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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?

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  • $\begingroup$ Probably you should window these segments of signal with a good window just before the FFT. And you should overlap the segments. Maybe 75% overlap. $\endgroup$ Aug 18 at 21:37
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  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.

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  • $\begingroup$ Thank you for the response, those are valuable resources and I'll go through them. This does not answer my question though, since many papers use FFT directly to extract "frequency domain features" and I need to understand what does that mean exactly. $\endgroup$
    – qalis
    Aug 19 at 13:04
  • $\begingroup$ @qalis Added some clarification. $\endgroup$ Aug 19 at 20:14
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    $\begingroup$ Now I understand that my confusion came from how broad the "frequency domain features" term is. Thank you! $\endgroup$
    – qalis
    Aug 19 at 20:24
  • $\begingroup$ @qalis I'll add that it can also refer to whenever a transform stays in frequency domain, in which case none of the above qualify - but this is a domain-specific usage. In general we call it "freq-dom features" as long as freq-domain manipulations were somehow involved (above, we "revert to time domain"). $\endgroup$ Aug 19 at 20:32

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