正弦波自相关不正确

Question

I'm generating a basic sine wave as follows:

import numpy as np
x = np.linspace(-10, 10, 200)
x = np.sin(x)

Which looks correct when plotted:

import matplotlib.pyplot as plt    
plt.plot(x)
plt.show()

But when I try to calculate and plot the normalized autocorrelation of this signal, I get some strange results:

autocorr = np.correlate(x, x, mode='full')    
autocorr /= autocorr[autocorr.argmax()]  # Normalize autocorrelation

plt.plot(autocorr)
plt.show()

Given a sine wave is perfectly periodic, I'm expecting the autocorrelation values to be 1.0 when in phase. However, my autocorrelation peaks get smaller with more time steps

Is there an error in my autocorrelation calculation? Or is there another correlation function I should be using?

Answer 1

That looks right. The reason you don't get repeating peaks at 1.0 is because correlate treats the signal as zero outside the data. You can confirm this by zero-padding the input signal and looking at its correlation, which will match what you see above. Try the following: it'll produce the same autocorrelation as your plot above.

x0 = np.hstack([np.zeros_like(x), x, np.zeros_like(x)])
ac0 = np.correlate(x0, x0, mode='full')
ac0 /= ac0.max()
plt.plot(ac0)