magnitude as the time-domain variance
nt.assert_true(
np.abs(np.log10(p1 / td_var)) < 1,
'Incorrect frequency normalization in MTM PSD')
# check the freq vector while we're here
nt.assert_true(f2.max() == 50, 'MTM PSD returns wrong frequency bins')
def fakequakes_allpsd(home, project_name, run_name):
'''
Compute PSDs for either all the synthetics fo a aprticular run or all the data
'''
from numpy import savez
from obspy import read
import nitime.algorithms as tsa
from glob import glob
from os import path, makedirs
#Decide what I'm going to work on
paths = glob(home + run_name + '/output/waveforms/' + run_name + '.*')
for k in range(len(paths)):
waveforms = glob(paths[k] + '/*.sac')
print('Working on ' + paths[k])
outpath = home + project_name + '/analysis/frequency/' + paths[
k].split('/')[-1]
if not path.exists(outpath):
makedirs(outpath)
for ksta in range(len(waveforms)):
sta = waveforms[ksta].split('/')[-1].split('.')[0]
n = read(paths[k] + '/' + sta + '.LYN.sac')
e = read(paths[k] + '/' + sta + '.LYE.sac')
u = read(paths[k] + '/' + sta + '.LYZ.sac')
outname = sta + '.psd'
#Compute spectra
fn, npsd, nu = tsa.multi_taper_psd(n[0].data,
Fs=1. / n[0].stats.delta,
adaptive=True,
jackknife=False,
low_bias=True,
NFFT=512)
fe, epsd, nu = tsa.multi_taper_psd(e[0].data,
Fs=1. / e[0].stats.delta,
adaptive=True,
jackknife=False,
low_bias=True,
NFFT=512)
fu, upsd, nu = tsa.multi_taper_psd(u[0].data,
Fs=1. / u[0].stats.delta,
adaptive=True,
jackknife=False,
low_bias=True,
NFFT=512)
#Write to file
savez(outpath + '/' + outname,
fn=fn,
fe=fe,
fu=fu,
npsd=npsd,
epsd=epsd,
upsd=upsd)
def multitaper_spectrogram(EEG, Fs, NW, window_length, window_step, EEG_segs=None, dpss=None, eigvals=None):
"""Compute spectrogram using multitaper estimation.
Arguments:
EEG -- EEG signal, size=(channel_num, sample_point_num)
Fs -- sampling frequency in Hz
NW -- the time-halfbandwidth product
window_length -- length of windows in seconds
window_step -- step of windows in seconds
Outputs:
psd estimation, size=(window_num, freq_point_num, channel_num)
frequencies, size=(freq_point_num,)
"""
#window_length = int(round(window_length*Fs))
#window_step = int(round(window_step*Fs))
nfft = max(1<<(window_length-1).bit_length(), window_length)
#freqs = np.arange(0, Fs, Fs*1.0/nfft)[:nfft//2+1]
if EEG_segs is None:
window_starts = np.arange(0,EEG.shape[1]-window_length+1,window_step)
#window_num = len(window_starts)
EEG_segs = detrend(EEG[:,list(map(lambda x:np.arange(x,x+window_length), window_starts))], axis=2)
_, pxx, _ = tsa.multi_taper_psd(EEG_segs, Fs=Fs, NW=NW, adaptive=False, jackknife=False, low_bias=True,
NFFT=nfft)#, dpss=dpss, eigvals=eigvals)
return pxx.transpose(1,2,0)
def get_psd_multitaper(data,
fs,
NW=None,
BW=None,
adaptive=False,
jackknife=True,
sides='default'):
'''
Computes power spectral density using Multitaper functions
Args:
data (nt, nch): time series data where time axis is assumed to be on the last axis
fs (float): sampling rate of the signal
NW (float): Normalized half bandwidth of the data tapers in Hz
BW (float): sampling bandwidth of the data tapers in Hz
adaptive (bool): Use an adaptive weighting routine to combine the PSD estimates of different tapers.
jackknife (bool): Use the jackknife method to make an estimate of the PSD variance at each point.
sides (str): This determines which sides of the spectrum to return.
Returns:
tuple: Tuple containing:
| **f (nfft):** Frequency points vector
| **psd_est (nfft, nch):** estimated power spectral density (PSD)
| **nu (nfft, nch):** if jackknife = True; estimated variance of the log-psd. If Jackknife = False; degrees of freedom in a chi square model of how the estimated psd is distributed wrt true log - PSD
'''
data = data.T # move time to the last axis
f, psd_mt, nu = tsa.multi_taper_psd(data, fs, NW, BW, adaptive, jackknife,
sides)
return f, psd_mt.T, nu.T
def source_spectra(home,project_name,run_name,run_number,rupt,nstrike,ndip):
'''
Tile plot of subfault source-time functions
'''
from numpy import genfromtxt,unique,zeros,where,arange,savez,mean
from mudpy.forward import get_source_time_function,add2stf
import nitime.algorithms as tsa
from string import rjust
outpath=home+project_name+'/analysis/frequency/'
f=genfromtxt(rupt)
num=f[:,0]
nfault=nstrike*ndip
#Get slips
all_ss=f[:,8]
all_ds=f[:,9]
all=zeros(len(all_ss)*2)
iss=2*arange(0,len(all)/2,1)
ids=2*arange(0,len(all)/2,1)+1
all[iss]=all_ss
all[ids]=all_ds
#Now parse for multiple rupture speeds
unum=unique(num)
#Count number of windows
nwin=len(where(num==unum[0])[0])
#Get rigidities
mu=f[0:len(unum),13]
#Get rise times
rise_time=f[0:len(unum),7]
#Get areas
area=f[0:len(unum),10]*f[0:len(unum),11]
for kfault in range(nfault):
if kfault%10==0:
print '... working on subfault '+str(kfault)+' of '+str(nfault)
#Get rupture times for subfault windows
i=where(num==unum[kfault])[0]
trup=f[i,12]
#Get slips on windows
ss=all_ss[i]
ds=all_ds[i]
#Add it up
slip=(ss**2+ds**2)**0.5
#Get first source time function
t1,M1=get_source_time_function(mu[kfault],area[kfault],rise_time[kfault],trup[0],slip[0])
#Loop over windows
for kwin in range(nwin-1):
#Get next source time function
t2,M2=get_source_time_function(mu[kfault],area[kfault],rise_time[kfault],trup[kwin+1],slip[kwin+1])
#Add the soruce time functions
t1,M1=add2stf(t1,M1,t2,M2)
#Convert to slip rate
s=M1/(mu[kfault]*area[kfault])
#remove mean
s=s-mean(s)
#Done now compute spectra of STF
fsample=1./(t1[1]-t1[0])
freq, psd, nu = tsa.multi_taper_psd(s,Fs=fsample,adaptive=True,jackknife=False,low_bias=True)
outname=run_name+'.'+run_number+'.sub'+rjust(str(kfault),4,'0')+'.stfpsd'
savez(outpath+outname,freq=freq,psd=psd)
def mt_power_spectrum(s, sample_rate, window_size, low_bias=False, bandwidth=5.0):
"""
Computes a jackknifed multi-taper power spectrum of a given signal. The jackknife is over
windowed segments of the signal, specified by window_size.
