Autocorrelation Function Question

[frenzal_dude]

Hi, we're learning about the autocorrelation function at uni, and I know it's meant to show similarities between a function and a delayed version of that function. But how does the autocorrelation show these similarities?

For example, if$$x(t)=Asinc(2Wt)$$ then $$R_x(\tau )=\frac{A^2}{2W}sinc(2W\tau)$$

How can you look at the resulting function and see what the similarities are?

Thanks for the help guys.
David

 

[marcusl]

The cross-correlation doesn't tell "similarities" so much as how correlated two functions are as they slide past each other. Autocorrelation is just cross-correlation where the functions are one and the same. To see why the autocorrelation of a sinc is another sinc, draw the function onto two slips of paper and visually perform the cross-correlation (multiply point by point and integrate) as you slide them past each other. At zero lag (offset) they line up and the correlation is one. As they slide apart, the amplitude falls, then goes negative when the big peak lines up with the first negative lobe. At large lag there's not much correlation (where one is big the other is small).