04-17-2019, 12:36 PM
u.a. stands for "arbitrary units". This is typically used when the exact unit is not relevant or not known, for example if you do not have the exact calibration of a tool but only analyze relative changes in any case. In this case we have decided to not use the exact unit because it is mostly irrelevant for an autocorrelation and it might be extremely misleading as students might mistake the autocorrelation for a time-based measurement. Also, we are adding the sensor input here, which makes its quantitative interpretation even more difficult.
The (analystical) autocorrelation is defined as
![[Image: 08ebc33ac065bbdc0ab02e2d10261a7064711976]](https://wikimedia.org/api/rest_v1/media/math/render/svg/08ebc33ac065bbdc0ab02e2d10261a7064711976)
so the unit would be the unit of x squared. In this case, the numerical autocorrelation works similarly and would have the unit m²/s⁴ (the exact implementation can be found here: https://github.com/Staacks/phyphox-andro...java#L1318). This by itself is difficult to interpret as a physical value. The autocorrelation is measure for "how much the function resembles itself" and the most sensible thing to do would be to normalize the result by the maximum value at τ=0.
On top of this, we do not know along which axis the user will create an oscillator. So, for this experiment to work on any axis, we are not calculating the autocorrelation of a single axis (or on the absolute value, which would give trouble as the direction is lost) but of the sum of all axes. Therefore, the interpretation is even more difficult if you are not oscillating along one of the three axes.
So, to sum this up. Technically, the unit is m²/s⁴, but usually you should not interpret it like this, but instead just look at the "self-similarity" relative to the first peak.
The (analystical) autocorrelation is defined as
so the unit would be the unit of x squared. In this case, the numerical autocorrelation works similarly and would have the unit m²/s⁴ (the exact implementation can be found here: https://github.com/Staacks/phyphox-andro...java#L1318). This by itself is difficult to interpret as a physical value. The autocorrelation is measure for "how much the function resembles itself" and the most sensible thing to do would be to normalize the result by the maximum value at τ=0.
On top of this, we do not know along which axis the user will create an oscillator. So, for this experiment to work on any axis, we are not calculating the autocorrelation of a single axis (or on the absolute value, which would give trouble as the direction is lost) but of the sum of all axes. Therefore, the interpretation is even more difficult if you are not oscillating along one of the three axes.
So, to sum this up. Technically, the unit is m²/s⁴, but usually you should not interpret it like this, but instead just look at the "self-similarity" relative to the first peak.