"""
sample_length_bins = min(len(s), int(window_size * sample_rate))
#break signal into chunks and estimate coherence for each chunk
nchunks = int(np.floor(len(s) / float(sample_length_bins)))
nleft = len(s) % sample_length_bins
#ignore the last chunk if it's too short
if nleft > (sample_length_bins / 2.0):
nchunks += 1
ps_freq = None
ps_ests = list()
for k in range(nchunks):
si = k*sample_length_bins
ei = min(len(s), si + sample_length_bins)
print 'si=%d, ei=%d, len(s)=%d' % (si, ei, len(s))
ps_freq,mt_ps,var = ntalg.multi_taper_psd(s[si:ei], Fs=sample_rate, adaptive=True, BW=bandwidth, jackknife=False,
low_bias=low_bias, sides='onesided')
ps_ests.append(mt_ps)
ps_ests = np.array(ps_ests)
ps_mean = ps_ests.mean(axis=0)
ps_std = ps_ests.std(axis=0, ddof=1)
return ps_freq,ps_mean,ps_std
def mt_signal_psd(self):
_, p, _ = tsa.multi_taper_psd(self.signal.data,
Fs=self.input.sampling_rate,
BW=self.bandwidth,
adaptive=self.adaptive,
low_bias=self.low_bias)
return p
def mt_power_spectrum(s, sample_rate, window_size, low_bias=False, bandwidth=5.0):
"""
Computes a jackknifed multi-taper power spectrum of a given signal. The jackknife is over
windowed segments of the signal, specified by window_size.
"""
sample_length_bins = min(len(s), int(window_size * sample_rate))
#break signal into chunks and estimate coherence for each chunk
nchunks = int(np.floor(len(s) / float(sample_length_bins)))
nleft = len(s) % sample_length_bins
#ignore the last chunk if it's too short
if nleft > (sample_length_bins / 2.0):
nchunks += 1
ps_freq = None
ps_ests = list()
for k in range(nchunks):
si = k*sample_length_bins
ei = min(len(s), si + sample_length_bins)
print 'si=%d, ei=%d, len(s)=%d' % (si, ei, len(s))
ps_freq,mt_ps,var = ntalg.multi_taper_psd(s[si:ei], Fs=sample_rate, adaptive=True, BW=bandwidth, jackknife=False,
low_bias=low_bias, sides='onesided')
ps_ests.append(mt_ps)
ps_ests = np.array(ps_ests)
ps_mean = ps_ests.mean(axis=0)
ps_std = ps_ests.std(axis=0, ddof=1)
return ps_freq,ps_mean,ps_std
def mtspecgram(sig, Fs, BW, window, timestep, plot=False, ax=None):
Nwin = int(round(window * Fs))
Nstep = int(round(timestep * Fs))
N = len(sig)
winstart = np.arange(0, N - Nwin + 1, Nstep)
nw = len(winstart)
nfft = max(nextpower2(Nwin), Nwin)
f = getgrid(Fs, nfft)
Nf = len(f)
S = np.zeros((Nf, nw))
for n in range(nw):
idx = np.arange(winstart[n], winstart[n] + Nwin - 1)
data = sig[idx]
f, s, nu = tsa.multi_taper_psd(data, Fs=Fs, BW=BW, NFFT=nfft)
S[:, n] = s
winmid = winstart + round(Nwin / 2.0)
t = winmid / float(Fs)
if plot == True:
plot_specgram(S, t, f, ax)
elif plot == 'dB':
plot_specgram(dB(S), t, f, ax)
return (S, t, f)
def mt_signal_psd(self):
_, p, _ = tsa.multi_taper_psd(self.signal.data,
Fs=self.input.sampling_rate,
BW=self.bandwidth,
adaptive=self.adaptive,
low_bias=self.low_bias)
return p
def test_gh57():
"""
https://github.com/nipy/nitime/issues/57
"""
data = np.random.randn(10, 1000)
for jk in [True,False]:
for adaptive in [True,False]:
f, psd, sigma = tsa.multi_taper_psd(data, adaptive=adaptive,
jackknife=jk)
def test_gh57():
"""
https://github.com/nipy/nitime/issues/57
"""
data = np.random.randn(10, 1000)
for jk in [True, False]:
for adaptive in [True, False]:
f, psd, sigma = tsa.multi_taper_psd(data,
adaptive=adaptive,
jackknife=jk)
def mt_noise_psd(self):
p = np.empty((self.noise.data.shape[0],
self.noise.data.shape[-1] // 2 + 1))
for i in range(p.shape[0]):
_, p[i], _ = tsa.multi_taper_psd(self.noise.data[i],
Fs=self.input.sampling_rate,
BW=self.bandwidth,
adaptive=self.adaptive,
low_bias=self.low_bias)
return np.mean(p, 0)
def mt_noise_psd(self):
p = np.empty(
(self.noise.data.shape[0], self.noise.data.shape[-1] / 2 + 1))
for i in range(p.shape[0]):
_, p[i], _ = tsa.multi_taper_psd(self.noise.data[i],
Fs=self.input.sampling_rate,
BW=self.bandwidth,
adaptive=self.adaptive,
low_bias=self.low_bias)
return np.mean(p, 0)
def get_freq_spectrum(timeseries_data, fsampling, fmin, fmax, plot=True):
"""Transform a clean, downsampled time series data into frequency domain
using the multi-taper method
Args:
timeseries_data ([type]): [N x t time series data, with N brain regions for source localized data or
N channels for sensor data. Duration = t time points, or t/fs seconds]
fsampling ([type]): [sampling frequency of timeseries_data, no default given because this will vary]
fmin (int, optional): Defaults to 2. [low cutoff frequency]
fmax (int, optional): Defaults to 45. [high cutoff frequency]
plot (boolean, optional): Defaults to True. [Plot the spectra?]
Returns:
freq_data (dict): [power spectrum for all input regions/channels]
frange: frequency vector ranging from fmin to fmax
Freq_range: frequency magnitudes within frange
"""
freq_data = {}
lpf = np.array([1, 2, 5, 2, 1])
lpf = lpf / np.sum(lpf)
freq_data = {}
for key in list(timeseries_data.keys()):
timedata = np.asarray(timeseries_data[key].astype(float))
f, psd, nu = tsa.multi_taper_psd(timedata,
Fs=fsampling,
NW=3,
BW=1,
adaptive=False,
jackknife=False)
Fdata = np.convolve(psd, lpf, mode="same")
freq_data[key] = Fdata
ind_fmin = np.abs(f - fmin).argmin()
ind_fmax = np.abs(f - fmax).argmin()
frange = f[ind_fmin:ind_fmax]
Freq_range = Freq_data[:, ind_fmin:ind_fmax]
if plot == True:
# fig1, ax1 = mpl.subplots(1, 1)
# Plotting source localized MEG data
plt.figure(num=1, figsize=[3, 1.5], dpi=300)
plt.xlabel("Frequency (Hz)")
plt.ylabel("Magnitude (dB)")
for g in range(len(Freq_data)):
plt.plot(frange, mag2db(Freq_range[g, :]))
else:
print("No plot")
return freq_data, frange, Freq_range
def test_multi_taper_psd_csd():
"""
Test the multi taper psd and csd estimation functions.
Based on the example in
doc/examples/multi_taper_spectral_estimation.py
"""
N = 2**10
n_reps = 10
psd = []
est_psd = []
est_csd = []
for jk in [True, False]:
for k in range(n_reps):
for adaptive in [True, False]:
ar_seq, nz, alpha = utils.ar_generator(N=N, drop_transients=10)
ar_seq -= ar_seq.mean()
fgrid, hz = tsa.freq_response(1.0,
a=np.r_[1, -alpha],
n_freqs=N)
psd.append(2 * (hz * hz.conj()).real)
f, psd_mt, nu = tsa.multi_taper_psd(ar_seq,
adaptive=adaptive,
jackknife=jk)
est_psd.append(psd_mt)
f, csd_mt = tsa.multi_taper_csd(np.vstack([ar_seq, ar_seq]),
adaptive=adaptive)
# Symmetrical in this case, so take one element out:
est_csd.append(csd_mt[0][1])
fxx = np.mean(psd, axis=0)
fxx_est1 = np.mean(est_psd, axis=0)
fxx_est2 = np.mean(est_csd, axis=0)
# Tests the psd:
psd_ratio1 = np.mean(fxx_est1 / fxx)
npt.assert_array_almost_equal(psd_ratio1, 1, decimal=-1)
# Tests the csd:
psd_ratio2 = np.mean(fxx_est2 / fxx)
npt.assert_array_almost_equal(psd_ratio2, 1, decimal=-1)
def test_multi_taper_psd_csd():
"""
Test the multi taper psd and csd estimation functions.
