Frequency Transformations of IIR Filters with Filter Bank Applications

Low-complexity half-band IIR filters implemented as two-path polyphase structures use all-pass sub-filters as polyphase components. With a simple first-order frequency transformation applied in the half-band filter all-pass sections, the new filter is obtained with the cut-off frequency at the desired position. In this paper, the authors apply the frequency transformations to construct minimum phase filters and filter pairs of desired regularity order, and with the cut-off frequency at an arbitrary location. In this way, an IIR filter design problem simplifies to the half-band filter design problem. Several solutions based on half-band filters and frequency transformations are shown: (i) multilevel IIR filter bank composed of IIR filter pairs with desirable regularity order and with changeable crossover frequency in sub-bands, (ii) IIR implementation of 2/3, 1/3 two-channel resempler, (iii) simple and effective approach to designing band-pass/band-stop filter pairs