Sampling, Aliasing, and the Nyquist Rate
A sensor sees the world only at the instants it takes a sample. If something changes faster than half the sample rate, the samples cannot tell it apart from something slower. That false slow signal is called an alias.
The Nyquist rate
To capture a signal of frequency \(f\), you must sample faster than twice that frequency. Otherwise the samples look exactly like a lower frequency, the alias:
What to notice
Set the wheel speed just below the frame rate and the filmed wheel turns slowly backward, like car wheels in movies. Set it equal to the frame rate and the wheel seems frozen. In the bottom plot, the red dots are the samples, and the dashed red curve is the slow wave that fits them just as well as the real fast one.
Robots run into aliasing with vibration and motor noise. A motor buzzing at 120 Hz, read by an IMU at 100 Hz, shows up as a fake 20 Hz wobble. That is why sensors filter out high frequencies before they sample.