Understanding White Gaussian Noise: Probability of Inclusion in [0.25A, 1.15A]

[nightworrier]

Homework Statement

Consider the random process X(t)=A+N(t), where A is a constant and N(t) is a white Gaussian
noise with spectral density equal to 1. The process X(t) is filtered with a system with impulse
response h(t)=u(t)exp(‐t/T).
Compute the probability that X(t), once filtered, is included in the interval [0.25A, 1.15A].

I have problems about white gaussian noise. I actually don't know the concept. I appreciate if you help me to figure it out this.

 

[poor mystic]

Hi Nightworrier
Many here will know this much better than i do, but I can say that Gaussian white noise is noise which is present at all frequencies at equal amplitude.
Essentailly if Gaussian white noise is filtered by some process X(t) you'll get an output from X(t) that looks a lot like the frequency-wise transfer function.
Hope that might be of value!

I remember a wonderful book by F.R. Connor on Noise which may be available at your library.

 

[nightworrier]

I am actually not familiar with that. I am a mechanical engineer and far from the idea of signals just trying to learn by myself. Could you tell the solution of this problem ? I want to understand the concept.

 

[poor mystic]

Dear Nightworrier
I apologise that I am unable to solve this problem, which lies beyond my skill. The reference I mentioned is very good, but it has been 30 years since I even looked at this kind of work.
I make this apology in the hope that some kind communications engnner may see that you still do not have the help that you need.