# I White noise & 1/f noise after a system h(t)

#### iVenky

Hi,

I am trying to solve this math equation on finding the variance of a noise after passing through a system whose impulse response is h(t)
X is the input noise of the system and Y is the output noise after system h(t)
if let's say variance of noise Y 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

σy2x2∫h2(u)du (integration limits are from -∞ to +∞)

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

σy2x2(∫h(u)du)2 (integration limits are from -∞ to +∞)

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

Related Set Theory, Logic, Probability, Statistics News on Phys.org

#### marcusl

Gold Member
This sounds like a homework problem. You need to post it in the appropriate Homework forum using the template to show your attempt at a solution.

"White noise & 1/f noise after a system h(t)"

### 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