Probability density function afterring

[m26k9]

Probability density function after filtering

Hello,

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.

 

[fresh_42]

Have a look at https://en.wikipedia.org/wiki/Convolution_of_probability_distributions and the links therein.