I was asked a question, as posted here, and the answer given is (A) i.e. $\frac{3}{2} A^2 N_0$.

My solution steps was:

  1. Finding the mean of the output process: Since input is gaussian the output will be also Gaussian, as per property of Gaussian variable.

  2. Finding the mean square value (MSV) of the process i.e. $\mathbb{E}(Y^2)$.

  3. Variance = MSV$-\mathbb{E}(Y)^2$

But I am confused do mean of output process will be zero? Since the input is zero-mean white Gaussian noise if yes how?

Is there any other way to solve the question?

enter image description here


1 Answer 1


The output process is clearly zero-mean because the LTI system cannot add a mean to the zero-mean input process. The variance of the filtered process is given by


which results in $3A^2N_0/2$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.