Based on the example in
doc/examples/multi_taper_spectral_estimation.py
"""
N = 2 ** 10
n_reps = 10
psd = []
est_psd = []
est_csd = []
for jk in [True, False]:
for k in range(n_reps):
for adaptive in [True, False]:
ar_seq, nz, alpha = utils.ar_generator(N=N, drop_transients=10)
ar_seq -= ar_seq.mean()
fgrid, hz = tsa.freq_response(1.0, a=np.r_[1, -alpha],
n_freqs=N)
psd.append(2 * (hz * hz.conj()).real)
f, psd_mt, nu = tsa.multi_taper_psd(ar_seq, adaptive=adaptive,
jackknife=jk)
est_psd.append(psd_mt)
f, csd_mt = tsa.multi_taper_csd(np.vstack([ar_seq, ar_seq]),
adaptive=adaptive)
# Symmetrical in this case, so take one element out:
est_csd.append(csd_mt[0][1])
fxx = np.mean(psd, axis=0)
fxx_est1 = np.mean(est_psd, axis=0)
fxx_est2 = np.mean(est_csd, axis=0)
# Tests the psd:
psd_ratio1 = np.mean(fxx_est1 / fxx)
npt.assert_array_almost_equal(psd_ratio1, 1, decimal=-1)
# Tests the csd:
psd_ratio2 = np.mean(fxx_est2 / fxx)
npt.assert_array_almost_equal(psd_ratio2, 1, decimal=-1)
def test_hermitian_multitaper_csd():
"""
Make sure CSD matrices returned by various methods have
Hermitian symmetry.
"""
sig = np.random.randn(4, 256)
_, csd1 = tsa.multi_taper_csd(sig, adaptive=False)
for i in range(4):
for j in range(i + 1):
xc1 = csd1[i, j]
xc2 = csd1[j, i]
npt.assert_equal(xc1, xc2.conj(), err_msg='MTM CSD not Hermitian')
_, psd, _ = tsa.multi_taper_psd(sig, adaptive=False)
for i in range(4):
npt.assert_almost_equal(
psd[i],
csd1[i, i].real,
err_msg='MTM CSD diagonal inconsistent with real PSD')
def test_hermitian_multitaper_csd():
"""
Make sure CSD matrices returned by various methods have
Hermitian symmetry.
"""
sig = np.random.randn(4,256)
_, csd1 = tsa.multi_taper_csd(sig, adaptive=False)
for i in range(4):
for j in range(i+1):
xc1 = csd1[i,j]
xc2 = csd1[j,i]
npt.assert_equal(
xc1, xc2.conj(), err_msg='MTM CSD not Hermitian'
)
_, psd, _ = tsa.multi_taper_psd(sig, adaptive=False)
for i in range(4):
npt.assert_almost_equal(
psd[i], csd1[i,i].real,
err_msg='MTM CSD diagonal inconsistent with real PSD'
)
# This is the 'true' value, corrected for one-sided spectral density functions
Sxx_true = Sw_true[0, 0].real
Syy_true = Sw_true[1, 1].real
"""
The other is an estimate based on a multi-taper spectral estimate from the
empirical signals:
"""
c_x = np.empty((L, w.shape[0]))
c_y = np.empty((L, w.shape[0]))
for i in range(N):
frex, c_x[i], nu = alg.multi_taper_psd(z[i][0])
frex, c_y[i], nu = alg.multi_taper_psd(z[i][1])
"""
We plot these on the same axes, for a direct comparison:
"""
ax01.plot(w, Sxx_true, 'b', label='true Sxx(w)')
ax01.plot(w, Sxx_est, 'b--', label='estimated Sxx(w)')
ax01.plot(w, Syy_true, 'g', label='true Syy(w)')
ax01.plot(w, Syy_est, 'g--', label='estimated Syy(w)')
ax01.plot(w, np.mean(c_x, 0), 'r', label='Sxx(w) - MT PSD')
ax01.plot(w, np.mean(c_y, 0), 'r--', label='Syy(w) - MT PSD')
# Load Realizations
Xp=np.load('Ice_Age_Realizations.npy')
# Remove Mean for all variables
IT=IT-np.mean(IT)
IP=IP-np.mean(IP)
Id18Op=Id18Op-np.mean(Id18Op)
d18Oi=d18Oi-np.mean(d18Oi)
Xpm=Xp-np.mean(Xp, axis=0)
#
# Compute Spectra For all variables
ITf, ITpsd_mt, ITnu = tsa.multi_taper_psd(IT, Fs=1.0,adaptive=False, jackknife=False)
IPf, IPpsd_mt, IPnu = tsa.multi_taper_psd(IP, Fs=1.0,adaptive=False, jackknife=False)
Id18Opf, Id18Oppsd_mt, Id18Opnu = tsa.multi_taper_psd(Id18Op, Fs=1.0,adaptive=False, jackknife=False)
d18Oif, d18Oipsd_mt, d18Oinu = tsa.multi_taper_psd(d18Oi, Fs=1.0,adaptive=False, jackknife=False)
Xpf=np.zeros((len(ITf),len(Xpm[1])))
Xpsd_mt=np.zeros((len(ITf),len(Xpm[1])))
Xpnu=np.zeros((len(ITf),len(Xpm[1])))
for i in range(len(Xpm[1])):
Xpf[:,i],Xpsd_mt[:,i],Xpnu[:,i]=tsa.multi_taper_psd(Xpm[:,i], Fs=1.0,adaptive=False, jackknife=False)
# Compute quantiles for spectra
from scipy.stats.mstats import mquantiles
import nitime.utils as tsu
signal = np.loadtxt(open("../build/signal.csv", "rb"),
delimiter=",",
skiprows=1)
restored = np.loadtxt(open("../build/restored.csv", "rb"),
delimiter=",",
skiprows=1)
inp_sampling_rate = 1000.
