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Published in:
2017 | OriginalPaper | Chapter
A Riemann–Hilbert Approach to Filter Design
Author : Elias Wegert
Published in: Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics
Publisher: Springer International Publishing
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The paper is devoted to interrelations between boundary value problems of Riemann–Hilbert type and optimization problems in spaces of bounded holomorphic functions which are motivated by optimal filter design. A numerical method of Newton type for the iterative solution of nonlinear Riemann–Hilbert problems is adapted for solving the optimization problem and its convergence is proved. The approach is illustrated by the design of a low-pass filter, which we discuss in some detail.My long-time acquaintance with Albrecht Böttcher, and in particular our journey to a conference on H∞ control at lake Como in 1990, form the background of the paper.