SDP design procedure for energy compaction IIR filters

We present a design method for optimal energy compaction IIR filters, where the numerator and denominator may have different degrees. The design is performed via iterative relaxations, where the numerator is optimized given the denominator, followed by optimization of denominator given the numerator. The two optimization problems involved are solved using semidefinite programming (SDP) techniques, where the real positiveness of the causal part of the product filter is formulated in two alternative ways: first using the Kalman-Yakubovich-Popov (KYP) lemma, and second, by a less-known parameterization (Genin et al., 2000; Stoica et al., 2000), which we show to be more convenient numerically. Numerical results show the effectiveness of the proposed method and the improvements when compared with optimal FIR compaction filters or constrained IIR compaction filters (restricted to have allpass polyphase components).