# Determining the probability of two signals, with added independent noise, being the same?

I have the first 100ms of two signals, each with a noise independent to that signal. I want to compare the two signals and determine the probability that these two signals are (minus noise) the same, and therefore come from the same source, i.e. if whether they are unique or not.

I am hoping there is a standard approach to a problem of this sort, and any hint in the right direction would be greatly appreciated. I did have a hacky machine learning approach, involving feature extraction and Euclidean space, but being a signal novice, I thought I'd ask here first.

• i think that "correlation" is what you're after.
– MBaz
Jan 28 '17 at 21:54
• What kind of noise is it? How are the signals structured? Jan 28 '17 at 22:01
• This could be an excellent question if you provided more details. How are the signals generated? What constitutes sameness (e.g., sinusoids of a same frequency, signals with a similar magnitude response, or something else)? What distortion do they undergo before you measure them (e.g., do they pass through some filter or other processing prior to being measured)? What kind of noise is in the measurement? I'd take a crack at it, if you provided these details.
– hops
Jan 29 '17 at 1:56