Study of vibrational resonance in nonlinear signal processing

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)'.

Automated summary

VR intentionally introduces high-frequency periodic vibrations to nonlinear systems to enhance efficiency in information processing tasks. Unlike stochastic resonance which adds random noise, VR is advantageous due to its ease of implementation and provides valuable insights for nonlinear signal processing through detailed modalities still under investigation. By injecting a range of high-frequency sinusoidal vibrations of the same amplitude at different frequencies, VR can enhance efficiency in estimating unknown signal parameters or detecting weak signals in noise. Additionally, the ability to consider high-frequency vibrations with differing frequencies as independent random variables at sampling times allows for probabilistic analysis similar to stochastic resonance, providing a theoretical basis for optimizing the VR effect in signal processing.