def corr_x_av_palm(vSeq, tSeq, zInd, yInd, xSeq, dInd):
dt = tSeq[-1] - tSeq[-2]
corr = []
for p in range(xSeq.size - dInd):
u0 = vSeq[:,zInd,yInd,p]
u1 = vSeq[:,zInd,yInd,p+dInd]
tmp = funcs.crosscorr_FFT(u1,u0,dt)
corr.append(tmp[1])
tau = tmp[0]
corr = np.average(np.array(corr),axis=0)
return tau, corr
def corr_x_av_sowfa(vSeq, tSeq, zInd, ySeq, xSeq, dInd):
dt = tSeq[-1] - tSeq[-2]
xNum = xSeq.size
yNum = ySeq.size
pInd_start = xNum*yNum*zInd
pInd_end = xNum*yNum*(zInd+1)
corr = []
for p in range(pInd_end - pInd_start - dInd):
u0 = vSeq[p]
u1 = vSeq[p+dInd]
tmp = funcs.crosscorr_FFT(u1,u0,dt)
corr.append(tmp[1])
tau = tmp[0]
corr = np.average(np.array(corr),axis=0)
return tau, corr
def crosscorr_palm(t_para, tSeq, dInd, zInd, xNum, vSeq):
t_start = t_para[0]
t_end = t_para[1]
t_delta = t_para[2]
fs = 1 / t_delta # sampling frequency
t_num = int((t_end - t_start) / t_delta + 1)
t_seq = np.linspace(t_start, t_end, t_num)
crosscorr_list = []
for p in range(0,xNum-dInd):
v0 = vSeq[:,zInd,0,p]
v1 = vSeq[:,zInd,0,p+dInd]
f0 = interp1d(tSeq, v0, kind='linear', fill_value='extrapolate')
v0_ = f0(t_seq)
f1 = interp1d(tSeq, v1, kind='linear', fill_value='extrapolate')
v1_ = f1(t_seq)
tau, corr, phase = funcs.crosscorr_FFT(v1_, v0_, 1/fs, norm_=True)
crosscorr_list.append(corr)
corr = np.average(np.array(crosscorr_list), axis=0)
return tau, corr
u1 = funcs.fourier_series(tSeq, ASeq, omgSeq, kSeq, x1, phiSeq)
# white noise
n0 = np.random.rand(t_N) * 5
n1 = np.random.rand(t_N) * 5
u0 += n0
u1 += n1
SNR0 = np.var(u0) / np.var(n0)
SNR1 = np.var(u1) / np.var(n1)
""" auto-correlation coefficient """
tau0, R0 = funcs.autocorr_FFT(u0, fs)
tau1, R1 = funcs.autocorr_FFT(u1, fs)
""" auto-correlation coefficient """
tau, R, phase__ = funcs.crosscorr_FFT(u0, u1, fs)
""" PSD """
segNum = int(120 * fs)
freq0, S0 = scipy.signal.csd(u0, u0, fs, nperseg=segNum, noverlap=None)
freq1, S1 = scipy.signal.csd(u1, u1, fs, nperseg=segNum, noverlap=None)
""" CSD """
segNum = int(120 * fs)
freq, S01 = scipy.signal.csd(u0, u1, fs, nperseg=segNum, noverlap=None)
S01_ = abs(S01)
phase_ = np.angle(S01)
""" coherence, co-coherence, phase """
segNum = int(120 * fs)
freq, coh, co_coh, phase = funcs.coherence(u0, u1, fs, segNum)
""" plot all figures """
allplot(tSeq, u0, u1, tau, tau0, tau1, R, R0, R1, freq, freq0, freq1, S0, S1,
S01_, coh, co_coh, phase)