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I've started recently working with the ADXL345 accelerometer with the goal of finding the velocity.

And so far, I'm getting "okay" results after applying a second-order Butterworth filter to the acceleration values.

enter image description here If you see in the picture below taken from the ADXL345 datasheet p14, we can see that for example, to get 50Hz of useful signal frequency, 100Hz of sampling frequency needs to be used, which I guess follows the Nyquist-Shannon theorem.

I've configured my code to take measurements from the accelerometer every 100Hz which means the period should be 10 ms, but when I plot the signal and apply a Butterworth signal with a cutoff frequency of 50Hz I get the same signal, which is good because I wanted that 50Hz signal, but I don't know how it works, how come I took measurements every 100Hz and still got a signal of 50Hz? Any help at this point would be greatly apperciated.

enter image description here

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Sorry for my bad English, but I will try to explain it. Shannon-Nyquist theorem states that signal has to be sampled at least twice the maximal frequency. If you sample your signal with frequency of 100Hz, as i like to think of it, you will get 50Hz of spectral component on each side of spectrum(because it is symmetrical, you have both the negative and positive frequencies). So I think of it this way: you have 100Hz of spectral content, but on both sides of y axis(witch represents amplitude), we have 50Hz of content. So our maximal signal frequency after sampling with frequency of 100Hz will be 50Hz.Here you can see how spectrum is symmetric

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