Noise distribution in multi-variate signal - research question

#1
Hello all,

I could use a hand with a question holding up some research. I am trying to calculate the signal to noise ratio on a signal which is the quotient of the difference and sum of two signals.

To frame this more simply, given two constants C1 and C2, and two zero-mean gaussian variables x1 and x2, I need to find the variance of z = (C1 + x1 - x2) / (C2 + x1 + x2). The only constraint would be C2>0. Possibly the constraint could be imposed that C2 > variance(x1+x2) if that is of any help.

Thanks in advance for any help you can give me.
 

BGM

TS Contributor
#2
What is the joint distribution of [math] X_1, X_2 [/math] - are they jointly follows a bivariate normal? (this include the case that you assume they are independent)
 
#3
What is the joint distribution of [math] X_1, X_2 [/math] - are they jointly follows a bivariate normal? (this include the case that you assume they are independent)
Sorry, yes, I should have stated that [math] X_1, X_2 [/math] are independent.