Abstract
An algorithm of Schur for characterizing power series that are bounded in the unit circle is shown to have applications to a variety of problems in science and engineering. These include speech analysis and synthesis, inverse scattering, decoding of error-correcting codes, synthesis of digital filters, modeling of random signals, Padé approximation for linear systems, and zero location of polynomials.
This work was supported in part by the U. S. Army Research Office, under Contract DAAG29-83-K-0028, the Air Force Office of Scientific Research, Air Force Systems Command under Contract AF83-0228. It is based on notes prepared for one of the May 1984 Schur Memorial Lectures while the author held an Erna and Jacob Michael Visiting Chair in the Department of Theoretical Mathematics at the Weizmann Institute of Science, Rehovot, Israel.
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Kailath, T. (1986). A Theorem of I. Schur and Its Impact on Modern Signal Processing. In: Gohberg, I. (eds) I. Schur Methods in Operator Theory and Signal Processing. Operator Theory: Advances and Applications, vol 18. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5483-2_2
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