(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The signal s(t) is a deterministic signal with the finite duration (0,T_{s}) and the energy E_{s}=∫s^{2}(t)dt. In the following system, n(t) is a normal noise with the mean zero and the power spectral density G_{n}(f)=η/2. Show that n_{o}(T_{s}) has a normal distribution with the mean zero and the variance (η/2)E_{s}.

2. Relevant equations

E[n_{o}(t)]=H(0)E[n(t)]

R_{nono}(τ)=h(τ)*h(-τ)*R_{nn}(τ)

(* is the convolution)

var(n_{o}(t))=R_{nono}(0)=∫G_{no}(f)df

(since E[n_{o}(t)]=0)

G_{no}(f)=|H(f)|^{2}G_{n}(f)

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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# Homework Help: Normal input to a LTI system

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