Autocorrelation function of the sequence

Question

Response to the following problem:

The lowpass equivalent representation of a PAM signal is

u(t) = Σ  I_ng(t-nT)                                 
         n

Suppose g(t) is a rectangular pulse and

I_n = a_n-a_n-2

where {an}is a sequence of uncorrelated binary-valued (1, -1) random variables that occur with equal probability.

1. Determine the autocorrelation function of the sequence {I_n}.

2. Determine the power density spectrum of u(t).

3. Repeat (2) if the possible values of the an are (0, 1).