# How can I measure the impact of noise on a FFT?

Please, I have to solve a problem and I really need some help.

I have to give an efficient method to consider a maximum amplitude as a starting point to consider as noise the whole spectrum below itself. Like on the example of the FFT below. Let's consider only on X axis, the red plot, the maxium peak is at a magnitude of 0.4, between 7 and 8 Hz. The next peak is at a magnitude of ~0.3, and the next after that is at ~0.25, and so on (in a decreasing order). How can I give a consistent method to find the threshold between noise and real signal in terms of magnitude.

The perfect answer would be transforming it in a closed-loop control where I could go adding transfer functions with natural frequencies corresponding to those peaks until the response are no longer affected (for a unitary step). But for that, I would have to tell the system what is the magnitude of each peak. That's where I lose myself...

Thank you very much in advance.

• I assume that you transform time to frequency. Using the frontmost blue curve, I estimate a raw S/N perhaps around 3 and not much better. This is very much the low end of signal quality. I fear that any attempt to pull out better information with software operations is a "hunt and guess" game. Such an approach will not improve S/N beyond what you have already in the raw data. Otherwise, you might find help in the theoretical functions for the time signal and its FFT. Fit the FFT to a Gaussian peak, invert that to a smoothed time domain signal, and minimize the residual or chi-squared fit. May 20, 2019 at 12:42