a The power spectrum of a process xt is sxw 11w22 Find the a

a) The power spectrum of a process, x(t), is

s_x(w)= 1/(1+w²)²

Find the autocorrelation function R_x(Tau)

b) Given a stochastic process (x(t)=ae^jwt) where a is a constant and w is a random variable with probability density (p(w). Show that the power spectrum (Sx(w)) is Sx(w)=2*pi*|a|²*p(w).

Solution