FFT range scaling

Spectral maps use the same FFT range for all the FFTs. The scale of the FFT range depends on the number of FFTs and on the overlap. The following equation links these 3 quantities to the time range of the analyzed data:

with NFFT the number of FFTs, overlap the normalized overlap (value comprised between 0 and 1), tstart and tend the start and end times of the analyzed data.

Thus when applying 100 FFTs with 20% overlap on data simulated from 0 to 200s, the FFT range is (200 - 0) / (1 + (100 - 1) * (1 - 0.2)) = 2.48s.

The FFT windows are regularly spaced in time, whatever the RPM is. The start point of each window can be computed as

Scaling the FFT range must be done carefully in order to obtain correct results. If the range is too small, the FFT calculation will be poor. If the FFT range is too big, the reference RPM will evolve greatly, resulting in imprecise spectral values.