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Probability density function afterring

  1. Jul 21, 2009 #1
    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: Jul 21, 2009
  2. jcsd
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