# How do I decide which frequencies are signal and which are noise?

I have an arbitrary recorded digial signal, on which I have run a Fourier transform. I'm not sure what conventions are on a case like this, but I have 1024 frequency bins. Second bin is the highest magnitude, at about 9500. From there they approximately exponentially decay. The first 13 bins are all above 1000. The last 500 bins are under 150, averaging around 60.

It would be useful for me to define some of these frequencies as "signal" and others as "noise." Is there a canonical way to do that? Perhaps by saying "all frequencies past X are less than 5% of peak" or "this gives us an SNR of 10:1" or "these frequencies have a value less than one standard deviation above mean" or something like that?

• There are many cases where all the FFT peaks are noise, and the signal is buried down in the noise floor. So the answer depends on your data, your system model (clean linear 2nd degree diff.eq?), and whether they are related. – hotpaw2 Sep 4 '19 at 2:22
• I think signal is defined as being useful information, and noise is any disturbance relative to the signal. In a philosophical sense, I suppose if you don’t know what you’re looking for then everything is noise. – Dan Szabo Sep 4 '19 at 2:45