The design of polyphase-based IIR multiband filters

This paper addresses a new approach for the design of multiband filters with step like magnitude responses and extremely flat, weighted passbands down to μdBs. Our new technique can also be used for the multiband step-wise approximation of arbitrary filter magnitude responses with precise transition band control. One marked advantage of the technique is that our basic building blocks are the modified polyphase (IIR) filters as reported in [1][3]. The points of transition from one flat-top to another, namely the multiple transition bands of our filter are completely free of cross-over oscillations. One other advantage of this technique is that we are not confined to employing IIRs only. To this end perfect reconstruction FIR filters as in [4] can also be used. In both the FIR and IIR cases our technique is general purpose and works for both real and complex valued filter coefficient cases. THE MODIFIED POLYPHASE HALFBAND BUILDING BLOCK Our polyphase structures suggested in [1]-[2] are very attractive for the design and implementation of halfband Lowpass and Highpass filters achieving very small passband ripples for a very small coefficient budget. Lowpass and highpass filter functions can be effected using the same coefficients, with exception of a sign change at one of the summation block. By combining lowpass and highpass filters as in Figure 1(a) we can get a very efficient two-band filter.