# Encoder sampling rate realization

I know that questions from a mechanical engineer might sound a little naive to you :), but here I go: I am trying to use an Arduino Uno as the brain for a DC brushless motor that we have for a project. The motor has a quadrature 2-channel magnetic encoder as I understand(!).

IG52-04 24VDC 285 RPM Gear Motor with Encoder

How do I know what the sampling rate of the Encoder is? Or how do I know if an Arduino microcontroller satisfies our requirement for reading the shaft angular position through the encoder based on Arduino's sampling speed?

The frequency of the encoder signals is directly related to encoder resolution and the motor shaft speed (before the gearbox since this is where it is attached). $$f_{enc} = CPR * u_M$$
where: $f_{enc}$ is the encoder output frequency, $CPR$ stands for "Counts Per Revolution", $u_M$ is the motor speed in $\frac{revolutions}{sec}$.
The Nyquist rate dictates the sampling frequency needs to be double the signal frequency. Note however that the two signals are offset by $90^o$ so it is like sampling a signal with a frequency $2f_{enc}$. Thus, the μC must use a sampling frequency of: $$F_s = 4f_{enc} = 4 * CPR * u_M$$