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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

σ

_{y}

^{2}=∫∫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)=σ

_{x}

^{2}δ(τ) (models a white noise), then

σ

_{y}

^{2}=σ

_{x}

^{2}∫h

^{2}(u)du (integration limits are from -∞ to +∞)

and if Rxx (τ)=σ

_{x}

^{2}(models a 1/f noise), then

σ

_{y}

^{2}=σ

_{x}

^{2}(∫h(u)du)

^{2}(integration limits are from -∞ to +∞)

I don't understand the math behind statistics that well

Thanks