This is a very cool question. Though I think we need a little bit of clarification.
So is this something like impedance values from two parts of a circuit where we expect that there might be a relationship, or is this more like results from two radio telescopes pointed in opposite directions where we hope but do not expect to find a specific correlation?
By similarity are you meaning correlation, or some similarity index?
Or is this looking for how different the mean of one signal is from the mean of the other signal?
Well, I am looking to compare one signal against a reference signal. Both signals are 2-dimensional complex values obtained by applying double random phase encoding technique.
Basically, two signals are from the same source (lets say one image) but one of the signals is distorted by adding some noises or manipulated a few bits of the original image. I am interested in checking to see weather two signals are still similar or not.