Optimizing the compaction gain in a class of IIR filters

In this paper we consider the optimization of com-paction gain for lters belonging to a restricted class of IIR lters, having the transfer function H(z) = 1 p 2 ? z ?2N + z ?1 A(z 2) where A(z) is a stable allpass lter. This parameter-ization has the advantage that perfect reconstruction condition is automatically fullllled (see (3) below). Our results represent a generalization off6] where only a rst order all-pass lter A(z) is considered, whereas here we consider a general N-th order all-pass lter. The problem of optimal compaction FIR lter design received wide attention in several recent papers 1]{ 3], but optimal IIR lter design was presented only for a very restricted lter class in 6]. The problem we discuss here, designing the IIR lter for optimum com-paction, is clearly important for coding applications, since it enables to achieve the same compaction gains as in FIR lter case, but for a much smaller number of parameters, as we show in the experimental section. The compaction gain is deened as the variance ratio 2 y == 2 x where x(n) is the input of the lterbank and y(n) is the output of the rst channel (see Figure 1). We consider the following equivalent expressions for the lter