Numerical Differential Formula via Linear Combinations of Sampled Data

Abstract

In this paper, we propose a method for obtaining accurate derivatives of observed signals on real time; we propose the Numerical Differential Formula via Linear Combinations of Sampled Data, based on a necessary and sufficient condition under which the linear combination of sampled data is the numerical differential formula. We investigate its property of differentiating general observation signal which includes random noises and give methods for minimizing the variance of error and for assigning the phase. A design approach using empirical rules simplifies selection of parameters by trial and error.