Optimal FIR and IIR Hilbert transformer design via LS and minimax fitting

A method for the design of both finite impulse response (FIR) and infinite impulse resonant (IIR) digital Hilbert transformers, based on a parameter estimation method for linear systems, is presented. The first approximation is performed in a least-squares (LS) sense in the complex domain. An iterative extension of the algorithm is also presented. It results in an approximation in a minimax (Chebyshev) sense and is also in the complex domain. The procedures described can be used for the design of digital filters other than Hilbert transformers since the desired frequency response is given point by point.>