Görner, Stephan; Potchinkov, Alexander; Reemtsen, Rembert The direct solution of nonconvex nonlinear FIR filter design problems by a SIP method. (English) Zbl 0993.93008 Optim. Eng. 1, No. 2, 123-154 (2000). The purpose of this paper is to give a general and precise formulation of the main FIR (Finite Impulse Response) filter design problems. Existence conditions of the solutions of these problems are provided, and results are presented on the convergence of the approximation errors and on the connection between frequency response and the magnitude/phase response problem. A new method for nonlinear SIP (Semi-Infinite Programming) is described (S. Görner, 1997), employing a dynamic discretization scheme in a first phase and solving a reduced continuous problem in a second phase to accelerate the convergence. The Görner method is shown to be convergent and to produce very good results when applied to a large variety of nonlinear design problems. This new method, together with the robust method of A. Potchinkov and R. Reemtsen (1995) for convex SIP, and with a method for unconstrained least-squares problems provides a set of algorithms that can efficiently solve most FIR filter design problems in the frequency domain.The investigated methods constitute also a promising tool for the solution of IIR (Infinite Impulse Response) filter design problems, which all are strongly nonlinear. The authors’ approach supports the generous idea that FIR and IIR filter design problems do not have so many peculiarities so as to justify the development of particular algorithms, but they are usually semi-infinite or, when discretized, finite optimization problems that should and can be solved by well-founded customary methods of general optimization. In particular, the new methods of Görner (1997) are capable of solving rather sophisticated nonlinear filter design SIP problems directly and accurately. Reviewer: Neculai Curteanu (Iaşi) Cited in 1 ReviewCited in 4 Documents MSC: 93B40 Computational methods in systems theory (MSC2010) 93C62 Digital control/observation systems 93E11 Filtering in stochastic control theory 90C34 Semi-infinite programming 93C10 Nonlinear systems in control theory 90C90 Applications of mathematical programming Keywords:SQP methods; FIR filter design; nonlinear semi-infinite programming; infinite impulse response filter design; frequency response; dynamic discretization; Görner method; nonlinear design; unconstrained least-squares problems; optimization Software:FSQP PDFBibTeX XMLCite \textit{S. Görner} et al., Optim. Eng. 1, No. 2, 123--154 (2000; Zbl 0993.93008) Full Text: DOI