Normalized correlation is used to measure how similar are two signals. I can understand similarity visually but I haven't seen a mathematical definition for the similarity of 2 signals anywhere. So I have 2 big questions that are bothering me:
Is there a mathematical definition for how similar two signals are?(similar in same fashion of visually similar)
With that definition, is there a proof that shows correlation is maximum between similar signals and not any other signal?
Okay so I thought about 1 and I have a mathematical definition for similar signals. Basically
s1 is similar to
s2 if they are proportional, that is
s2 = a.s1. So we can focus on question 2 now :). A proof that says out of all functions out there, the correlation of
s2 is maximum only if