Autocorrelation?

Question

say i have a digital signal sequence s(n) which is 100 samples long. If i do an autocorrelation how many samples do i get in the output signal sequence? Can you give the equation for the autocoreelation function?

Answer 1

EDITED ANSWER 6/9/06

For real digital signal defined as x(n) from n=0 to n=99 the autocorrelation is

R(j) = sum(over n) [ x(n)(x(n-j) ]

The first sample in the autocorrelation (for j = 0) is

R(0) = x(0)^2 + x(1)^2 +x(2)^2 + .... + x(99)^2

The second sample (for j = 1) would be

R(1) = x(1)x(0) + x(2)x(1) + x(3)x(2) + .... + x(99)x(98)

The third sample (for j = 2) is

R(2) = x(2)x(0) + x(3)*x(1) + x(4)x(2) + ... + x(99)x(97)

when you get to the 100th sample (for j = 99)

R(99) = x(99)x(0) [the rest are zero]

So j goes from 0 to 99, or 100 samples

Edit:

oops, I forgot the negative values of j these can go from -99 to -1:

R(-99) = x(99)x(0)

R(-1) = x(0)x(1) + x(1)x(2) + x(2)x(3) + ... +x(98)x(99)

So there are in fact 199 sample points in the autocorrelation, and the result is symmetric around j = 0.

Answer 2

the edited answer agrees with what I came up with.