lb = 0 # Hz
ub = 1000 # Hz
_, signal_spectra, _ = tsa.multi_taper_psd(signal,
Fs=inp_sampling_rate,
BW=None,
adaptive=True,
low_bias=True)
_, noise_spectra, _ = tsa.multi_taper_psd(restored - signal,
Fs=inp_sampling_rate,
BW=None,
adaptive=True,
low_bias=True)
freqs = np.linspace(0, inp_sampling_rate / 2, signal.shape[-1] / 2 + 1)
f = plt.figure()
ax = f.add_subplot(1, 2, 1)
ax_snr_info = f.add_subplot(1, 2, 2)
lb_idx, ub_idx = tsu.get_bounds(freqs, lb, ub)
freqs = freqs[lb_idx:ub_idx]
TT = TT - np.mean(TT)
TP = TP - np.mean(TT)
Td18Op = Td18Op - np.mean(Td18Op)
TV = TV - np.mean(TV)
TRH = TRH - np.mean(TRH)
TC = TC - np.mean(TC)
TS = Td18Os - np.mean(Td18Os)
Xpm = Xp - np.mean(Xp, axis=0)
#
# Compute Spectra For all variables
TTf, TTpsd_mt, TTnu = tsa.multi_taper_psd(TT,
Fs=1.0,
adaptive=False,
jackknife=False)
TPf, TPpsd_mt, TPnu = tsa.multi_taper_psd(TP,
Fs=1.0,
adaptive=False,
jackknife=False)
Td18Opf, Td18Oppsd_mt, Td18Opnu = tsa.multi_taper_psd(Td18Op,
Fs=1.0,
adaptive=False,
jackknife=False)
TVf, TVpsd_mt, TVnu = tsa.multi_taper_psd(TV,
Fs=1.0,
adaptive=False,
jackknife=False)
TRHf, TRHpsd_mt, TRHnu = tsa.multi_taper_psd(TRH,
Fs=1.0,
def get_freq_spectrum_notdict(timeseries_data,
fsampling,
fmin=2,
fmax=45,
N=68,
downsample_factor=4,
plot=True):
"""[When input data is not in a dict format. Filters timeseries_data with a band pass filter designed
with cutoff frequencies [fmin, fmax], the filtered time series will be downsampled by a factor of
downsample_factor with a low-pass filter. The downsampled time series is then transformed into the
frequency domain using the multi-taper method]
Args:
timeseries_data ([type]): [N x t time series data, with N brain regions for source localized data or
N channels for sensor data. Duration = t time points, or t/fs seconds]
fsampling ([type]): [sampling frequency of timeseries_data, no default given because this will vary]
downsample_factor ([type]): Defaults to 4. [The ratio to downsample data, for example, 600 Hz MEG data
will be downsampled to 150 Hz. This will be used in the decimate function,
which has a low-pass filter built in to eliminate harmonic contamination]
fmin (int, optional): Defaults to 2. [low cutoff frequency]
fmax (int, optional): Defaults to 45. [high cutoff frequency]
N (int, optional): Defaults to 68. [number of regions or number of channels]
plot (boolean, optional): Defaults to True. [Plot the spectra?]
Returns:
Freq_data[type]: [power spectrum for all input regions/channels]
f : frequency vector/bins for power spectrum
"""
fs = fsampling
fvec = np.linspace(fmin, fmax, 40)
hbp = firls(
101,
np.array([0, 0.2 * fmin, 0.9 * fmin, fmax - 2, fmax + 5, 100]) * 2 /
fs,
desired=np.array([0, 0, 1, 1, 0, 0]),
) # for detrending, a bandpass
lpf = np.array([1, 2, 5, 2, 1])
lpf = lpf / np.sum(lpf)
ind_del = (
hbp.size
) # number of coefficients in hbp. Delete that number in beginning of signal due to filtering
Freq_data = []
for row in timeseries_data:
q = lfilter(hbp, 1, row)
q = q[ind_del:-1]
ds_q = decimate(q, downsample_factor, axis=0)
f, psd, nu = tsa.multi_taper_psd(ds_q,
Fs=fs / downsample_factor,
NW=3,
BW=1,
adaptive=False,
jackknife=False)
Fdata = np.convolve(psd, lpf, mode="same")
Freq_data.append(Fdata)
Freq_data = np.asarray(Freq_data)
assert Freq_data.shape[
0] == N # make sure we have N regions/channels spectra
ind_fmin = np.abs(f - fmin).argmin()
ind_fmax = np.abs(f - fmax).argmin()
frange = f[ind_fmin:ind_fmax]
Freq_range = Freq_data[:, ind_fmin:ind_fmax]
if plot == True:
# fig1, ax1 = mpl.subplots(1, 1)
# Plotting source localized MEG data
plt.figure(num=1, figsize=[3, 1.5], dpi=300)
plt.xlabel("Frequency (Hz)")
plt.ylabel("Magnitude (dB)")
for g in range(len(Freq_data)):
plt.plot(frange, mag2db(Freq_range[g, :]))
else:
print("No plot")
output = (Freq_data, fvec, Freq_range, frange)
return output
Sd18Op=np.load('HIDDEN_d18OP.npy')
Sd18Os=np.load('HIDDEN_d18OS.npy')
H1=np.load('HIDDEN_PDRIP_T_025.npy')
H2=np.load('HIDDEN_PDRIP_T_05.npy')
H3=np.load('HIDDEN_PDRIP_T_1.npy')
H4=np.load('HIDDEN_PDRIP_T_5.npy')
H1=H1-np.mean(H1)
H2=H2-np.mean(H2)
H3=H3-np.mean(H3)
H4=H4-np.mean(H4)
H1f, H1psd_mt, H1nu = tsa.multi_taper_psd(H1, Fs=1.0,adaptive=False, jackknife=False)
H2f, H2psd_mt, H2nu = tsa.multi_taper_psd(H2, Fs=1.0,adaptive=False, jackknife=False)
H3f, H3psd_mt, H3nu = tsa.multi_taper_psd(H3, Fs=1.0,adaptive=False, jackknife=False)
H4f, H4psd_mt, H4nu = tsa.multi_taper_psd(H4, Fs=1.0,adaptive=False, jackknife=False)
ST=ST-np.mean(ST)
SP=SP-np.mean(SP)
Sd18Op=Sd18Op-np.mean(Sd18Op)
Sd18Os=Sd18Os-np.mean(Sd18Os)
STf, STpsd_mt, STnu = tsa.multi_taper_psd(ST, Fs=1.0,adaptive=False, jackknife=False)
SPf, SPpsd_mt, SPnu = tsa.multi_taper_psd(SP, Fs=1.0,adaptive=False, jackknife=False)
Sd18Opf, Sd18Oppsd_mt, Sd18Opnu = tsa.multi_taper_psd(Sd18Op, Fs=1.0,adaptive=False, jackknife=False)
Sd18Osf, Sd18Ospsd_mt, Sd18Osnu = tsa.multi_taper_psd(Sd18Os, Fs=1.0,adaptive=False, jackknife=False)
# get channel names (attribute added during export)
print raw_ts.ch_names[:3]
###############################################################################
# investigate spectral density
import matplotlib.pyplot as plt
import nitime.algorithms as tsa
ch_sel = raw_ts.ch_names.index('MEG 0122')
data_ch = raw_ts.data[ch_sel]
f, psd_mt, nu = tsa.multi_taper_psd(data_ch,
Fs=raw_ts.sampling_rate,
BW=1,
adaptive=False,
jackknife=False)
# Convert PSD to dB
psd_mt = 10 * np.log10(psd_mt)
plt.close('all')
plt.plot(f, psd_mt)
plt.xlabel('Frequency (Hz)')
plt.ylabel('Power Spectrald Density (db/Hz)')
plt.title('Multitaper Power Spectrum \n %s' % raw_ts.ch_names[ch_sel])
plt.show()
p1 = Rectangle((0, 0), 0.5, 0.5, fc="Black")
