Abstract
In recursive digital filter design, the amplitude characteristic of an ideal filter has to be translated into a rational function that is pole-free on the closed unit disk and preferably has real coefficients. This is possible through a causal transformation utilizing the tolerance allowance. In this paper we study the degree of uniform approximation by rational functions that fulfill the filter criteria and can be computed by interpolation or the method of least-squares inverses.
The research of this author was supported by the U. S. Army Research Office under Contract No. DAAG 29-81-K-0133.
This author is a Visiting Scholar at Texas A&M University during 1983–1984.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Chui, C. K. and Chan, A. K., Application of approximation theory methods to recursive digital filter design, IEEE Trans. on ASSP, 30 (1982), 18–24.
Robinson, E. A, Statistical Communication and Detection, Hafner, New York, 1967.
Rusak, V. N., Direct methods in rational approximation with free poles, Dokl. Akad. Nauk BSSR, 22 (1978), 18–20.
Rusak, V. N., Rational Functions as Approximation Apparatus, Beloruss. Gos. Univ., Minsk, 1979.
Suetin, P. K., Fundamental properties of polynomials orthogonal on a contour, Russian Math. Surveys, 21 (1966), 35–84.
Szabados, J., Rational approximation in complex domain, Studia Sci. Math. Hungarian, 4 (1969), 335–340.
Szabados, J., Rational approximation to analytic functions on an inner part of the domain of analyticity, in Approximation Theory, ed. by A. Talbot, Academic Press, New York, 1970, pp. 165–177.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1984 Springer-Verlag
About this paper
Cite this paper
Chui, C.K., Shen, XC. (1984). Degree of rational approximation in digital filter realization. In: Graves-Morris, P.R., Saff, E.B., Varga, R.S. (eds) Rational Approximation and Interpolation. Lecture Notes in Mathematics, vol 1105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072412
Download citation
DOI: https://doi.org/10.1007/BFb0072412
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-13899-0
Online ISBN: 978-3-540-39113-5
eBook Packages: Springer Book Archive