arXiv subjects

Konstantin A. Rybakov

Publications and source records attributed to Konstantin A. Rybakov.

8 recordsLinked to original sources

arXiv2026

Applying the Spectral Method for Modeling Linear Filters: Bessel, Papoulis, and Legendre Filters

This paper proposes a new technique for computer simulation of linear filters. It allows simulating continuous-time linear filters based on the spectral method for analyzing linear control systems. Applying the spectral method implies that the input and output signals are represented by ordered sets of expansion coefficients in a chosen basis, and the filter itself is specified by a two-dimensional nonstationary transfer function. The described technique is tested on Bessel, Papoulis, and Legendre filters of various orders. For each filter, the corresponding two-dimensional nonstationary transfer function, i.e., the matrix of the linear transformation relating expansion coefficients of the input and output signals, is obtained.

eess.SP↗

arXiv2026

Forming invariant stochastic differential systems with a given first integral

This article proposes a method for forming invariant stochastic differential systems, namely dynamic systems with trajectories belonging to a given smooth manifold. The Itô or Stratonovich stochastic differential equations with the Wiener component describe dynamic systems, and the manifold is implicitly defined by a differentiable function. A convenient implementation of the algorithm for forming invariant stochastic differential systems within symbolic computation environments characterizes the proposed method. It is based on determining a basis associated with a tangent hyperplane to the manifold. The article discusses the problem of basis degeneration and examines variants that allow for the simple construction of a basis that does not degenerate. Examples of invariant stochastic differential systems are given, and numerical simulations are performed for them.

math.PR↗

arXiv2026

Applying the Spectral Method for Modeling Linear Filters: Butterworth, Linkwitz-Riley, and Chebyshev filters

This paper proposes a new technique for computer modeling linear filters based on the spectral form of mathematical description of linear systems. It assumes the representation of input and output signals of the filter as orthogonal expansions, while filters themselves are described by two-dimensional non-stationary transfer functions. This technique allows one to model the output signal in continuous time, and it is successfully tested on the Butterworth, Linkwitz-Riley, and Chebyshev filters with different orders.

eess.SP↗

arXiv2026

On Approximate Representation of Fractional Brownian Motion

This paper considers the orthogonal expansion of the fractional Brownian motion relative to the Legendre polynomials. Such an expansion has not only theoretical but also practical interest, since it can be applied to approximate and simulate the fractional Brownian motion in continuous time. The relations for the mean square approximation error are presented, and a comparison with the previously obtained result is carried out.

math.PR↗

arXiv2025

On the orthogonal expansion of iterated Stratonovich stochastic integrals

We consider a class of functions for which the multiple Stratonovich stochastic integral or equivalent iterated Stratonovich stochastic integral with square integrable weights is defined by the orthogonal expansion. The equality of the trace of expansion coefficients matrix for these functions and the corresponding integral trace is established.

math.PR↗

arXiv2025

Analysis and conditional optimization of projection estimates for distribution of random variable using Legendre polynomials

Algorithms for jointly obtaining projection estimates of the density and distribution function of a random variable using Legendre polynomials are proposed. For these algorithms, a problem of the conditional optimization is solved. Such optimization allows one to increase the approximation accuracy with minimum computational costs. The proposed algorithms are tested on examples with different degrees of smoothness of the density. A projection estimate of the density is compared to a histogram that is often used in applications to estimate distributions.

stat.CO↗

arXiv2025

On Spectral Approach to the Synthesis of Shaping Filters

This paper describes various approaches to modeling a random process with a given rational power spectral density. The main attention is paid to the spectral form of mathematical description, which allows one to obtain a relation for the shaping filter using a transfer function without any additional calculations. The paper provides all necessary relations for the implementation of the shaping filter based on the spectral form of mathematical description.

eess.SY↗

arXiv2025

Spectral Representation and Simulation of Fractional Brownian Motion

The paper gives a new representation for the fractional Brownian motion that can be applied to simulate this self-similar random process in continuous time. Such a representation is based on the spectral form of mathematical description and the spectral method. The Legendre polynomials are used as the orthonormal basis. The paper contains all the necessary algorithms and their theoretical foundation, as well as the results of numerical experiments.

math.PR↗