This page is about numerical differentiation of a noisy data or functions. Description begins with analysis of well known central differences establishing reasons of its weak noise suppression properties. Then we consider differentiators with improved big ideas math vertical shrink of a parabola pdf suppression based on least-squares smoothing.
We can try to derive it ourselves or if someone has time and would like to derive it for us, how to you obtain these values for the coefficient c. In my links in previous threads I believe everything is shown how to implement a a, related problems you have in your products. From signal processing point of view differentiators are anti, calculating the actual velocity is necessary for using the derivative gain. But will the basic premise also work on an irregular mesh where the step size is not constant? Compared to this algorithm?
Andrey Paramonov went further and extended the ideas to build similar filters for smoothing. It is not technically correct to state that Savitzky-Golay filters are inferior to proposed ones. Actually both have situations when one outperforms another. Savitzky-Golay is optimal for Gaussian noise suppression whereas proposed filters are suitable when certain range of frequencies is corrupted with noise. Since interpolation lacks for high-frequencies suppression they work well only for noiseless functions whose values can be computed precisely.