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pythonnumpycross-correlation
Saeed
Saeed

Reputation: 688

Recover the time shift from nympy.correlate result in Python

This is not a duplicate question since other answers only explain how to plot the cross-correlation function and do not explain how you can get the time difference. Given a sin signal and shifted version, we should be able to get the time delay between them. I have created a sin signal and shifted it by t_d=0.05. The following is my code and its output:

import numpy as np
import matplotlib.pyplot as plt
fs = 1000
x = np.linspace(0, 1, fs)
f = 5
t_shift = 0.05
y = np.sin(2*np.pi*f*x)
y_shifted = np.sin(2*np.pi*f*(x-t_shift))
fig, ax = plt.subplots()
ax.plot(x, y, x, y_shifted)
plt.show()

enter image description here

By normalizing signals and applying numpy.correlate we get the following:

y_norm = (y-y.mean())/y.std()
y_shifted_norm = (y_shifted - y_shifted.mean())/y_shifted.std()
cc = np.correlate(y_norm, y_shifted_norm, 'full')
fig, ax = plt.subplots()
ax.plot(range(len(cc)), cc)
plt.show()

enter image description here

Question From the indices of cross-correlation function, how can I get t_shift=0.05?

Upvotes: 0

Views: 330

Answers (1)

Hanno Reuvers
Hanno Reuvers

Reputation: 636

@Sepide. It seems to me as if you are trying to maximise the correlation between the signal y and a shifted version of y_shifted. This might be accomplished using np.correlate() but it seems nontrivial indeed to recover the time shifts in the signals. In the solution below I manually shift the time series and compute the correlation coefficient using np.corrcoef. As soon as this Pearson correlation coefficient equals 1, the two signals are aligned.

import numpy as np
import matplotlib.pyplot as plt

# Setting
fs = 1000
x = np.linspace(0, 1, fs)
f = 5
t_shift = 0.05
t_step = 1/fs

# Data
y = np.sin(2*np.pi*f*x)
y_shifted = np.sin(2*np.pi*f*(x-t_shift))

# Compute correlation
MaxTimeShift = 200
CorrelationList = np.empty((MaxTimeShift,1));
CorrelationList[:] = np.NaN
# Compute correlation for various shifts
for iter in range(MaxTimeShift):
    CorrelationList[iter] = np.corrcoef( y[0:801].T, y_shifted[iter:(801+iter)].T)[0,1]

# Plot 1
plt.figure(1)
plt.plot(x, y, x, y_shifted)
plt.show()

# Plot 2
plt.figure(2)
ShiftList = t_step*np.arange(MaxTimeShift)
plt.plot(ShiftList, CorrelationList)
plt.title("Correlation coefficient")
plt.show()

print("The time shift between the signals is: ", ShiftList[np.argmax(CorrelationList)])

Upvotes: 1

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