Optimal signal-to-noise ratio in stochastic time-delayed bistable systems

AbstractThe occurrence of stochastic resonance in bistable systems undergoing anomalous diffusions, which arise from density-dependent fluctuations, is investigated with an emphasis on the analytical formulation of the problem as well as a possible analytical derivation of key quantifiers of stochastic resonance. The nonlinear Fokker–Planck equation describing the system dynamics, together with the corresponding Ito–Langevin equation, is formulated. In the linear response regime, analytical expressions of the spectral amplification, of the signal-to-noise ratio and of the hysteresis loop area are derived as quantifiers of stochastic resonance. These quantifiers are found to be strongly dependent on the parameters controlling the type of diffusion; in particular, the peak characterizing the signal-to-noise ratio occurs only in close ranges of parameters. Results introduce the relevant information that, taking into consideration the interactions of anomalous diffusive systems with a periodic signal, can provide a better understanding of the physics of stochastic resonance in bistable systems driven by periodic forces.

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Geometric Approach to Analytic Marginalisation of the Likelihood Ratio for Continuous Gravitational Wave Searches

Universe ◽

10.3390/universe7060174 ◽

2021 ◽

Vol 7 (6) ◽

pp. 174

Author(s):

Karl Wette

Keyword(s):

Gravitational Wave ◽

Likelihood Ratio ◽

Signal To Noise Ratio ◽

Geometric Approach ◽

The Other ◽

Efficient Computation ◽

Likelihood Ratios ◽

Signal To Noise ◽

Noise Ratio ◽

Optimal Signal

The likelihood ratio for a continuous gravitational wave signal is viewed geometrically as a function of the orientation of two vectors; one representing the optimal signal-to-noise ratio, and the other representing the maximised likelihood ratio or F-statistic. Analytic marginalisation over the angle between the vectors yields a marginalised likelihood ratio, which is a function of the F-statistic. Further analytic marginalisation over the optimal signal-to-noise ratio is explored using different choices of prior. Monte-Carlo simulations show that the marginalised likelihood ratios had identical detection power to the F-statistic. This approach demonstrates a route to viewing the F-statistic in a Bayesian context, while retaining the advantages of its efficient computation.

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Optimal signal-to-noise ratio for silicon nanowire biochemical sensors

Applied Physics Letters ◽

10.1063/1.3608155 ◽

2011 ◽

Vol 98 (26) ◽

pp. 264107 ◽

Cited By ~ 76

Author(s):

Nitin K. Rajan ◽

David A. Routenberg ◽

Mark A. Reed

Keyword(s):

Signal To Noise Ratio ◽

Silicon Nanowire ◽

Signal To Noise ◽

Biochemical Sensors ◽

Noise Ratio ◽

Optimal Signal

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Mass Sensitivity or Gravimetric Satellites

10.5194/gstm2020-19 ◽

2020 ◽

Author(s):

Robert Spero

Keyword(s):

Signal To Noise Ratio ◽

Satellite Tracking ◽

Point Mass ◽

Laser Ranging ◽

Signal To Noise ◽

Orbital Parameters ◽

The Earth ◽

Noise Ratio ◽

Optimal Signal ◽

Instrument Sensitivity

A point mass on the surface of the Earth gives the highest frequency content for orbiting gravimetry, with&#160; the maximum frequency for gradiometers or satellite-to-satellite tracking determined by orbital altitude.&#160; Frequency-domain expressions are found for&#160; measurements of a point-like source on the surface of the Earth.&#160; The response of orbiting gradiometers such as GOCE and satellite-to-satellite tracking missions such as GRACE-FO are compared. The optimal signal-to-noise ratio as a function&#160; of noise in the measurement apparatus is computed, and from that the minimum detectable mass is inferred. The point mass magnitude that gives signal-to-noise ratio = 3 is for GOCE&#160; M_3=200 Gton and&#160; for the laser ranging interferometer measurement on GRACE-FO&#160; M_3= 0.5 Gton. For the laser ranging interferometer measurement, the optimal filter for detecting point-like masses has a passband of 1 to 20 mHz,&#160; differing from the 0.3 to 20 mHz admittance filter of Ghobadi-Far et al. (2018), which is not specialized for detecting point-like masses. M_3 for&#160; future GRACE-like missions with different orbital parameters and improved instrument sensitivity is explored, and the optimum spacecraft separation is found.

