Topic

# Stochastic resonance

About: Stochastic resonance is a(n) research topic. Over the lifetime, 5170 publication(s) have been published within this topic receiving 103071 citation(s).

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24 Mar 1975TL;DR: It is shown that in treating periodic interference the adaptive noise canceller acts as a notch filter with narrow bandwidth, infinite null, and the capability of tracking the exact frequency of the interference; in this case the canceller behaves as a linear, time-invariant system, with the adaptive filter converging on a dynamic rather than a static solution.

Abstract: This paper describes the concept of adaptive noise cancelling, an alternative method of estimating signals corrupted by additive noise or interference. The method uses a "primary" input containing the corrupted signal and a "reference" input containing noise correlated in some unknown way with the primary noise. The reference input is adaptively filtered and subtracted from the primary input to obtain the signal estimate. Adaptive filtering before subtraction allows the treatment of inputs that are deterministic or stochastic, stationary or time variable. Wiener solutions are developed to describe asymptotic adaptive performance and output signal-to-noise ratio for stationary stochastic inputs, including single and multiple reference inputs. These solutions show that when the reference input is free of signal and certain other conditions are met noise in the primary input can be essentiany eliminated without signal distortion. It is further shown that in treating periodic interference the adaptive noise canceller acts as a notch filter with narrow bandwidth, infinite null, and the capability of tracking the exact frequency of the interference; in this case the canceller behaves as a linear, time-invariant system, with the adaptive filter converging on a dynamic rather than a static solution. Experimental results are presented that illustrate the usefulness of the adaptive noise cancelling technique in a variety of practical applications. These applications include the cancelling of various forms of periodic interference in electrocardiography, the cancelling of periodic interference in speech signals, and the cancelling of broad-band interference in the side-lobes of an antenna array. In further experiments it is shown that a sine wave and Gaussian noise can be separated by using a reference input that is a delayed version of the primary input. Suggested applications include the elimination of tape hum or turntable rumble during the playback of recorded broad-band signals and the automatic detection of very-low-level periodic signals masked by broad-band noise.

4,091 citations

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01 Jan 2008

Abstract: Stochastic resonance (SR) - a counter-intuitive phenomenon in which the signal due to a weak periodic force in a nonlinear system can be {\it enhanced} by the addition of external noise - is reviewed A theoretical approach based on linear response theory (LRT) is described It is pointed out that, although the LRT theory of SR is by definition restricted to the small signal limit, it possesses substantial advantages in terms of simplicity, generality and predictive power The application of LRT to overdamped motion in a bistable potential, the most commonly studied form of SR, is outlined Two new forms of SR, predicted on the basis of LRT and subsequently observed in analogue electronic experiments, are described

2,402 citations

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TL;DR: The theoretical and experimental foundations of the RASTA method are reviewed, the relationship with human auditory perception is discussed, the original method is extended to combinations of additive noise and convolutional noise, and an application is shown to speech enhancement.

Abstract: Performance of even the best current stochastic recognizers severely degrades in an unexpected communications environment. In some cases, the environmental effect can be modeled by a set of simple transformations and, in particular, by convolution with an environmental impulse response and the addition of some environmental noise. Often, the temporal properties of these environmental effects are quite different from the temporal properties of speech. We have been experimenting with filtering approaches that attempt to exploit these differences to produce robust representations for speech recognition and enhancement and have called this class of representations relative spectra (RASTA). In this paper, we review the theoretical and experimental foundations of the method, discuss the relationship with human auditory perception, and extend the original method to combinations of additive noise and convolutional noise. We discuss the relationship between RASTA features and the nature of the recognition models that are required and the relationship of these features to delta features and to cepstral mean subtraction. Finally, we show an application of the RASTA technique to speech enhancement. >

1,946 citations

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Abstract: We review the behavior of theoretical models of excitable systems driven by Gaussian white noise. We focus mainly on those general properties of such systems that are due to noise, and present several applications of our findings in biophysics and lasers. As prototypes of excitable stochastic dynamics we consider the FitzHugh–Nagumo and the leaky integrate-and-fire model, as well as cellular automata and phase models. In these systems, taken as individual units or as networks of globally or locally coupled elements, we study various phenomena due to noise, such as noise-induced oscillations, stochastic resonance, stochastic synchronization, noise-induced phase transitions and noise-induced pulse and spiral dynamics. Our approach is based on stochastic differential equations and their corresponding Fokker–Planck equations, treated by both analytical calculations and/or numerical simulations. We calculate and/or measure the rate and diffusion coefficient of the excitation process, as well as spectral quantities like power spectra and degree of coherence. Combined with a multiparametric bifurcation analysis of the corresponding cumulant equations, these approaches provide a comprehensive picture of the multifaceted dynamical behaviour of noisy excitable systems.

1,260 citations

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TL;DR: A detailed theoretical and numerical study of stochastic resonance, based on a rate equation approach, results in an equation for the output signal-to-noise ratio as a function of the rate at which noise induces hopping between the two states.

Abstract: The concept of stochastic resonance has been introduced previously to describe a curious phenomenon in bistable systems subject to both periodic and random forcing: an increase in the input noise can result in an improvement in the output signal-to-noise ratio. In this paper we present a detailed theoretical and numerical study of stochastic resonance, based on a rate equation approach. The main result is an equation for the output signal-to-noise ratio as a function of the rate at which noise induces hopping between the two states. The manner in which the input noise strength determines this hopping rate depends on the precise nature of the bistable system. For this reason, the theory is applied to two classes of bistable systems, the double-well (continuous) system and the two-state (discrete) system. The theory is tested in detail against digital simulations.

1,197 citations