Discrete time model of self-oscillations with spectral line widening

Abstract

An algorithm for generating quasi-harmonic self-oscillations with a uniformly widened spectral line is presented. The algorithm is based on the equation of motion of the Thomson-type DT-oscillator, which introduced a random effect in the form of band-pass white noise. Two types of effects are implemented: additive and parametric. Spectral characteristics of generated self-oscillations were analyzed by numerical experiment. The additive algorithm is shown to generate self-oscillations with amplitude-frequency fluctuations. Frequency fluctuations set the Lorentz (resonant) shape of the central part of the self-oscillation power spectrum, amplitude fluctuations form a noise pedestal of the spectral line. Based on the analysis of statistical characteristics of fluctuations in the frequency of the DT-oscillator with additive noise impact, a parametric algorithm for generating quasi-harmonic self-oscillations is proposed. In it, the resonance frequency of the oscillating system of the Thomson DT-oscillator is subject to random perturbations. The results of numerical experiments with generators of quasi-harmonic oscillations are given.

Keywords

• self-oscillation
• spectral line
• uniform widening
• frequency fluctuations
• discrete time
• difference equation of self-oscillations
• random perturbations