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 with factors of two, and quadrature mirror filter (QMF) banks with perfect magnitude reconstruction, are proposed. The structures are composed of identical all-pass subfilters that are interconnected via extra multipliers. For the case of interpolation and decimation filters, the overall transfer function corresponds in the simplest case to several half-band infinite-impulse response (IIR) filters in cascade. To achieve a smaller passband ripple than for a cascade design, a design procedure that has been used earlier for single-rate filters is used. In this approach, the design is split into designs 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 designs of a prototype FIR filter and a half-band IIR filter. One major advantage of the proposed filter structures over the corresponding conventional (half-band filter) structures is that the required coefficient word length for the all-pass filters is substantially reduced, implying that the maximal sample frequency can he substantially increased for a given VLSI technology. Further, for interpolation and decimation, the arithmetic complexity may be reduced in comparison with both the conventional structures and straightforward cascade structures. Simple recurrence formulas for computation of the interconnecting multipliers, given the overall transfer function, are derived. Several examples are included which compare the proposed structures with the corresponding conventional and straightforward cascade structures.