Question

Q1) Let X(t) be a zero-mean WSS process with

$R_{x}(\tau )=e^{-\left | \tau \right |}$

X(t) is input to an LTI system with

Let Y(t) be the output.

a) Find the mean of Y(t)

b) Find the PSD of the output S_Y(f)
c) Find R_Y(0)

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Q2)

The random process X(t) is called a white Gaussian noise process if X(t) is a stationary Gaussian random process with zero mean,

$\mu _{x}=0 \ ,$ and flat power spectral density,

Let X(t) be a white Gaussian noise process that is input to an LTI system with transfer function

a) Find PSD of the output S_y(f)

b) Find the mean square of Y(t)

0 otherwise s.(n)-N ,for all f |H(f) otherwise 0

Answer 1

Summary - it is basic problem so I have shown step by step solution
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