Uncertainty propagation for Normalising Signals

[Livethefire]

I am measuring an average signal through a range of filters and compute the standard deviation of that signal over a certain range on my image plate. Now I want to normalise all of the signals to an arbitrary filter signal - does the standard equation of uncertainty propagation hold?

http://en.wikipedia.org/wiki/Propagation_of_uncertainty

Presumably, normalising to one filter should force the uncertainty of that filter to zero, but the addition sign in the equation makes sure that is never true.

Thanks for any help.

Edit: I have never come across what the rho term is in the ratio equation - that might answer my question.

 

[Valerie Park]

Yes, the standard equation of uncertainty propagation holds in this case. The rho term in the ratio equation is the correlation coefficient between two variables. If the two variables are independent (i.e. they are not related to each other), then the correlation coefficient is zero, and the equation reduces to the standard equation of uncertainty propagation.