On a Design of FIR Digital Filters with Equiripple Error Function

Abstract

A particular class of digital filters are FIR filters with exactly linear phase for all frequencies. Several methods have been presented to design such filters without and with extra constraints in the time and/or frequency domain [1–3]. In these methods, the design of a linear phase FIR filter is formulated as a real approximation problem. However, in some applications there is a need to design filters with more general specifications. In these situations, both the magnitude and the phase responses of the filter are arbitrary. In order to design such filters, a complex approximation problem must be solved. Such problems arise, for example, in the design of FIR filters with approximately linear phase in the passband which have less group delay than exactly linear phase filters, and in the design of FIR equalizers. Several approaches have been proposed to solve the complex approximation problem [4–10]. In some of them, the complex approximation problem is converted into a real-valued problem.