Optimal design of infinite impulse response hilbert transformers
Satoru Shimizu, Takashi Yahagi, Marco Aurélio Amaral Henriques · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1995
Abstract This paper proposes a new method for designing the optimal infinite impulse response (IIR) Hilbert transformer. Until now, finite impulse response (FIR) filters have mostly been used in the design of the digital filter for the circuit such as the Hilbert transformer, where the linear‐phase response is required. Several methods have been proposed for designing the IIR filter, which, however, had problems in the complexity of the algorithm or the accuracy of the designed Hilbert transformer. This paper considers first the FIR Hilbert transformer as a model. the design of the tap coefficients for the IIR filter which gives the same output as that of the model, when the same input is given, is reduced to the parameter estimation problem when the Kalman filter is used for control. Then the IIR Hilbert transformer is designed in the time domain. To obtain a better response, an evaluation funclion is defined that represents the error from the ideal frequency response. the tap coefficients are fine‐adjusted by the Fletcher‐Powell method so that the evaluation function is minimized. By this approach, it is possible to design the IIR Hilbert transformer while maintaining the stability and the phase linearity, which are the features of the FIR filter. the 16th‐order IIR Hilbert transformer actually is designed by the proposed method, and it is shown that a performance better than the 30th‐ and the 31st‐order reference FIR Hilbert transformers can be realized.