Probability density function afterring

  • Thread starter m26k9
  • Start date
Probability density function after filtering


I am trying to find how a random variable will transform once gone through
a filter.

For example, I have a random sequence x(t), going through a filter h(t). Thus,
y(t) = x(t)*h(t) ; % '*' is convolution.

Now I want to find out how the PDF of y(t). Is there a certain analytical method to find this?
Suppose x(t) is Gaussian with a certain mean and variance. How will this mean and variance will be chaned when this signal goes through a low-pass filter. (Going through a low pass filter will give a Gaussian signal due to Central Limit theorem, but how will the PDF characteristics change).

Any advice or references are greatly appreciated.

Thank you.
Last edited:

Want to reply to this thread?

"Probability density function afterring" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads