# Unit step integration

1. Feb 15, 2008

### wildman

1. The problem statement, all variables and given/known data
The random variable C is uniform in the interval (0,T). Find the autocorrelation
$$R_x(t_1,t_2)$$ if X(t) = U(t-C) where U is a unit step function.

2. Relevant equations

3. The attempt at a solution

$$R_x (t_1,t_2) = \int_{-\infty}^{\infty} U(t_1-c) U(t_2-c) f(c) dc$$

$$R_x (t_1,t_2) = \frac{1}{T}\int_0^T U(t_1-c) U(t_2-c) dc$$

I get stuck here. How do you integrate two shifted unit step functions?

Last edited: Feb 15, 2008
2. Feb 15, 2008

### CompuChip

Divide the interval into three parts (assuming t1 < t2)
1. c < t1
2. t1 < c < t2
3. t2 < c
On each of these, what are the values of the step functions? What is their product? Now split the integral and do each part separately.

3. Feb 15, 2008

### wildman

Oh yeah, THANKS!