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The discrete mapping of the oscillator witch nonlinear disspation and frequency detecting

Keywords:

V.V. Zaitsev – Ph.D. (Phis.-Math.), professor of the department of radiophysics, Samara State University. E-mail: zaitsev@samsu.ru
A.V. Karlov (jr.) – Ph.D. (Phis.-Math.), senior Research scientist, JSC «Concern «Automation». E-mail: KarlovAV@oao-avtomatika.ru


Modern nonlinear dynamics examines the evolution of dynamical systems in both continuous and discrete time. In the discrete-time nonlinear dynamics objects can serve as the basis for digital signal processing algorithms . The search for such systems should be considered as one of the problems of nonlinear dynamics of discrete time. In the present report for the synthesis of discrete time- oscillating system used impulse invariant together with parametric synthesis systems. Get a new version of Discrete Thomson type oscillator . As iterable map, it gives a simple algorithm to generate a time series . The analysis of the establishment of self-oscillations in the resulting system is given. The dynamics of the oscillations is typical for self-oscillation isochronous Thomson oscillator. This gives reason to use the suggested mapping algorithms for nonlinear filtering of discrete signals. An example of practical application of the proposed mapping algorithm detection of the Doppler frequency signal is given. The algorithm is based on modeling of processes in the ring phase-locked loop of discrete oscillator.
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