OPTIMAL-DESIGN OF INFINITE IMPULSE-RESPONSE HILBERT TRANSFORMERS

This paper proposes a new method for designing the optimal infinite im pulse response (IIR) Hilbert transformer. Until now, finite impulse re sponse (FIR) filters have mostly been used in the design of the digita l filter for the circuit such as the Hilbert transformer, where the li near-phase response is required. Several methods have been proposed fo r designing the IIR filter, which, however, had problems in the comple xity of the algorithm or the accuracy of the designed Hilbert transfor mer. This paper considers first the FIR Hilbert transformer as a model . The design of the tap coefficients for the IIR filter which gives th e same output as that of the model, when the same input is given, is r educed to the parameter estimation problem when the Kalman filter is u sed for control. Then the lip Hilbert transformer is designed in the t ime domain. To obtain a better response, an evaluation function is def ined that represents the error from the ideal frequency response. The tap coefficients are fine-adjusted by the Fletcher-Powell method so th at the evaluation function is minimized. By this approach, it is possi ble to design the lip Hilbert transformer while maintaining the stabil ity and the phase linearity, which are the features of the FIR filter. The 16th-order lip Hilbert transformer actually is designed by the pr oposed method, and it is shown that a performance better than the 30th - and the 31st-order reference FIR Hilbert transformers can be realize d.