Linear phase FIR differentiator design based on maximum signal-to-noise ratio criterion

In this paper, a new approach to the design of digital FIR differentiators is presented. The differentiator is linear phase and has zero derivatives at DC frequency. The design is based on the maximization of signal-to-noise ratio (SNR) at the output of the differentiator. The optimal filter coefficients are obtained from the generalized eigenvector associated with the maximum eigenvalue of a pair of symmetric matrices. Estimation of the time derivative of polynomial signal, sinusoidal signal and handwritten Chinese signature is used to demonstrate that the proposed method provides better accuracy and higher SNR than the conventional differentiator methods.