Estimation of samples of the derivative of a signal based on the signal difference derivative

A technique of designing a discrete-time FIR filter called A-DD for converting the backward difference derivative of a discrete-time signal into a train of samples of the first order derivative of the analogue counterpart of this signal is presented. The power of the proposed technique is illustrated by showing the performance of the Lagrangian A-DD, offering very high accuracy in a specified frequency range, thus being especially useful in measurement applications. This design is compared with the results for windowing technique using a rectangular window. The proposed A-DD can be applied in scanning interferometry, in the estimation of the instantaneous frequency and as a digital equalization filter matching the inverse of the zero-order-hold frequency response