Frequency Transformations of IIR Filters with Filter Bank Applications

Low-complexity half-band IRh 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, we 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.