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Proposition of deposition and bias conditions for optimal signal-to-noise-ratio in resistor- and FET-type gas sensors

Nanoscale ◽

10.1039/d0nr04406g ◽

2020 ◽

Vol 12 (38) ◽

pp. 19768-19775 ◽

Cited By ~ 1

Author(s):

Wonjun Shin ◽

Gyuweon Jung ◽

Seongbin Hong ◽

Yujeong Jeong ◽

Jinwoo Park ◽

...

Keyword(s):

Gas Sensors ◽

Signal To Noise Ratio ◽

Optimal Performance ◽

Signal To Noise ◽

Noise Ratio ◽

Optimal Signal

Response alone cannot fully evaluate the performance of sensors, and the signal-to-noise-ratio should additionally be considered to design gas sensors with optimal performance.

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STOCHASTIC RESONANCE IN BISTABLE AND EXCITABLE SYSTEMS: EFFECT OF NON-GAUSSIAN NOISES

Fluctuation and Noise Letters ◽

10.1142/s0219477503001440 ◽

2003 ◽

Vol 03 (04) ◽

pp. L365-L371 ◽

Cited By ~ 23

Author(s):

M. A. FUENTES ◽

C. J. TESSONE ◽

H. S. WIO ◽

R. TORAL

Keyword(s):

Stochastic Resonance ◽

Gaussian Noise ◽

Signal To Noise Ratio ◽

Signal To Noise ◽

Excitable System ◽

Ratio Curve ◽

Bistable Systems ◽

Excitable Systems ◽

Noise Ratio ◽

Non Gaussian

We analyze stochastic resonance in systems driven by non-Gaussian noises. For the bistable double well we compare the signal-to-noise ratio resulting from numerical simulations with some quasi-analytical results predicted by a consistent Markovian approximation in the case of a colored non-Gaussian noise. We also study the FitzHugh–Nagumo excitable system in the presence of the same noise. In both systems, we find that, as the noise departs from Gaussian behavior, there is a regime (different for the excitable and the bistable systems) in which there is a notable robustness against noise tuning since the signal-to-noise ratio curve broadens and becomes less sensitive to the actual value of the noise intensity. We also compare our results with some experiments in sensory systems.

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The robustness of the differential quantizer in the case of the variable signal to noise ratio

Serbian Journal of Electrical Engineering ◽

10.2298/sjee1701149c ◽

2017 ◽

Vol 14 (1) ◽

pp. 149-160

Author(s):

Lazar Cokic ◽

Aleksandra Marjanovic ◽

Sanja Vujnovic ◽

Zeljko Djurovic

Keyword(s):

Speech Signal ◽

Signal To Noise Ratio ◽

Noise Signal ◽

Fixed Number ◽

Signal To Noise ◽

Input And Output ◽

Noise Ratio ◽

The Difference ◽

Optimal Signal ◽

Theoretical Overview

In this paper a short theoretical overview of differential quantizer and its implementations is given. Afterward, the effect of the order of prediction in differential quantizer and the effect of the difference in order of predictor in the input and output of differential quantizer is analyzed. Then it was proceeded with the examination of the robustness of the differential quantizer in the case in which a noise signal is brought to the input of the differential quantizer, instead of the clean speech signal. The analysis was conducted with a uniform distribution, as well as the noise with the gaussian distribution, and the obtained results were adequately commented on. Also, experimentally a limit was set which refers to the intensity of the noise and still enable results which are better that a regular uniform quantizer. The whole analysis is done by using the fixed number of bits in quantization, i.e. 12-bit quantizer is used in all the implementations of differential quantizer. In the conclusion of this paper there is a discussion about the possibility of implementing a differential quantizer which will be able to recognize which noise attacks the system, and in addition to that, in what form it adapts its coefficients so that it at any moment acquires the optimal signal to noise ratio.

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