legend([p1,p2],[r'Original Timeseries (1 Year = 1 Data Point)','1000 Age-Perturbed Realizations [5$\%$]'],loc=3,fontsize=14,frameon=False)
plt.show()
#======================================================================================
Xp=np.load('Palmyra_Age_Perturbed.npy')
# Remove Mean for all variables
CST=SST-np.mean(SST)
CSS=SSS-np.mean(SSS)
Cd18O=Cd18O-np.mean(Cd18O)
Xpm=Xp-np.mean(Xp, axis=0)
# Compute Spectra For all variables
CSTf, CSTpsd_mt, CSTnu = tsa.multi_taper_psd(CST, Fs=1.0,adaptive=False, jackknife=False)
CSSf, CSSpsd_mt, CSSnu = tsa.multi_taper_psd(CSS, Fs=1.0,adaptive=False, jackknife=False)
Cd18Of, Cd18Opsd_mt, Cd18Onu = tsa.multi_taper_psd(Cd18O, Fs=1.0,adaptive=False, jackknife=False)
Xpf=np.zeros((len(CSTf),len(Xpm[1])))
Xpsd_mt=np.zeros((len(CSTf),len(Xpm[1])))
Xpnu=np.zeros((len(CSTf),len(Xpm[1])))
for i in range(len(Xpm[1])):
Xpf[:,i],Xpsd_mt[:,i],Xpnu[:,i]=tsa.multi_taper_psd(Xpm[:,i], Fs=1.0,adaptive=False, jackknife=False)
# Compute quantiles for spectra
from scipy.stats.mstats import mquantiles
nast_e.trim(starttime=time_epi)
nast_u.trim(starttime=time_epi)
katnp_n.trim(starttime=time_epi)
katnp_e.trim(starttime=time_epi)
katnp_u.trim(starttime=time_epi)
kkn4_n[0].data = r_[0, diff(kkn4_n[0].data) / 0.2]
kkn4_e[0].data = r_[0, diff(kkn4_e[0].data) / 0.2]
kkn4_u[0].data = r_[0, diff(kkn4_u[0].data) / 0.2]
nast_n[0].data = r_[0, diff(nast_n[0].data) / 0.2]
nast_e[0].data = r_[0, diff(nast_e[0].data) / 0.2]
nast_u[0].data = r_[0, diff(nast_u[0].data) / 0.2]
fn_kkn4, npsd_kkn4, nu = tsa.multi_taper_psd(kkn4_n[0].data,
Fs=1. / kkn4_n[0].stats.delta,
adaptive=True,
jackknife=False,
low_bias=True)
fe_kkn4, epsd_kkn4, nu = tsa.multi_taper_psd(kkn4_e[0].data,
Fs=1. / kkn4_e[0].stats.delta,
adaptive=True,
jackknife=False,
low_bias=True)
fu_kkn4, upsd_kkn4, nu = tsa.multi_taper_psd(kkn4_u[0].data,
Fs=1. / kkn4_u[0].stats.delta,
adaptive=True,
jackknife=False,
low_bias=True)
fn_nast, npsd_nast, nu = tsa.multi_taper_psd(nast_n[0].data,
Fs=1. / nast_n[0].stats.delta,
# index at certain time
print raw_ts.at(110.5)
# get channel names (attribute added during export)
print raw_ts.ch_names[:3]
###############################################################################
# investigate spectral density
import matplotlib.pyplot as plt
import nitime.algorithms as tsa
ch_sel = raw_ts.ch_names.index('MEG 0122')
data_ch = raw_ts.data[ch_sel]
f, psd_mt, nu = tsa.multi_taper_psd(data_ch, Fs=raw_ts.sampling_rate,
BW=1, adaptive=False, jackknife=False)
# Convert PSD to dB
psd_mt = 10 * np.log10(psd_mt)
plt.close('all')
plt.plot(f, psd_mt)
plt.xlabel('Frequency (Hz)')
plt.ylabel('Power Spectrald Density (db/Hz)')
plt.title('Multitaper Power Spectrum \n %s' % raw_ts.ch_names[ch_sel])
plt.show()
# --- Direct Spectral Estimator freqs, d_sdf = alg.periodogram(ar_seq) dB(d_sdf, d_sdf) # --- Welch's Overlapping Periodogram Method via mlab mlab_sdf, mlab_freqs = pp.mlab.psd(ar_seq, NFFT=N) mlab_freqs *= np.pi / mlab_freqs.max() mlab_sdf = mlab_sdf.squeeze() dB(mlab_sdf, mlab_sdf) ### Taper Bandwidth Adjustments NW = 4 # --- Regular Multitaper Estimate f, sdf_mt, nu = alg.multi_taper_psd(ar_seq, width=NW, adaptive=False, jackknife=False) dB(sdf_mt, sdf_mt) # OK.. grab the number of tapers used from here Kmax = nu[0] / 2 # --- Adaptively Weighted Multitapter Estimate # -- Adaptive weighting from Thompson 1982, or Percival and Walden 1993 f, adaptive_sdf_mt, nu = alg.multi_taper_psd(ar_seq, width=NW, adaptive=True, jackknife=False) dB(adaptive_sdf_mt, adaptive_sdf_mt) # --- Jack-knifed intervals for regular weighting----------------------------- # currently returns log-variance _, _, jk_var = alg.multi_taper_psd(ar_seq, width=NW, adaptive=False, jackknife=True) # the Jackknife mean is approximately distributed about the true log-sdf # as a Student's t distribution with variance jk_var ... but in
def MTM_specgram(data,movingwin=[0.2, 0.050],**kwargs):
'''modeled from mtspecgramc.m
data: format: time x trials (i.e. data[:,0] is 1 trial)
movingwin: is in the format of [window, window_step] e.g. [0.2, 0.05] sec
kwargs:
tapers: in the form of [TW, K] e.g. [5/2 5]
pad: (padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs: (sampling frequency)
fpass: (frequency band to be used in the calculation in the form fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
trialave (average over trials/channels when 1
Output:
S (spectrum in form time x frequency x channels/trials if trialave=0;
in the form time x frequency if trialave=1)
t (times)
f (frequencies)
'''
if 'tapers' in kwargs.keys():
tapers = kwargs['tapers']
else:
tapers = [5/2, 5]
if 'pad' in kwargs.keys():
pad = kwargs['pad']
else:
pad = 0
if 'Fs' in kwargs.keys():
Fs = kwargs['Fs']
else:
Fs = 1000
if 'fpass' in kwargs.keys():
fpass = kwargs['fpass']
else:
fpass = [0, 100]
if 'trialave' in kwargs.keys():
trialave = kwargs['trialave']
else:
trialave = 0
num_trials = data.shape[1]
N = data.shape[0] #ms of trials
Nwin=round(Fs*movingwin[0])
Nstep=round(Fs*movingwin[1])
t_power = 1
while 2**t_power < Nwin:
t_power +=1
nfft = 2**(t_power+pad)
#f=getfgrid(Fs,nfft,fpass)wi
#f = np.arange(0,501,5)
winstart=np.arange(0,N-Nwin,Nstep)
nw=len(winstart)
#Dimensions of S: trials x num_win (t) x f
for n in range(nw):
datawin=data[int(winstart[int(n)]):int(winstart[int(n)])+int(Nwin),:].T
if datawin.shape[1] < nfft :
dat = np.zeros(( datawin.shape[0], nfft ))
pad = (nfft - datawin.shape[1])
if pad%2: #Odd:
pad1 = pad2 = np.floor(pad/2.)
elif not pad%2:
pad1 = pad2 = pad/2
dat[:, pad1:(datawin.shape[1]+pad2)] = datawin
elif nfft == datawin.shape[1]:
dat = datawin
else:
raise Exception("Not implemented yet...")
