An Algorithmic Procedure for Designing Hybrid FIR/IIR Digital Filters

A wide variety of digital filter-design methods have been proposed and studied in the past several years. 1-9 Generally, these design methods can be classified as analytical or algorithmic, depending on the form of solution of the approximation problem which is used. Additionally, the resulting designs are classified as finite impulse response (FIR) or infinite impulse response (IIR), depending on the filter properties, FIR filters have the property that they can be easily designed to have exactly linear phase. Furthermore, linear-phase FIR filters can be designed to approximate an arbitrary magnitude response to within given tolerances by using a sufficiently high order, IIR filters cannot achieve a linear-phase response exactly, but are capable of approximating sharp cutoff filters with considerably lower order filters than are required for the FIR designs which meet identical magnitude specifications. 10 Thus, for many practical filter applications, there is a trade-off between the exact linear-phase response obtainable using an FIR filter and the reduced filter order obtainable using an IIR filter. In this paper, a hybrid design is proposed which bridges the gap, somewhat, between the FIR and IIR filters. The hybrid filter is a particular class of IIR filter where the degree of the numerator of its system 89