Consider a signal F1(x) with a variance var1, and a signal F2(x) = a*F1(x-b) with another variance var2.
So, what becomes the variance var3 of the signal F3(x) resulting from:
F3(x) = F1(x) + F2(x).
Kieran M R Hunt
Some important identities:
Var(aX-b) = a^2 Var(X)
Var(X1 + X2) = Var(X1) + Var(X2) + 2*Covar(X1,X2)
Covar(X,aX) = a*Var(X)
If we assume no lag autocorrelation exists in your signal then Covar(X,X(x-b))=0
Thence Var(F3) = Var(F1) + Var(F2) + 2*Covar(F1,F2)
= Var(F1) + a^2*Var(F1) + 0
= (1+a^2) * Var(F1)
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Fadhil Abdulabbas Abidi
My Dear
var(x1+x2)=var(x1)+var(x2)+(-)cov(x1,x2)
and answer Mr. Kieran Hunt is very good about subject
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