Interpreting Autocorrelation Results

[starlite]

Hello! I'm using Audacity 2.4.1 for birdsong analysis and I'm hoping to use autocorrelation to get information on key frequencies of the call. I have a couple questions, listed below:

1. Does autocorrelation show the center frequency? If not, what is the difference?

2. What exactly does autocorrelation show? The audacity manual says it is "the key frequencies," does this just mean the most prominent/ the ones with the highest amplitude?

3. I'm attaching some images below, showing the spectrogram and the plots.
the spectrogram:

spectrogram

Screen Shot 2020-06-11 at 11.29.15 AM.png (1.7 MiB) Viewed 185 times

the plot spectrum:

plot spectrum

Screen Shot 2020-06-11 at 11.29.38 AM.png (208.31 KiB) Viewed 185 times

the standard autocorrelation:

standard autocorrelation

Screen Shot 2020-06-11 at 11.30.00 AM.png (157.89 KiB) Viewed 185 times

the enhanced autocorrelation:

enhanced autocorrelation

Screen Shot 2020-06-11 at 11.30.17 AM.png (184.13 KiB) Viewed 185 times

The highest peak I get from the FFT spectrum vs. the autocorrelation spectrum are different -- why is this and which one should I trust?

4. How should I decide what bin size to use for the autocorrelation?

5. Does it matter if I use enhanced vs standard autocorrelation? Is there a possibility of getting skewed results if I choose one and what are some precautions to take?

Thank you so much in advance

[steve]

Wikipedia explain autocorrelation better than I can: https://en.wikipedia.org/wiki/Autocorrelation

[starlite]

Hi! Thanks for the link! So what I'm getting is an autocorrelation just shows frequencies that reappear many times in a signal?

[steve]

This is the way that I think of autocorrelation:

Imagine that you have a sine wave, with a frequency of 100 Hz. That waveform has peaks at intervals of 0.01 seconds.
Now imagine that you make a duplicate copy of it, and align the two waveforms one above the other - the two waveforms will exactly correlate.

Now gradually shift the duplicate waveform slowly to the right.
At first the correlation between the two waveforms decreases.
When the duplicate has been shifted (delayed) by 0.005 seconds, the two waveforms are exactly out of phase - peaks in one are where the troughs appear in the other.
But then if you continue shifting the duplicate copy, the peaks gradually start lining up again- correlation is increasing.
When the duplicate has shifted by 0.01 seconds, the peaks once again line up - we have correlation again.

As we continue shifting the duplicate, we see that maximum correlation occurs every 0.01 seconds.
If we draw a graph with the "delay time" on the X axis, and the amount of correlation on the Y axis, we get a graph like this:
(Audacity's other types of autocorrelation are variations of this algorithm, which may show points of interest more clearly, depending on what you are looking for.)

autocorrelation.png (53.98 KiB) Viewed 177 times

[starlite]

Hi! Thank you so much, that absolutely clears things up! So autocorrelation doesn't really give information about frequencies, more about the periodicity of a signal?

[steve]

Yes, though if you know the periodicity of a signal, then you know the frequency because frequency = 1/periodicity, or as more commonly stated:
frequency=1/wavelength

[starlite]

Oh, awesome that makes so much more sense. Thank you for your help and detailed replies!

[starlite]

Actually! I just wanted to clarify one more thing -- so for the example Autocorrelation spectrum in your post, the maximum correlation occurs every 0.01 seconds. So if the period is 0.01s, the key frequency is 100 Hz? What do the frequency values on the other peaks indicate? Thanks again!

[steve]

if the period is 0.01s, the key frequency is 100 Hz? What do the frequency values on the other peaks indicate?

They're just multiples of the "key frequency".

I'm using Audacity 2.4.1 for birdsong analysis and I'm hoping to use autocorrelation to get information on key frequencies of the call

I think that the normal spectrum view (and track spectrogram view) will be more useful.

[starlite]

Cool, thank you so much for helping me with this! I'll look into the other views you suggested as well. Thanks again!!