[math] Fundamental frequency of fft

[Aeris <ae...@imirhil.fr>]

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Hello World !

I have a question about FastFourierTransformer.
I'm unable to retrieve fundamental frequency of the fft.

Mathematically, it could be 2π / samble size, but this formula doesn't
seems working.

I apply FFT to a 1Hz sinus, sampled at 20Hz during 1 minute.
So sample size is 1.200, zero-padded to 2.048 (upper 2-pow), and
fundamental could be 3mHz (2π / 2.048).

Theorical FFT of this sinus must be 2 peaks, at f = -1Hz and f = 1Hz.
But obtained FFT presents 2 peaks, at n ~ 100 and n ~ 1950, so f =
(100-1024) × 3mHz ~ -5,66Hz and f = (1950-1024) × 3mHz ~ 5,66Hz.
Seems the mathematical theory doesn't apply here…

Stranger, FFT on 0.1Hz sinus presents 2 peaks at n ~ 10 and n ~ 2030,
leading to f ~ ±6,22Hz…
A signal at a lower frequency leads to an FFT at a higher spectrum…

So, am I wrong somewhere ?
And how I can calculate the fundamental frequency from
FastFourierTransformer.transform(double[]) ?

Thanks in advance
- -- 
Aeris
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