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Thread: Noise distribution in multi-variate signal - research question

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    Noise distribution in multi-variate signal - research question




    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.

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    Re: Noise distribution in multi-variate signal - research question

    What is the joint distribution of X_1, X_2 - are they jointly follows a bivariate normal? (this include the case that you assume they are independent)

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    Re: Noise distribution in multi-variate signal - research question


    Quote Originally Posted by BGM View Post
    What is the joint distribution of X_1, X_2 - are they jointly follows a bivariate normal? (this include the case that you assume they are independent)
    Sorry, yes, I should have stated that X_1, X_2 are independent.

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