New approach to clustered look-ahead pipelined IIR digital filters

Authors Lim and Liu (see IEEE Trans. Signal Process., vol. 40, no. 7, p.1643-51, 1992) recently introduced the “minimum order augmentation” technique for pipelining IIR digital filters which guarantees the addition of the least number of superfluous poles to obtain a stable pipelined IIR filter while maintaining a “clustered look-ahead” pipeline structure. Unfortunately, this minimization of the superfluous poles comes at the expense of adding additional denominator multipliers. In this paper, we introduce a “minimum order clustered look-ahead” that achieves the minimum number of superfluous poles possible while minimizing the total-number of multipliers for a “clustered look-ahead” pipeline structure. We show that while our new technique does in some instances require more superfluous poles, the increase in hardware complexity with respect to incremental augmentation is lower when compared to the Lim and Liu approach. A MATLAB computer program is described which allows the design of any order pipelined IIR filter. Examples demonstrate that stable “clustered look-ahead” pipelined IIR filters can be designed with the minimum number of superfluous poles (as achieved by Lim and Liu), but with fewer denominator multipliers thus reducing significantly the computational complexity in many cases. Furthermore, an analytic solution to the second-order case gives a very practical approach to pipelined IIR filter design with great insight into the stability characteristics of pipelined IIR filters