# How it works¶

The FFT takes a set of gyro samples, performs frequency analysis on that set and yields a set of frequency bins with associated energies representing how “much” of a noise signal is in that bin. For example if we take a set of samples of length 32 - referred to as the FFT length or window size, N - this would yield a set of frequency bins each of width fs / 32 where fs is the sampling frequency of the samples. Since these samples are from the gyros the sampling rate is most commonly 1KHz and therefore each bin is approximately 32Hz wide. FFT analysis will give an energy value for each bin representing the amount of noise energy of that frequency in the bin. So for instance if our motor noise is at 80Hz most of the energy will be in the third bin and we can thus tell from the energy values the approximate frequency of the noise. The highest frequency that can be detected by an FFT is the Nyquist frequency of fs / 2

Clearly increasing the FFT length yields much higher frequency resolution and one might think therefore that we should always use long FFTs. Two facts prevent this. Firstly the calculation of an FFT costs roughly O(N log N) in CPU time, thus longer FFTs quickly become prohibitively expensive. Secondly FFTs have a Heisenberg-like relationship between frequency and time - you can choose high time resolution or high frequency resolution, but you cannot have both at the same time. For multicopters time resolution is important because the calculated frequency might be used to drive time-sensitive controls such as the dynamic harmonic notch. Thus the choice of FFT length should be made carefully based on how accurate the frequency calculation needs to be versus the timeliness of the result. For larger multicopters or helicopters a high frequency resolution can be beneficial, whereas for smaller copters with sensitive attitude control high time resolution is important. The default of 32 generally works well and can be run on F4 processors. Higher values such as 128 require F7 processors and anything above this should typically only be run on an H7.

An alternative to increasing the FFT length is to decrease the sample rate to yield higher frequency resolution. This has the drawback of reducing the highest frequency that can be detected, but for some lower frequency platforms (e.g. helicopters) this might be appropriate.