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

A novel method for the design of digital finite impulse response (FIR) and infinite impulse response (IIR) Hilbert transformers using the least squares (LS) and the minimax criteria is presented. The LS approximation is performed in the complex domain. Also presented is an iterative extension of the algorithm, which results in a minimax (Chebyshev) approximation, also in the complex domain. For FIR filters the results are the same as those of the optimal methods known from the literature. For the same task, stable IIR filters have also been successfully designed. The procedures proposed are usable for the design of digital filters other than Hilbert transformers, since the desired frequency response can be given point by point.<>