if 'small_f_steps' in kwargs.keys():
f, psd_est, nu = tsa.multi_taper_psd(dat,Fs=Fs, NFFT=nfft)
else:
f, psd_est, nu = tsa.multi_taper_psd(dat,Fs=Fs)
if n==0:
S = np.zeros(( num_trials, nw, len(f[f<fpass[1]]) ))
#print len(f), psd_est.shape, len(nu), S.shape, len(f<fpass[1])
S[:,n,:] = psd_est[:,f<fpass[1]]
t=(winstart+round(Nwin/2))/float(Fs)
if trialave:
S = np.mean(S,axis=0)
return S, f, t
import matplotlib.pyplot as plt
import nitime.utils as utils
import nitime.timeseries as ts
import nitime.viz as viz
from nitime import algorithms as tsa
import nitime.utils as tsu
signal = np.loadtxt(open("../build/signal.csv", "rb"), delimiter=",", skiprows=1)
restored = np.loadtxt(open("../build/restored.csv", "rb"), delimiter=",", skiprows=1)
inp_sampling_rate = 1000.0
lb = 0 # Hz
ub = 1000 # Hz
_, signal_spectra, _ = tsa.multi_taper_psd(signal, Fs=inp_sampling_rate, BW=None, adaptive=True, low_bias=True)
_, noise_spectra, _ = tsa.multi_taper_psd(
restored - signal, Fs=inp_sampling_rate, BW=None, adaptive=True, low_bias=True
)
freqs = np.linspace(0, inp_sampling_rate / 2, signal.shape[-1] / 2 + 1)
f = plt.figure()
ax = f.add_subplot(1, 2, 1)
ax_snr_info = f.add_subplot(1, 2, 2)
lb_idx, ub_idx = tsu.get_bounds(freqs, lb, ub)
freqs = freqs[lb_idx:ub_idx]
snr = signal_spectra / noise_spectra
ax.plot(freqs, np.log(signal_spectra[lb_idx:ub_idx]), label="Signal")
def allpsd(home,project_name,run_name,run_number,GF_list,d_or_s,v_or_d,decimate,lowpass):
'''
Compute PSDs for either all the synthetics fo a aprticular run or all the data
'''
from numpy import genfromtxt,where,log10,savez
from obspy import read
from mudpy.forward import lowpass as lfilter
from mudpy.green import stdecimate
import nitime.algorithms as tsa
#Decide what I'm going to work on
sta=genfromtxt(home+project_name+'/data/station_info/'+GF_list,usecols=0,dtype='S')
gf=genfromtxt(home+project_name+'/data/station_info/'+GF_list,usecols=[4,5],dtype='f')
datapath=home+project_name+'/data/waveforms/'
synthpath=home+project_name+'/output/inverse_models/waveforms/'
outpath=home+project_name+'/analysis/frequency/'
if v_or_d.lower()=='d':
kgf=0 #disp
datasuffix='kdisp'
synthsuffix='disp'
elif v_or_d.lower()=='v':
kgf=1 #disp
datasuffix='kvel'
synthsuffix='vel'
if d_or_s.lower()=='d': #We're working on observed data
path=datapath
suffix=datasuffix
else: #We're looking at syntehtics from a certain run
path=synthpath
suffix=synthsuffix
i=where(gf[:,kgf]==1)[0]
for k in range(len(i)):
print 'Working on '+sta[i[k]]
if d_or_s.lower()=='d': #Read data
n=read(path+sta[i[k]]+'.'+suffix+'.n')
e=read(path+sta[i[k]]+'.'+suffix+'.e')
u=read(path+sta[i[k]]+'.'+suffix+'.u')
outname=sta[i[k]]+'.'+suffix+'.psd'
if lowpass!=None:
fsample=1./e[0].stats.delta
e[0].data=lfilter(e[0].data,lowpass,fsample,10)
n[0].data=lfilter(n[0].data,lowpass,fsample,10)
u[0].data=lfilter(u[0].data,lowpass,fsample,10)
if decimate!=None:
n[0]=stdecimate(n[0],decimate)
e[0]=stdecimate(e[0],decimate)
u[0]=stdecimate(u[0],decimate)
else: #Read synthetics
n=read(path+run_name+'.'+run_number+'.'+sta[i[k]]+'.'+suffix+'.n.sac')
e=read(path+run_name+'.'+run_number+'.'+sta[i[k]]+'.'+suffix+'.e.sac')
u=read(path+run_name+'.'+run_number+'.'+sta[i[k]]+'.'+suffix+'.u.sac')
outname=run_name+'.'+run_number+'.'+sta[i[k]]+'.'+suffix+'.psd'
#Compute spectra
fn, npsd, nu = tsa.multi_taper_psd(n[0].data,Fs=1./n[0].stats.delta,adaptive=True,jackknife=False,low_bias=True)
fe, epsd, nu = tsa.multi_taper_psd(e[0].data,Fs=1./e[0].stats.delta,adaptive=True,jackknife=False,low_bias=True)
fu, upsd, nu = tsa.multi_taper_psd(u[0].data,Fs=1./u[0].stats.delta,adaptive=True,jackknife=False,low_bias=True)
#Convert to dB
npsd=10*log10(npsd)
epsd=10*log10(epsd)
upsd=10*log10(upsd)
#Write to file
savez(outpath+outname,fn=fn,fe=fe,fu=fu,npsd=npsd,epsd=epsd,upsd=upsd)
def get_spectrum(v, N, dt=None, method="welch", detrend=False, **kwargs):
"""Compute a lagged correlation between two time series
These time series are assumed to be regularly sampled in time
and along the same time line.
Parameters
----------
v: ndarray, pd.Series
Time series, the index must be time if dt is not provided
N: int
Length of the output
dt: float, optional
Time step
method: string
Method that will be employed for spectral calculations.
Default is 'welch'
detrend: str or function or False, optional
Turns detrending on or off. Default is False.
See:
- https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.signal.periodogram.html
- https://krischer.github.io/mtspec/
- http://nipy.org/nitime/examples/multi_taper_spectral_estimation.html
"""
if v is None:
_v = np.random.randn(N)
else:
_v = v.iloc[:N]
if dt is None:
dt = _v.reset_index()["index"].diff().mean()
if detrend and not method == "welch":
print("!!! Not implemented yet except for welch")
if method == "welch":
from scipy import signal
dkwargs = {
"window": "hann",
"return_onesided": False,
"detrend": detrend,
"scaling": "density",
}
dkwargs.update(kwargs)
f, E = signal.periodogram(_v, fs=1 / dt, axis=0, **dkwargs)
elif method == "mtspec":
from mtspec import mtspec
lE, f = mtspec(data=_v,
delta=dt,
time_bandwidth=4.0,
number_of_tapers=6,
quadratic=True)
elif method == "mt":
import nitime.algorithms as tsa
dkwargs = {
"NW": 2,
"sides": "twosided",
"adaptive": False,
"jackknife": False
}
dkwargs.update(kwargs)
lf, E, nu = tsa.multi_taper_psd(_v, Fs=1 / dt, **dkwargs)
f = fftfreq(len(lf)) * 24.0
# print('Number of tapers = %d' %(nu[0]/2))
return pd.Series(E, index=f)
def mtm(ys,
ts,
NW=None,
BW=None,
detrend=None,
sg_kwargs=None,
gaussianize=False,
standardize=False,
adaptive=False,
jackknife=True,
low_bias=True,
sides='default',
nfft=None):
''' Retuns spectral density using a multi-taper method.
Based on the function in the time series analysis for neuroscience toolbox: http://nipy.org/nitime/api/generated/nitime.algorithms.spectral.html
Parameters
----------
ys : array
a time series
ts : array
time axis of the time series
NW : float
The normalized half-bandwidth of the data tapers, indicating a
multiple of the fundamental frequency of the DFT (Fs/N).
Common choices are n/2, for n >= 4.
BW : float
The sampling-relative bandwidth of the data tapers
detrend : str
If None, no detrending is applied. Available detrending methods:
- None - no detrending will be applied (default);
- linear - a linear least-squares fit to `ys` is subtracted;
- constant - the mean of `ys` is subtracted
- savitzy-golay - ys is filtered using the Savitzky-Golay filters and the resulting filtered series is subtracted from y.
