An approach to the design of IIR Hilbert transformers

An approach to the design of the causal IIR Hilbert transformer is presented. When the `care´ band is symmetric about the frequency, F/4-one-fourth of the sampling frequency-a Hilbert transformer can be easily derived from designing a bireciprocal prototype lowpass filter; in the non-symmetrical case, the optimum frequencies are obtained directly by making use of an optimization method and the coefficients of the transfer function are determined by solving a corresponding nonlinear equation system. The designed results are realized with the concept of the wave digital filter (WDF), so the digital structures possess all the advantages of WDF, such as low sensitivity to the changes in the coefficients, large dynamic range and good stability. Some examples are also given in this paper to illustrate the design procedure