Study of vibrational resonance in nonlinear signal processing

Abstract

Vibrational resonance (VR) intentionally applies high-frequency periodic vibrations to a nonlinear system, in order to obtain enhanced efficiency for a number of information processing tasks. Note that VR is analogous to stochastic resonance where enhanced processing is sought via purposeful addition of a random noise instead of deterministic high-frequency vibrations. Comparatively, due to its ease of implementation, VR provides a valuable approach for nonlinear signal processing, through detailed modalities that are still under investigation. In this paper, VR is investigated in arrays of nonlinear processing devices, where a range of high-frequency sinusoidal vibrations of the same amplitude at different frequencies are injected and shown capable of enhancing the efficiency for estimating unknown signal parameters or for detecting weak signals in noise. In addition, it is observed that high-frequency vibrations with differing frequencies can be considered, at the sampling times, as independent random variables. This property allows us here to develop a probabilistic analysis—much like in stochastic resonance—and to obtain a theoretical basis for the VR effect and its optimization for signal processing. These results provide additional insight for controlling the capabilities of VR for nonlinear signal processing. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

Vibrational and stochastic resonances in driven nonlinear systems

“…Construction of logic gates exploiting resonance phenomena in nonlinear systems by Murali et al [22]. Study of vibrational resonance in nonlinear signal processing by Pan et al [21]. …”

“…Finally, Pan et al [21] discuss the application of vibrational resonance to nonlinear signal processing. They report scenarios in which VR can be optimized for the improved performance of nonlinear sensors by optimally tuning the amplitude of high-frequency periodic vibrations injected into the sensor arrays.…”

“…Some of the recent developments of VR and SR are fascinating, and include logical, entropic, anti-and ghost-VR/SR. Moreover, the applications of VR have been gaining momentum in diverse disciplines and a wide range of its occurrences and applications relating to communications systems, signal output identification, filtering, optimization and control, separation and extraction, and a host of advanced and promising technological processes for improved efficiency and operating conditions, have now been reported [1,[16][17][18][19][20][21][22][23].…”

Vibrational resonance by using a real-time scale transformation method

“…Moreover, VR can control SR to achieve better signal enhancement [6]. This phenomenon has attracted considerable interest of many scholars and has been applied to many fields, including nonlinear dynamics [7], liquid crystals [8], biology [9][10][11], optics systems [12,13], nano-electromechanical resonators [14], ecological systems [15], image processing [16,17], signal processing [18][19][20][21], etc.…”

Effect of Modulated Signals on Vibrational Resonance in a Harmonically Trapped Potential System

“…Various types of resonance can be realized in nonlinear systems such as the stochastic resonance [1,2], coherence resonance [3,4], auto resonance [5,6], ghost resonance [7][8][9], chaos resonance [10,11], parametric resonance [12,13] and vibrational resonance [14][15][16][17][18]. The present paper is concerned with vibrational resonance.…”