Min-Max Approximation of Transfer Functions With Application to Filter Design

This paper investigates the problem of frequency-specific (FS) model approximation of transfer functions using a min-max approach. The objective is to find an approximation model for a transfer function such that the maximum error gain over a specific frequency range is minimized. First, a linear matrix inequality condition characterizing the FS gain of a transfer function is derived by using the generalized Kalman-Yakubovich-Popov lemma, and then a simple iterative approach is proposed to optimize the approximation model. Numerical experiments show that the proposed approach can produce better approximation models over a specific frequency range than some existing approaches. Moreover, it is indicated how to apply the proposed approximation approach to the design problem of infinite impulsive response digital filters, and design examples clearly illustrate that the proposed design flow can generate filters comparable with the latest design method.