A random process is composed of sample functions of the form where n(t) is a wide sense stationary random process with the auto correlation function R n ( Iuml ), and n k n(kT s ) (a) If T s is chosen to satisfy R n (kT s ) 0, k 1,2, so that the samples n k n(kT s ) are orthogonal, use Equation (7 ...

The suggested approach is to apply wh ...

A random process is composed of sample functions of the form where n(t) is a wide-sense stationary

Question:

A random process is composed of sample functions of the form

ο0 ο0 Σ δυ- ΚT ) = Σ η, δ- ΚT) |x(t) = n (t) k=-00 k=-o

where n(t) is a wide-sense stationary random process with the auto correlation function R_n(Ï„), and n_k = n(kT_s).

(a) If T_s is chosen to satisfy

R_n(kT_s) = 0, k = 1,2,..

so that the samples n_k = n(kT_s) are orthogonal, use Equation (7.35) to show that the power spectral density of x(t) is R„, (0) = f,R„(0) = f,n²(t), -∞ < ƒ < ∞ T. un S,(f) =

(b) If x(t) is passed through a filter with impulse response h(t) and frequency response function H(f), show that the power spectral density of the output random process, y(t), is