- emd - Empirical mode decomposition
sg_kwargs : dict
The parameters for the Savitzky-Golay filters. see pyleoclim.utils.filter.savitzy_golay for details.
gaussianize : bool
If True, gaussianizes the timeseries
standardize : bool
If True, standardizes the timeseries
adaptive : {True/False}
Use an adaptive weighting routine to combine the PSD estimates of
different tapers.
jackknife : {True/False}
Use the jackknife method to make an estimate of the PSD variance
at each point.
low_bias : {True/False}
Rather than use 2NW tapers, only use the tapers that have better than
90% spectral concentration within the bandwidth (still using
a maximum of 2NW tapers)
sides : str (optional) [ 'default' | 'onesided' | 'twosided' ]
This determines which sides of the spectrum to return.
For complex-valued inputs, the default is two-sided, for real-valued
inputs, default is one-sided Indicates whether to return a one-sided
or two-sided
Returns
-------
res_dict : dict
the result dictionary, including
- freq (array): the frequency vector
- psd (array): the spectral density vector
See Also
--------
pyleoclim.utils.spectral.periodogram : Estimate power spectral density using a periodogram
pyleoclim.utils.spectral.welch : Retuns spectral density using the welch method
pyleoclim.utils.spectral.lomb_scargle : Return the computed periodogram using lomb-scargle algorithm
pyleoclim.utils.spectral.wwz_psd : Return the psd of a timeseries using wwz method.
pyleoclim.utils.filter.savitzy_golay : Filtering using Savitzy-Golay
pyleoclim.utils.tsutils.detrend : Detrending method
'''
# preprocessing
ts = np.array(ts)
ys = np.array(ys)
if len(ts) != len(ys):
raise ValueError('Time and value axis should be the same length')
# remove NaNs
ys, ts = clean_ts(ys, ts)
# check for evenly-spaced
check = is_evenly_spaced(ts)
if check == False:
raise ValueError('For the MTM method, data should be evenly spaced')
# preprocessing
ys = preprocess(ys,
ts,
detrend=detrend,
sg_kwargs=sg_kwargs,
gaussianize=gaussianize,
standardize=standardize)
# calculate sampling frequency fs
dt = np.median(np.diff(ts))
fs = 1 / dt
# spectral analysis
freq, psd, nu = nialg.multi_taper_psd(ys,
Fs=fs,
NW=NW,
BW=BW,
adaptive=adaptive,
jackknife=jackknife,
low_bias=low_bias,
sides=sides,
NFFT=nfft) # call nitime func
# fix the zero frequency point
if freq[0] == 0:
psd[0] = np.nan
# output result
res_dict = {
'freq': np.asarray(freq),
'psd': np.asarray(psd),
}
return res_dict
dB(welch_psd, welch_psd)
fig04 = plot_spectral_estimate(freqs, psd, (welch_psd,), elabels=("Welch",))
"""
.. image:: fig/multi_taper_spectral_estimation_04.png
Next, we use the multi-taper estimation method. We estimate the spectrum:
"""
f, psd_mt, nu = tsa.multi_taper_psd(
ar_seq, adaptive=False, jackknife=False
)
dB(psd_mt, psd_mt)
"""
And get the number of tapers from here:
"""
Kmax = nu[0]/2
"""
#p = d18O p for SPEEDY
# Remove Mean for all variables
echam_p = ECHAM_p - np.mean(ECHAM_p)
echam_piso = ECHAM_piso - np.mean(ECHAM_piso)
echam_ice = ECHAM_ice - np.mean(ECHAM_ice)
quel_data = quel2 - np.mean(quel2)
quel_speedy = quel - np.mean(quel)
p_speedy = p - np.mean(p)
#
# Compute Spectra For all variables
ef, epsd_mt, enu = tsa.multi_taper_psd(echam_p,
Fs=1.0,
adaptive=False,
jackknife=False)
epf, eppsd_mt, epnu = tsa.multi_taper_psd(echam_piso,
Fs=1.0,
adaptive=False,
jackknife=False)
eif, eipsd_mt, einu = tsa.multi_taper_psd(echam_ice,
Fs=1.0,
adaptive=False,
jackknife=False)
queldf, queldpsd_mt, queldnu = tsa.multi_taper_psd(quel_data,
Fs=1.0,
adaptive=False,
jackknife=False)
quelsf, quelspsd_mt, quelsnu = tsa.multi_taper_psd(quel_speedy,
t=np.arange(1000,2005,1)
dt=1.0
# Load Age-perturbed data:
Bchron=np.load('Cave_Age_Realizations.npy')
# Remove Mean for all variables
Xpm=Bchron-np.mean(Bchron, axis=0)
#
ST=ST-np.mean(ST)
SP=SP-np.mean(SP)
Sd18Op=Sd18Op-np.mean(Sd18Op)
Sd18Os=Sd18Os-np.mean(Sd18Os)
Sd18Oc=Sd18Oc-np.mean(Sd18Oc)
# Compute Spectra For all variables
STf, STpsd_mt, STnu = tsa.multi_taper_psd(ST, Fs=1.0,adaptive=False, jackknife=False)
SPf, SPpsd_mt, SPnu = tsa.multi_taper_psd(SP, Fs=1.0,adaptive=False, jackknife=False)
Sd18Opf, Sd18Oppsd_mt, Sd18Opnu = tsa.multi_taper_psd(Sd18Op, Fs=1.0,adaptive=False, jackknife=False)
Sd18Osf, Sd18Ospsd_mt, Sd18Osnu = tsa.multi_taper_psd(Sd18Os, Fs=1.0,adaptive=False, jackknife=False)
Sd18Ocf, Sd18Ocpsd_mt, Sd18Osnu = tsa.multi_taper_psd(Sd18Oc, Fs=1.0,adaptive=False, jackknife=False)
Xpf=np.zeros((len(STf),len(Xpm[1])))
Xpsd_mt=np.zeros((len(STf),len(Xpm[1])))
Xpnu=np.zeros((len(STf),len(Xpm[1])))
for i in range(len(Xpm[1])):
Xpf[:,i],Xpsd_mt[:,i],Xpnu[:,i]=tsa.multi_taper_psd(Xpm[:,i], Fs=1.0,adaptive=False, jackknife=False)
# Compute quantiles for spectra
def source_spectra(home, project_name, run_name, run_number, rupt, nstrike,
ndip):
'''
Tile plot of subfault source-time functions
'''
from numpy import genfromtxt, unique, zeros, where, arange, savez, mean
from mudpy.forward import get_source_time_function, add2stf
import nitime.algorithms as tsa
outpath = home + project_name + '/analysis/frequency/'
f = genfromtxt(rupt)
num = f[:, 0]
nfault = nstrike * ndip
#Get slips
all_ss = f[:, 8]
all_ds = f[:, 9]
all = zeros(len(all_ss) * 2)
iss = 2 * arange(0, len(all) / 2, 1)
ids = 2 * arange(0, len(all) / 2, 1) + 1
all[iss] = all_ss
all[ids] = all_ds
#Now parse for multiple rupture speeds
unum = unique(num)
#Count number of windows
nwin = len(where(num == unum[0])[0])
#Get rigidities
mu = f[0:len(unum), 13]
#Get rise times
rise_time = f[0:len(unum), 7]
#Get areas
area = f[0:len(unum), 10] * f[0:len(unum), 11]
for kfault in range(nfault):
if kfault % 10 == 0:
print('... working on subfault ' + str(kfault) + ' of ' +
str(nfault))
#Get rupture times for subfault windows
i = where(num == unum[kfault])[0]
trup = f[i, 12]
#Get slips on windows
ss = all_ss[i]
ds = all_ds[i]
#Add it up
slip = (ss**2 + ds**2)**0.5
#Get first source time function
t1, M1 = get_source_time_function(mu[kfault], area[kfault],
rise_time[kfault], trup[0], slip[0])
#Loop over windows
for kwin in range(nwin - 1):
#Get next source time function
t2, M2 = get_source_time_function(mu[kfault], area[kfault],
rise_time[kfault],
