filters - Derive velocity and acceleration from position

I generate random spike data that represent the ouput from a rotary encoder. Here the output of my algorithm: The first plot is position, then velocity and then acceleration. Even though I downsample my position vector and pass it to a average filter of 20 points, the derivative are very sensitive as you can see. I check the following question: have position, want to calculate velocity and acceleration. Few option seem to be available , but I don't get the answer , the Savitzky-Golay Filters is just a smoothing function, I don't get how he get the velocity, also what are the orther alternatives.