# Autocorrelation function of a signal

1. May 2, 2010

### caesius

1. The problem statement, all variables and given/known data
x(t) is a random signal taking the values 1 and -1 with equal probability in each time interval Tn of length T, i.e.

Tn : (n-1)T $$\leq$$ t $$\leqn$$ T

Find the autocorrelation function Rx($$\tau$$)

2. Relevant equations
From a quick glance at our notes:

Rx(t1, t2) = E{X(t1)X(t2)}

3. The attempt at a solution
That above function doesn't really make sense to me but it's all we've got. Seriously where do I start with this problem? We've just been thrown into the control section of this course with very little background. I don't even really understand what the question is saying, I can see that

T1 : 0 $$\leq$$ t $$\leq$$ T
T2 : T $$\leq$$ t $$\leq$$ 2T
T3 : 2T $$\leq$$ t $$\leq$$ 3T
...

but how does that help? Isn't that just a complicated way of saying the interval is T long?