scholarly journals NON-LINEAR OSCILLATORS IN DISCRETE TIME: ANALYSIS AND SYNTHESIS OF DYNAMIC SYSTEMS

2021 ◽  
Author(s):  
Valeriy Zaycev ◽  
Alalvan Kasim
Keyword(s):  
Discrete Time ◽  
Dynamic Systems ◽  
Digital Filters ◽  
Time Analysis ◽  
Radio System ◽  
Oscillating Systems ◽  
Non Linear ◽  
Analysis And Synthesis

A physically justified method of synthesis of nonlinear oscillating systems oscillating in discrete time (DT) is proposed. Synthesized dynamic systems are used as nonlinear discrete (digital) filters and basic models of radio system elements.

scholarly journals Quasi-harmonic self-oscillations in discrete time: analysis and synthesis of dynamic systems

2022 ◽  
Vol 24 (4) ◽  
pp. 19-24
Author(s):  
Valery V. Zaitsev ◽  
Alexander V. Karlov
Keyword(s):  
Discrete Time ◽  
Oscillatory System ◽  
Discrete Models ◽  
Van Der Pol Oscillator ◽  
Time Analysis ◽  
Van Der Pol ◽  
Analog System ◽  
Analysis And Synthesis ◽  
The Difference ◽  
System Prototype

For sampling of time in a differential equation of movement of Thomson type oscillator (generator) it is offered to use a combination of the numerical method of finite differences and an asymptotic method of the slowl-changing amplitudes. The difference approximations of temporal derivatives are selected so that, first, to save conservatism and natural frequency of the linear circuit of self-oscillatory system in the discrete time. Secondly, coincidence of the difference shortened equation for the complex amplitude of self-oscillations in the discrete time with Eulers approximation of the shortened equation for amplitude of self-oscillations in analog system prototype is required. It is shown that realization of such approach allows to create discrete mapping of the van der Pol oscillator and a number of mappings of Thomson type oscillators. The adequacy of discrete models to analog prototypes is confirmed with also numerical experiment.

The digital function filters – algorithms and applications

2013 ◽  
Vol 61 (2) ◽  
pp. 371-377
Author(s):  
M. Siwczyński ◽  
A. Drwal ◽  
S. Żaba
Keyword(s):  
Digital Filters ◽  
Phase Shifters ◽  
Square Root ◽  
Real Power ◽  
The Real ◽  
Distributed Parameters ◽  
Digital Modeling ◽  
Analysis And Synthesis ◽  
Basic Functions ◽  
Recursive Formulas

Abstract The simple digital filters are not sufficient for digital modeling of systems with distributed parameters. It is necessary to apply more complex digital filters. In this work, a set of filters, called the digital function filters, is proposed. It consists of digital filters, which are obtained from causal and stable filters through some function transformation. In this paper, for several basic functions: exponential, logarithm, square root and the real power of input filter, the recursive algorithms of the digital function filters have been determined The digital function filters of exponential type can be obtained from direct recursive formulas. Whereas, the other function filters, such as the logarithm, the square root and the real power, require using the implicit recursive formulas. Some applications of the digital function filters for the analysis and synthesis of systems with lumped and distributed parameters (a long line, phase shifters, infinite ladder circuits) are given as well.

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