Abstract
IIR filters can give the same magnitude performance with fewer parameters than FIR filters. However, they cannot have exact linear phase. Their design is more complicated due to the difficulty in ensuring stability and to the non-convexity of the optimization problems. In this short chapter, we give few guidelines for the optimization of IIR filters, insisting on algorithms that use positive polynomials. For 1D filters, we discuss two design problems, using magnitude and approximate linear phase as design criteria; in the latter case, stability domains based on positive realness are an important tool. The method for approximate linear phase is then extended to 2D, for the case when passband and stopband are described by the positivity of some polynomials.
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