Adaptive Differentiation Filter

As an essential tool for describing dynamic systems, the concept of derivatives has been deeply rooted in all aspects of modern science. In engineering practice, due to the complexity and unknownness of the process of interest and the discreteness nature of the collected data, people need a method to obtain the derivative information of the dynamic process from these discrete data, that is, numerical differentiation method. Unfortunately, the disturbance introduced from the dynamic process itself and the data acquisition process make the collected data noisy. The existing numerical differentiation methods are susceptible to such noise in the data, making them perform poorly when faced with data from the real world. In this paper, a new numerical differentiation method is proposed. It works like a 1-D FIR filter whose tap coefficients are generated based on signal and can estimate (higher-order) derivatives from noisy sampled data of given functions. The proposed method shows much better robustness against noise and consistency against signal frequency varying than existing methods.