High-speed recursive filter structures composed of identical all-pass subfilters for interpolation, decimation, and QMF banks with perfect magnitude reconstruction

High-speed recursive filter structures for interpolation and decimation wit h factors of two, and quadrature mirror filter (QMF) banks with perfect mag nitude reconstruction, are proposed. The structures are composed of identic al all-pass subfilters that are interconnected via extra multipliers, For t he case of interpolation and decimation filters, the overall transfer funct ion corresponds in the simplest case to several half-band infinite-impulse response (IIR) filters in cascade, To achieve a smaller passband ripple tha n for a cascade design, a design procedure that has been used earlier for s ingle-rate filters is used. In this approach, the design is split into desi gns of a prototype finite-impulse response (FIR) filter and a half-band IIR filter. For the case of QMF banks, the design is again separated into desi gns of a prototype FIR filter and a half-band IIR filter. One major advanta ge of the proposed filter structures over the corresponding conventional (h alf-band filter) structures is that the required coefficient word length fo r the allpass filters is substantially reduced, implying that the maximal s ample frequency can be substantially increased for a given VLSI technology. Further, for interpolation and decimation, the arithmetic complexity may b e reduced in comparison with both the conventional structures and straightf orward cascade structures. Simple recurrence formulas for computation of th e interconnecting multipliers, given the overall transfer function, are der ived. Several examples are included which compare the proposed structures w ith the corresponding conventional and straightforward cascade structures.