Design of FIR digital differentiator using discrete Hartley transform and backward difference

In this paper, the design of digital differentiator is presented. First, the interpolation formula of discrete-time sequence is derived by using discrete Hartley transform (DHT). Then, the DHT-based interpolation formula is applied to design FIR digital differentiator by using backward difference formula. The filter coefficients are easily computed because closed-form design is obtained. Finally, design examples are demonstrated to show the proposed method has smaller design error than the conventional window method and maximally flat design using the same parameters.