Why does DataStudio compute velocity from x(t) the way it does?

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SUMMARY

DataStudio computes velocity using the formula v(t) = (x(t + 3Δt/2) - x(t - 3Δt/2)) / 3Δt to provide a more stable measurement by averaging over a larger time interval. This method reduces the impact of high-frequency noise, making it more suitable for scenarios where acceleration is not constant, such as in mass-spring systems. In contrast, the alternative formula v(t) = (x(t + Δt/2) - x(t - Δt/2)) / Δt, while mathematically equivalent under constant acceleration, is less effective in noisy environments. The discussion highlights the importance of using smoothing techniques in velocity calculations for improved accuracy.

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damosuz
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A motion sensor gives the position of an object at times separated by Δt. DataStudio then calculates velocity by this method:

v(t) = (x(t + 3Δt/2) - x(t - 3Δt/2)) / 3Δt

I wonder why it doesn't do it like this: v(t) = (x(t + Δt/2) - x(t - Δt/2)) / Δt

I know it gives the same v if acceleration is constant since in both cases it corresponds to average speed in the middle of the interval, but if acceleration is not constant (e.g. mass-spring) it must give a value for v that is not as accurate.

Thank you.
 
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Maybe the velocity is averaged over multiple timesteps as a smoothing (filtering) feature. An average velocity computed using every single sample might have too much high frequency jitter due to noise.
 

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