As the title states, I am looking for established methods to quantify the difference in two FFTs. I have come across methods such as using cross correlation in the time domain or the coherence estimate of the power spectral density of two signals, but these methods seem more geared toward finding similarities in signals rather than differences.
I am running an experiment with a treatment and control group and I think the treatment is causing a change in some periodic motion which I am measuring optically and ultimately I want to quantify that change into a single number or metric.
I have thought of perhaps normalizing the FFTs of the two signals I am comparing and finding what frequency value is 50% of the area under the curve for the FFT. The idea being that if the peaks of the FFTs in my treatment group shift then so should the point of 50% of the area under the curve. But I'm not sure if this is a sensible approach.
Thanks for any assistance!