Question

2. Let Y(t) = (x(0)+)(\pi) where X(t) is a Poisson process with autocorrelation function Rxx(t1, tz) = tīta + min(tı, tz), and 6 ~ U(0,2%) is independent of X(t). a. Is X(t) W.S.S.? b. If so, find its power spectral density. [25]

Answer 1

ANSWER:

Given equation

$\small Y(t)=e^{j(X(t)+\Theta )(\pi)}$

X(t) is a poisson process with autocorrelation function

$\small R_{XX}(t_{1},t_{2})= t_{1}t_{2} + min(t_{1},t_{2})$

$\small \Theta \sim U(0 ,2\pi)$ is independent of x(t)

a)

X(t) is not wide sense stationary(W.S.S) because autocorrelation function of  
Rxx(t1, t2
is not a function of  
t - ta
. So its not a WSS.

b)

power spectral density is not meaningful.

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