Closed-form design of maximally flat FIR Hilbert transformers, differentiators, and fractional delayers by power series expansion

In this paper, novel closed-form designs of the FIR Hilbert transformers, m aximally flat digital differentiators and fractional delayers are proposed, The transfer functions of these filters are analytically obtained by expan ding some suitable functions into power series. Efficient implementations c an be derived from the resultant transfer functions, The weighting coeffici ents and the building blocks of these filters are explicitly expressed in c losed form. The proposed filter structures are more robust to the coefficie nt quantization than the direct form.