Low-order IIR filter bank design

The advantage of infinite-impulse response (IIR) filters over finite-impulse response (FIR) ones is that the former require a much lower order (much fewer multipliers and adders) to obtain the desired response specifications. However, in contrast with well-developed FIR filter bank design theory, there is no satisfactory methodology for IIR filter bank design. The well-known IIR filters are mostly derived by rather heuristic techniques, which work in only narrow design classes. The existing deterministic techniques usually lead to too high order IIR filters and thus cannot be practically used. In this paper, we propose a new method to solve the low-order IIR filter bank design, which is based on tractable linear-matrix inequality (LMI) optimization. Our focus is the quadrature mirror filter bank design, although other IIR filter related problems can be treated and solved in a similar way. The viability of our theoretical development is confirmed by extensive simulation.

I. Introduction

The TRADEOFFF between infinite-impulse response (IIR) filter and finite-impulse response (FIR) one is that the former requires much lower orders for a given desired specification. This means that IIR filters require much fewer multipliers and adders for digital implementation and are very efficient. The commonly used IIR filters are the Chebyshev, Butterworth and Elliptic filters derived from the corresponding analog filters. The existing deterministic methodologies often lead to too high order IIR filters so the mentioned tradeoff between IIR and FIR filters are hardly enhanced. It is especially true in the IIR filter bank design problem (see e.g., [14], [16], [17], [21], [22] for its applications to image processing and communication), which is formulated as follows (see Fig. 1).