Design of IIR Hilbert Transformers Based on Weighted Optimization for Magnitude and Phase Responses

Abstract

In this paper, a new design method of IIR Hilbert transformers is proposed by using a nonlinear optimization algorithm. The initial conditions for nonlinear optimization are given by controlling the tap values of IIR Hilbert transformer in the time domain. A parameter optimization technique is used to obtain an IIR Hilbert transformer whose output characteristics in the time domain are close to those of the reference FIR Hilbert transformer. Then, the tap values are optimized by the Fletcher-Powell method in the frequency domain. In the proposed method, the performance criterion for optimization consists of two functions. One represents the error of magnitude response and the other represents that of phase responses. The error ratio of magnitude and phase responses is controlled by different weights to each function. Finally, some examples of IIR Hilbert transformers using this method are shown.