http://ieeexplore.ieee.org/iel5/5/31294/01456141.pdf

Number theory in digital signal processing

The local-topological method for nonlinear dynamical analysis of cardiosignals is presented. The theoretic basis of the local-topological method for determining a minimum attractor embedding dimension is proposed. The investigation of digitized cardiosignals using local-topological analysis of chaotic attractor trajectories is carried out.

https://ieeexplore.ieee.org/iel5/7056/19013/00880038.pdf

Biomedical signal processing based on estimation of minimal dimension embedding of chaotic attractor

An express-reconstruction of distorted speech signals based on a fast filtering algoritlun for inverting linear convolution by sectioning method combined with effective realvalued split radix fast Fourier transform (FFT) algorithms are proposed.

An express-reconstruction of distorted speech by inverse filtering method.

For reconstructing digital signals (images), a fast algorithm is proposed for inverting long linear convolutions by sectioning, together with effective real-valued fast Fourier transform (FFT) algorithms on a split base.

A fast algorithm for calculating the inverse convolution for signal and image reconstruction

Decomposition methods of nonlinear operators describing the behavior of system in state space (phase space) are very important for analysis, identification and modeling of nonlinear dynamical systems (NDS), in particular NDS with self-organization (or complex NDS [1], [2]). The aim of this paper is derivation and classification of matrix series describing decomposition of vector functions from phase space variables and NDS operators into state space [3],[4],[5]. This paper also develops some statements of matrix decomposition and main principles for analysis of attractors of complex NDS.

Analysis of attractors of complex dynamical systems based on matrix decomposition.

The theoretic substantiation of a locally topological method for defining a minimum attractor embedding dimension on the basis of state-space method of a dynamic system description is supposed. The numerical modeling of various types of discrete dynamic systems on the computer is carried out with the purpose of verification of theoretical principles, which are the underlying ones for a minimum dimension computation method of such system attractor embedding.

Minimal attractor embedding dimension for discrete dynamic system based on state-space method

A fast algorithm of realizing a method of inverting a long liner convolution is presented. It is based on the procedure of sectionalization combined with effective real-valued split- radix fast Fourier transformation (FFT) algorithm for solving problems of restoration digital signals (images). The minimal multiplicative complexity of such algorithm is obtained.

Minimal multiplicative complexity and fast restoration algorithm of digital signals and images

This paper shows on how the real algorithms for the reduction a modulo arbitrary polynomial and fast Vandermonde transform (FVT) are realized on computer using fast Fourier transform (FFT). This real-valued FVT algorithm on the developed fast reduction polynomial algorithm is based. The realization of FVT algorithm on computer with real multiplicative complexity O(2Nlog 2 2N) and real additive complexity O(6Nlog 2 2N) is obtained. New FVT algorithm is applied in digital signal, filtering and interpolation problems.

Fast algorithms for reduction a modulo polynomial and vandermonde transform using FFT

This paper investigates the approach for revealing pathological speech signal based on estimating specific geometric structure of Lorenz attractor in a chaotic regime. Analysis of the Lorenz attractor on the basis of proposed nonlinear decomposition into matrix series is developed. This analysis permits to estimate the values of characteristic parameters (including control one) of Lorenz attractors and predict their evolution in time. This paper shows that estimation of control parameter of Lorenz attractor in the chaotic regime permits to distinguish even very similar speech signals.

Distinguishing and recognition of pathological speech based on estimation of control parameter of chaotic attractor.

The theoretical ground of the method for defining a geometric characteristic as minimal attractor embedding dimension m0 on the basis of matrix decomposition for different types of dynamical systems is proposed. On the subset of chaotic attractor in Euclidean space Rm a function z(m) is constructed. It defines a measure of topological instability of the attractor when enlarging state space dimension (Rm → Rm+1). The value of z(m) changes monotonously when enlarging m, but if m, ≤ m0 then z(m) does not depend on m. The computer confirmation of the theoretical results is presented. The investigation of digital electrocardiosignals using local-topological analysis of chaotic attractor trajectories is carried out.

Helena B. Minervina

Papers

Minimal attractor embedding dimension for discrete dynamic system based on state-space method

Minimal multiplicative complexity and fast restoration algorithm of digital signals and images

Fast algorithms for reduction a modulo polynomial and vandermonde transform using FFT

Distinguishing and recognition of pathological speech based on estimation of control parameter of chaotic attractor.

Restoration of dynamical systems attractors and estimation of their geometric characteristics into state-space