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Normal input to a LTI system

by asmani
Tags: input, normal
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Apr7-12, 04:54 AM
P: 86
1. The problem statement, all variables and given/known data

The signal s(t) is a deterministic signal with the finite duration (0,Ts) and the energy Es=∫s2(t)dt. In the following system, n(t) is a normal noise with the mean zero and the power spectral density Gn(f)=η/2. Show that no(Ts) has a normal distribution with the mean zero and the variance (η/2)Es.

2. Relevant equations


(* is the convolution)

(since E[no(t)]=0)


3. The attempt at a solution

I know how to derive mean and variance , but don't know how to show normality. The prof just mentioned in the class that if the input to a LTI system is normal, then the output is so. How to prove this?

Thanks in advance.
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