trup[kwin + 1], slip[kwin + 1])
#Add the soruce time functions
t1, M1 = add2stf(t1, M1, t2, M2)
#Convert to slip rate
s = M1 / (mu[kfault] * area[kfault])
#remove mean
s = s - mean(s)
#Done now compute spectra of STF
fsample = 1. / (t1[1] - t1[0])
freq, psd, nu = tsa.multi_taper_psd(s,
Fs=fsample,
adaptive=True,
jackknife=False,
low_bias=True)
outname = run_name + '.' + run_number + '.sub' + str(kfault).rjust(
4, '0') + '.stfpsd'
savez(outpath + outname, freq=freq, psd=psd)
def get_freq_spectrum(timeseries_data,
fsampling,
fmin=2,
fmax=45,
N=68,
downsample_factor=4):
"""[Filters timeseries_data with a band pass filter designed with cutoff frequencies [fmin, fmax],
the filtered time series will be downsampled by a factor of downsample_factor with a low-pass
filter. The downsampled time series is then transformed into the frequency domain using the
multi-taper method]
Args:
timeseries_data ([type]): [N x t time series data, with N brain regions for source localized data or
N channels for sensor data. Duration = t time points, or t/fs seconds]
fsampling ([type]): [sampling frequency of timeseries_data, no default given because this will vary]
downsample_factor ([type]): Defaults to 4. [The ratio to downsample data, for example, 600 Hz MEG data
will be downsampled to 150 Hz. This will be used in the decimate function,
which has a low-pass filter built in to eliminate harmonic contamination]
fmin (int, optional): Defaults to 2. [low cutoff frequency]
fmax (int, optional): Defaults to 45. [high cutoff frequency]
N (int, optional): Defaults to 68. [number of regions or number of channels]
Returns:
Freq_data[type]: [power spectrum for all input regions/channels]
f : frequency vector/bins for power spectrum
"""
fs = fsampling
fvec = np.linspace(fmin, fmax, 40)
hbp = firls(
101,
np.array([0, 0.2 * fmin, 0.9 * fmin, fmax - 2, fmax + 5, 100]) * 2 /
fs,
desired=np.array([0, 0, 1, 1, 0, 0]),
) # for detrending, a bandpass
lpf = np.array([1, 2, 5, 2, 1])
lpf = lpf / np.sum(lpf)
ind_del = (
hbp.size
) # number of coefficients in hbp. Delete that number in beginning of signal due to filtering
Freq_data = {}
for key in list(timeseries_data.keys()):
data = timeseries_data[key]
data = data.astype(float)
row = np.asarray(data)
q = lfilter(hbp, 1, row)
q = q[ind_del:-1] # delete transient portions
ds_q = decimate(q, downsample_factor, axis=0)
f, psd, nu = tsa.multi_taper_psd(ds_q,
Fs=fs / downsample_factor,
NW=3,
BW=1,
adaptive=False,
jackknife=False)
Fdata = np.convolve(psd, lpf, mode="same")
Freq_data[key] = Fdata
assert (
len(Freq_data) == N
) # make sure we have correct number of regions/channels in the spectra
# ind_fmin = np.abs(f-fmin).argmin()
# ind_fmax = np.abs(f-fmax).argmin()
# frange = f[ind_fmin:ind_fmax]
# FMEGrange = Freq_data[:,ind_fmin:ind_fmax]
return Freq_data, f
def allpsd(home, project_name, run_name, run_number, GF_list, d_or_s, v_or_d,
decimate, lowpass):
'''
Compute PSDs for either all the synthetics fo a aprticular run or all the data
'''
from numpy import genfromtxt, where, log10, savez
from obspy import read
from mudpy.forward import lowpass as lfilter
from mudpy.green import stdecimate
import nitime.algorithms as tsa
#Decide what I'm going to work on
sta = genfromtxt(home + project_name + '/data/station_info/' + GF_list,
usecols=0,
dtype='S')
gf = genfromtxt(home + project_name + '/data/station_info/' + GF_list,
usecols=[4, 5],
dtype='f')
datapath = home + project_name + '/data/waveforms/'
synthpath = home + project_name + '/output/inverse_models/waveforms/'
outpath = home + project_name + '/analysis/frequency/'
if v_or_d.lower() == 'd':
kgf = 0 #disp
datasuffix = 'kdisp'
synthsuffix = 'disp'
elif v_or_d.lower() == 'v':
kgf = 1 #disp
datasuffix = 'kvel'
synthsuffix = 'vel'
if d_or_s.lower() == 'd': #We're working on observed data
path = datapath
suffix = datasuffix
else: #We're looking at syntehtics from a certain run
path = synthpath
suffix = synthsuffix
i = where(gf[:, kgf] == 1)[0]
for k in range(len(i)):
print('Working on ' + sta[i[k]])
if d_or_s.lower() == 'd': #Read data
n = read(path + sta[i[k]] + '.' + suffix + '.n')
e = read(path + sta[i[k]] + '.' + suffix + '.e')
u = read(path + sta[i[k]] + '.' + suffix + '.u')
outname = sta[i[k]] + '.' + suffix + '.psd'
if lowpass != None:
fsample = 1. / e[0].stats.delta
e[0].data = lfilter(e[0].data, lowpass, fsample, 10)
n[0].data = lfilter(n[0].data, lowpass, fsample, 10)
u[0].data = lfilter(u[0].data, lowpass, fsample, 10)
if decimate != None:
n[0] = stdecimate(n[0], decimate)
e[0] = stdecimate(e[0], decimate)
u[0] = stdecimate(u[0], decimate)
else: #Read synthetics
n = read(path + run_name + '.' + run_number + '.' + sta[i[k]] +
'.' + suffix + '.n.sac')
e = read(path + run_name + '.' + run_number + '.' + sta[i[k]] +
'.' + suffix + '.e.sac')
u = read(path + run_name + '.' + run_number + '.' + sta[i[k]] +
'.' + suffix + '.u.sac')
outname = run_name + '.' + run_number + '.' + sta[
i[k]] + '.' + suffix + '.psd'
#Compute spectra
fn, npsd, nu = tsa.multi_taper_psd(n[0].data,
Fs=1. / n[0].stats.delta,
adaptive=True,
jackknife=False,
low_bias=True)
fe, epsd, nu = tsa.multi_taper_psd(e[0].data,
Fs=1. / e[0].stats.delta,
adaptive=True,
jackknife=False,
low_bias=True)
fu, upsd, nu = tsa.multi_taper_psd(u[0].data,
Fs=1. / u[0].stats.delta,
adaptive=True,
jackknife=False,
low_bias=True)
#Convert to dB
npsd = 10 * log10(npsd)
epsd = 10 * log10(epsd)
upsd = 10 * log10(upsd)
#Write to file
savez(outpath + outname,
fn=fn,
fe=fe,
fu=fu,
npsd=npsd,
epsd=epsd,
upsd=upsd)
method=dict(this_method='welch',
NFFT=N))
welch_freqs *= (np.pi / welch_freqs.max())
welch_psd = welch_psd.squeeze()
dB(welch_psd, welch_psd)
fig04 = plot_spectral_estimate(freqs, psd, (welch_psd, ), elabels=("Welch", ))
"""
.. image:: fig/multi_taper_spectral_estimation_04.png
Next, we use the multitaper estimation method. We estimate the spectrum:
"""
f, psd_mt, nu = tsa.multi_taper_psd(ar_seq, adaptive=False, jackknife=False)
dB(psd_mt, psd_mt)
"""
And get the number of tapers from here:
"""
Kmax = nu[0] / 2
"""
We calculate a Chi-squared model 95% confidence interval 2*Kmax degrees of
freedom (see [Percival1993]_ eq 258)
"""