Calculate the mean and autocorrelation

Question

Assignment:

1. For what values of the parameters A, B ∈ R the functions below can be

a) PSDs of stationary rps with finite power

P₁(f) = A rect(ƒ) + b triang(Tƒ/2)

P₂(ƒ) = e^A|ƒ| - e^B|ƒ|

b) Autocorrelations of stationary rps

 x₃(mT) = {A, m = 0 B, m = ±1 O, |m|≥ 2

x₄(x) = A sinc(x/T - B)

2. Starting from the binary random process x_n, n ∈ Z, with iid random variables and probability mass distribution

Px(1) = Px(-1) = 1/2,

a) Calculate the mean, autocorrelation, PSD and the first order PMD of the process y_n y_n = x_n + x_n-1/2 and determine whether it has iid random variables itself.

b) Determine whether the signal Z_n = x_n x_{n -1} has iid random variables.