Autocorrelation: zero crossing

Question

I am trying to calculate the fundamental frequency (pitch) from autocorrelation method. Below is the figure of the signal I have.

The autocorrelation that I calculated by the following code in python is given in the picture below:

        N = len(kiri) #here kiri is the input signal shown in the above pic
        nlags=N/2
        r = np.zeros(nlags) #
        m=np.zeros(nlags)
        for lag in range(nlags):
            for nl in range(N - lag):
                r[lag] += kiri[nl] * kiri[nl + lag]

Now what I want to know is that, is the autocorrelation supposed to have zero crossings in all cases of input signals? if yes, then does that mean the abouve autocorrelation result is wrong ?

When I try to use the above autocorrelation results to calculate pitch using Mcleod Pitch Method, the NSDF function does not have zero crossings hence unable to calculate pitch. (link for reference of this method is in the comments)

Is this autocorrelation calculation method correct ? Or since the input signal itself is not exactly a periodic signal, the autocorrelation won't have zero crossings ?

Please help.

Answer 1

Yes, the autocorrelation can have zero crossings. A negative autocorrelation value means that the two signals are anti-correlated, i.e. they have similar magnitude, but opposite sign.

If you want to find the pitch, I would recommend reading "Spectral Analysis of Signals", by Petre Stoica and Randolph Moses, it reviews the most common methods and their properties.

Answer 2

Maybe error in somewhere! If a non-zero signal hasn't DC ie. its average value=0 then its autocorrelation function should have zero crossings. I do not know an exception, but that of course is not a proof.

Addendum: Test your autocorrelator. Input a sinewave and see, if there occur alternate plus and minus peaks at delays which are multiples of a half period.

You probably can subtract the average from your signal without substantial overhead to the calculations. Then the average surely is zero.