Optimization of IIR compaction filters with fixed angles poles

We present a new design method for IIR compaction filters, where the numerator and denominator may have different degrees. The method sets the poles at fixed angles given by the ideal brickwall filter and optimizes the numerator. The method relies 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 filter may be implemented with significantly less parameters than the FIR counterparts that achieve the same compaction gain.