Abstract
Suprathreshold stochastic resonance (SSR) is a distinct form of stochastic resonance, which occurs in multilevel parallel threshold arrays with no requirements on signal strength. In the generic SSR model, an optimal weighted decoding scheme shows its superiority in minimizing the mean square error (MSE). In this study, we extend the proposed optimal weighted decoding scheme to more general input characteristics by combining a Kalman filter and a least mean square (LMS) recursive algorithm, wherein the weighted coefficients can be adaptively adjusted so as to minimize the MSE without complete knowledge of input statistics. We demonstrate that the optimal weighted decoding scheme based on the Kalman–LMS recursive algorithm is able to robustly decode the outputs from the system in which SSR is observed, even for complex situations where the signal and noise vary over time.
Highlights
Stochastic resonance in multi-threshold systems was initially investigated in [1], where the input signal is subthreshold
It is interesting to note that the above-mentioned decoding scheme using the Kalman–least mean square (LMS) recursive algorithm can be applied to an array composed of arbitrary nonlinear elements
We will explore two cases of input characteristics, i.e. stationary and non-stationary, to examine the mean square error (MSE) distortion performance of optimal weighted decoding scheme based on the Kalman– LMS recursive algorithm
Summary
Stochastic resonance in multi-threshold systems was initially investigated in [1], where the input signal is subthreshold. The concept of suprathreshold stochastic resonance (SSR) was introduced in multi-threshold systems [2,3,4]. In the seminal works of Stocks and co-workers [2,3,4], the nonlinearity in each element of the model is assumed to be a binary quantizer. Such threshold systems can be described as stochastic signal quantizers that have been analysed in terms of lossy source coding and quantization theory [14,15,16]. Our results show that under certain conditions the performance of the optimally weighted quantizer response is superior to that of the original unweighted arrays [17,18]
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