SDP design procedures for near-optimum IIR compaction filters

In this paper we present two new design methods for IIR compaction filters, where the numerator and denominator may have different degrees. In the first method, the design is performed via iterative relaxations, where the numerator is optimized given the denominator, followed by optimization of denominator given the numerator. The second method sets the poles at fixed angles given by the ideal brickwall filter and optimizes the numerator. Both methods rely on semidefinite programming optimization, using an appropriate parameterization of positive real polynomials. Experimental results show compaction gains near the upper bound given by the ideal filter. The IIR filters may be implemented with significantly less parameters than the FIR counterparts achieving the same compaction gain.