Power of noise after passing through a system h(t)

[iVenky]

**Reposting this again, as I was asked to post this on a homework forum**
1. Homework Statement
Hi,

I am trying to solve this math equation (that I found on a paper) on finding the variance of a noise after passing through an LTI system whose impulse response is h(t)
X(t) is the input noise of the system and Y(t) is the output noise after system h(t)
if let's say variance of noise Y(t) is
σy²=∫∫Rxx(u,v)h(u)h(v)dudv

where integration limits are from -∞ to +∞. Rxx is the autocorrelation function of noise X. Can you show that if Rxx (τ)=σx² δ(τ) (models a white noise), then

σy²=σx²∫h²(u)du (integration limits are from -∞ to +∞)

and if Rxx (τ)=σx² (models a 1/f noise), then

σy²=σx²(∫h(u)du)² (integration limits are from -∞ to +∞)

I don't understand the math behind statistics that well
Thanks

Homework Equations

Can I write σy²=∫∫Rxx(u,v)h(u)h(v)dudv as
σy²=∫∫Rxx(τ)h(u)h(u+τ)dudτ
if noise X(t) is stationary process?
However, I am not sure how Rxx (τ)=σx² δ(τ) or σx² results in those different equations shown above

The Attempt at a Solution

Same as before

 

[iVenky]

Hi,
Can you tell me if there is a better forum for this question to get an answer?