Extracting "frequency domain features" from signal for classification

Question

I have a real signal with only nonnegative values (actigraph measurements). Many papers say they use "frequency domain features" for classification, such as mean, variance etc. But I'm confused as how to actually interpret "frequency domain" here.

I have seen two different approaches:

1. Calculate FFT, calculate magnitude at each frequency bin (i.e. $\sqrt{re^2 + im^2}$), then extract features from this array of values, e.g. mean, variance

2. Cut time domain into time bins (e.g. every minute, or every hour), for each calculate total power, i.e. calculate power spectral density and sum the elements. Extract features from array of total powers for all time bins, e.g. mean, variance

Which approach is more correctly "frequency domain features" extraction? Or am I completely confused and I should do this in entirely different way?

Answer 1

1. CWT/STFT/Synchrosqueezing
2. Scattering -- lecture
3. MFCC
4. Learning references

I recommend against FFT and its simple manipulations; it produces at best a non-robust representation with weak representative power - but you get even less unless you use complex numbers since magnitude-only tosses much information and phase is largely unusable due to high entropy.

What are "frequency domain features"

In general, it's an umbrella term for features derived from methods that utilize the frequency domain - i.e. manipulations of Fourier transform. As such all of above qualifies.

The idea is we seek to exploit oscillatory behavior and periodicity of a process; if there's neither, then such features are likely useless. However, the full scope of nonstationary signals (for which FFT is ill-suited) encompasses a wide range of natural behaviors for which periodicity becomes entirely optional, and oscillations somewhat optional. However, the less oscillatory the signal, the less sparse and more brittle against noise the features.