Normal input to a LTI system

by asmani
Tags: input, normal
asmani is offline
Apr7-12, 04:54 AM
P: 84
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.
Attached Thumbnails
Phys.Org News Partner Science news on
Better thermal-imaging lens from waste sulfur
Hackathon team's GoogolPlex gives Siri extra powers
Bright points in Sun's atmosphere mark patterns deep in its interior

Register to reply

Related Discussions
Signals And Systems - Determine System Output given Impulse Response and System Input Engineering, Comp Sci, & Technology Homework 0
I need input, I invented a number system... General Math 24
Normal frequencies and normal modes of a multi-part system Advanced Physics Homework 1
Uncorrelated input to a DPCM system? Electrical Engineering 0
3 Member force system-Could use some input Engineering, Comp Sci, & Technology Homework 3