In this paper, we propose a rectangular weighting function that can be used in the method of iteratively reweighted least squares (IRWLS) for designing equiripple all-pass IIR filters. The purpose of introducing this weighting function is to improve the convergence performance in the solution of the IRWLS. The height of each rectangle is designed to be equal to the local maximum of each ripple, and the width of each rectangle is designed so that the area of each rectangle becomes equal to the area of each ripple. Here, the ripple is the absolute value of the phase error. We show experimentally that the convergence performance in the solution of the IRWLS can be improved by using the proposed weighting function.

This paper describes synthesis of a complex RiCR filter with a finite transmission zero except zero frequency. The frequency response of the proposed filter is similar to the conventional elliptic filter. The proposed filter can be composed of fewer elements than the conventional one. A new kernel function is proposed. As an example, a fifth-order RiCR filter is designed. We compare the proposed filter with the conventional complex elliptic filter from the viewpoint of the frequency response and the number of the required elements.