Optimizing the compaction gain in a class of IIR filters

In this paper we consider the optimization of compaction gain for filters belonging to a restricted class of IIR filters, having the transfer function H(z)=1//spl radic/2(z/sup -2N/+z/sup -1/A(z/sup 2/)) where A(z) is a stable all-pass filter. This parameterization has the advantage that the perfect reconstruction condition is automatically fulfilled. Our results represent a generalization of the work by Tugan et al. (1997) where only a first order all-pass filter A(z) is considered, whereas here we consider a general N-th order all-pass filter. The problem of optimal compaction FIR filter design received wide attention in several recent papers, but optimal IIR filter design was presented only for a very restricted filter class. The problem we discuss here, designing the IIR filter for optimum compaction, is clearly important for coding applications, since it enables one to achieve the same compaction gains as in the FIR filter case, but for a much smaller number of parameters, as we show in the experimental section.