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

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Discussion Overview

The discussion revolves around understanding white Gaussian noise in the context of a random process defined by X(t)=A+N(t), where N(t) represents the noise. Participants explore the implications of filtering this process and the probability of the resulting output falling within a specified interval.

Discussion Character

  • Homework-related, Conceptual clarification

Main Points Raised

  • One participant expresses a lack of understanding of white Gaussian noise and seeks help with the concept.
  • Another participant explains that Gaussian white noise is present at all frequencies with equal amplitude and suggests that filtering will yield an output resembling the frequency-wise transfer function.
  • A participant identifies themselves as a mechanical engineer unfamiliar with signal processing and requests a solution to the problem to aid in understanding.
  • One participant apologizes for their inability to solve the problem and hopes that someone with relevant expertise will provide assistance.

Areas of Agreement / Disagreement

Participants generally agree on the complexity of the topic and the need for further clarification, but there is no consensus on a solution to the problem presented.

Contextual Notes

Some participants express limitations in their knowledge of signal processing, which may affect their ability to engage with the problem effectively.

nightworrier
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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.
 
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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.
 
Last edited:
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.
 
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.
 

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