A modified transfer function for frequency sampling filters: theory, design, and applications

Abstract

The article is devoted to frequency sampling filters (FSF). FSFs are highly efficient linear-phase digital filters that can be significantly more computationally efficient than Parks–McClellan FIR filters. FSFs are well-suited for implementing filter banks, which can be used to construct high-performance spectrum analyzers. Although these filters have been known for a long time, they have not been widely adopted despite their efficiency. This article presents the authors’ perspective on the reasons behind the limited use of FSFs. A new original method for forming the transfer function (TF) of FSFs using an ideal analog prototype is proposed. The proposed method fundamentally differs from the longestablished classical approach. The TF of an analog filter that meets the require-ments of absolute linearity in the phase response (PR) was considered. The bilinear z-transform method was applied to this ideal TF. By applying L’Hˆopital’s rule, an analytical expression for determining the weighting coefficients of the resulting TF was obtained. The article presents examples of calculated FSFs and a filter bank based on them. Tables of the optimized weighting coefficients and plots of their attenuation characteristics are provided. An improved block diagram of the FSF is also presented. The characteristics of the classical FSF TF and the proposed (alternative) FSF TF are analyzed and compared to determine their advantages and disadvantages.