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, maximally flat digital differentiators and fractional delayers are proposed. The transfer functions of these filters are analytically obtained by expanding some suitable functions into power series. Efficient implementations can be derived from the resultant transfer functions. The weighting coefficients and the building blocks of these filters are explicitly expressed in closed form. The proposed filter structures are more robust to the coefficient quantization than the direct form