Статья
2020
Discrete-Time Systems with Frequency Response of the Markov-Stieltjes Type
A. R. Mirotin, I. S. Kovaleva
Русская математика
https://doi.org/10.3103/S1066369X20060067
Abstract / Full Text
A class of discrete-time filters (systems) is selected, the frequency characteristics of which are functions of the Markov-Stieltjes type. A description of these filters is given in terms of their system function and impulse response. The properties of stationarity, causality, stability, and reversibility are investigated. A wide class of filters with rational transfer functions is indicated, which is subject to the main results of the work.
Author information
- Francisk Skaryna Gomel State University, 104 Sovetskaya str., Gomel, 246019, Republic of BelarusA. R. Mirotin & I. S. Kovaleva
References
- Kovalëva, I.S., Mirotin, A.R. “The Markov-Stieltjes Transform of Measures and Discrete-time Systems”, Probl. Fiz. Mat. Tekh. 1 (38), 56–60 (2019).
- Kovalyova, I.S., Mirotin, A.R. “Theorem on a Convolution for the Markov-Stieltjes Transform”, Probl. Fiz. Mat. Tekh. 3 (16), 66–70 (2013).
- Mirotin, A.R., Kovalyova, I.S. “The Markov-Stieltjes Transform on Hardy and Lebesgue Spaces”, Integral Transforms and Special Funct. 27 (12), 995–1007 (2016).
- Mirotin, A.R., Kovalyova, I.S. “Corrigendum to our paper «The Markov-Stieltjes Transform on Hardy and Lebesgue spaces»”, Integral Transforms and Special Funct. 28 (5), 421–422 (2017).
- Kovaleva, I.S., Mirotin, A.R. “The Generalized Markov-Stieltjes Operator on Hardy and Lebesgue Spaces”, Tr. Inst. Mat. 25 (1) 39–50 (2017).
- Mirotin, A.R. Harmonic Analysis on Abelian Semigroups (GSU named after F. Skorina, Gomel, 2008) [in Russian].
- King, F.W. Hilbert Transforms: in 2 Vol., V.1 (Cambridge Univ. Press, Cambridge, 2009).
- Vyacheslavov, N.S., Mochalina, E.P. “Rational Approximations of Functions of Markov-Stieltjes Type in Hardy Spaces Hp, 0 < p ≤ ∞”, Moscow Univ. Math. Bull. 63 (4), 125–134 (2008).
- Krein, M.G., Nudelman, A.A. The Problem of Markov Moments and Extremal Problems (Nauka, Moscow, 1973) [in Russian].
- Nikolski, N.K. Operators, Functions, and Systems: An Easy Reading, V.1 (American Math. Soc., Providence, 2002).
- Siebert, W. Circuits, Signals, and Systems (MIT Press, 1986; Mir, Moscow, 1988).
- Pekarskii, A.A. “Best Uniform Rational Approximations of Markov Functions”, St. Petersburg Math. 7 (2), 277–285 (1996).
- Andersson, J.-E. “Rational Approximation to Function Like xα in Integral Norms”, Anal. Math. 14 (1), 11–25 (1988).
- Andersson, J.-E. “Best Rational Approximation to Markov Functions”, Approxim. Theory 76 (2), 219–232 (1994).
- Papoulis, A. Signal Analysis (McGrow Hill, New York, 1977).
- Hamming, R.W. Digital Filters (Englewood cliffs, N.J, 1977; Sovetskoe Radio, Moscow, 1980).
- Mirotin, A.R., Atvinovskii, A.A. “On Some Properties of the Functional Calculus of Closed Operators in a Banach Space”, Probl. Fiz. Mat. Tekh. 4, 63–67 (2016).
- Atvinovskii, A.A., Mirotin, A.R. “On Some Functional Calculus of Closed Operators in a Banach Space. II”, Russian Math. (Iz. VUZ) 59 (5), 1–12 (2015).
- Atvinovskii, A.A., Mirotin, A.R. “Inversion of a Class of Operators in a Banach Space and Some of its Applications”, Probl. Fiz. Mat. Tekh. 3 (16), 55–60 (2013).
- Widder, D.V. The Laplace Transform (Princeton Univ. Press, N.J., 1946).
- Akhiezer, N.I. The Classical Problem of Moments and Some Related Questions (Fizmatlit, Moscow, 1961) [in Russian].