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Volumn 57, Issue 6, 1998, Pages 6470-6479

Evaluation of stochastic-resonance-based detectors of weak harmonic signals in additive white Gaussian noise

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EID: 0000945802     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.57.6470     Document Type: Article
Times cited : (111)

References (154)
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    • SR occurs in multistable systems as well 3, which exhibit several maxima in the output SNR curve vs noise
    • SR occurs in multistable systems as well 3, which exhibit several maxima in the output SNR curve vs noise.
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    • Bistable systems with multiplicative noise with or without additive noise have been shown to exhibit SR in 567
    • Bistable systems with multiplicative noise with or without additive noise have been shown to exhibit SR in 567.
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    • Extensions of the SR concept to transient, wideband signals have been discussed in terms of Kullback’s 9 and Shannon’s (mutual) input-output entropy 10. The SR-enhanced channel capacity of a simple binary channel with level crossing detector has been studied in 11
    • Extensions of the SR concept to transient, wideband signals have been discussed in terms of Kullback’s 9 and Shannon’s (mutual) input-output entropy 10. The SR-enhanced channel capacity of a simple binary channel with level crossing detector has been studied in 11.
  • 12
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    • An extension to colored (correlated, Gaussian) noise is possible 13 and has been discussed by several authors 14151617. Also, SR in bistable systems affected by 1/f 18, narrow-band 19, monochromatic 20, and chaos-related 21 noises has been studied
    • An extension to colored (correlated, Gaussian) noise is possible 13 and has been discussed by several authors 14151617. Also, SR in bistable systems affected by 1/f 18, narrow-band 19, monochromatic 20, and chaos-related 21 noises has been studied.
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    • SR in multithreshold devices 30 is synonomous with dithering in analog-to-digital converters 31.
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    • It has been argued that these systems could describe biomembrane specific-ion channels 35
    • It has been argued that these systems could describe biomembrane specific-ion channels 35.
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    • As an example, the SNR enhancement reported in 2728 occurs at relatively large input SNR values (D≪A, in the notation of 2728), well within the capabilities of standard-detection techniques, and is thus almost irrelevant from the viewpoint of signal detection
    • As an example, the SNR enhancement reported in 2728 occurs at relatively large input SNR values (D≪A, in the notation of 2728), well within the capabilities of standard-detection techniques, and is thus almost irrelevant from the viewpoint of signal detection.
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    • An infinite output-SNR system has been described in 112.
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    • nonlinear systems there is no clear-cut definition of the noise background (no superposition). In 114 the (discrete) output spectral amplitude is used to estimate the output power spectral density (PSD). The noise power within the (known) spectral bin of the signal is estimated by taking the (average) of the total (signal and noise) power several bins away. The signal power is then obtained by subtracting the noise power from the total (signal and noise) power in the signal bin
    • In nonlinear systems there is no clear-cut definition of the noise background (no superposition). In 114 the (discrete) output spectral amplitude is used to estimate the output power spectral density (PSD). The noise power within the (known) spectral bin of the signal is estimated by taking the (average) of the total (signal and noise) power several bins away. The signal power is then obtained by subtracting the noise power from the total (signal and noise) power in the signal bin.
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    • The performance loss was found to decrease by increasing the number of (coupled) nonlinear elements 114
    • The performance loss was found to decrease by increasing the number of (coupled) nonlinear elements 114.
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    • Other choices are possible. An alternative definition of SR in terms of residence-time distributions was introduced in 120. This definition seems more general since it covers cases where no PDF simmetry breaking occurs 121 (e.g., SR in linear systems with multiplicative noise 41
    • Other choices are possible. An alternative definition of SR in terms of residence-time distributions was introduced in 120. This definition seems more general since it covers cases where no PDF simmetry breaking occurs 121 (e.g., SR in linear systems with multiplicative noise 41).
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    • LCDs will not be discussed here, since, despite a renewed SR-related popularity, they are pretty old 123 and have been well understood since the early 1960s (see, e.g., 124), including the study of jitter (zero-crossing noise), which has been curiously overlooked in many recent papers on the subject. LCD parameter optimization has been discussed in 125
    • LCDs will not be discussed here, since, despite a renewed SR-related popularity, they are pretty old 123 and have been well understood since the early 1960s (see, e.g., 124), including the study of jitter (zero-crossing noise), which has been curiously overlooked in many recent papers on the subject. LCD parameter optimization has been discussed in 125.
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    • Several techniques have been envisaged to solve Eq. (5). The problem was recast in 129 in terms of a master equation for the stable-well populations, which was solved under the weak-signal and adiabatic approximations. The original master-equation adiabatic approach 129 was subsequently extended to the nonlinear (and/or weak noise) case in 130131. Time-dependent perturbation-expansion-based approximate solutions were worked out in 132133. A rigorous approach, based on Floquet theory, was developed by P. Jung and co-workers 134135136. More recently, an efficient path-integral solution technique was applied in 106. An exact solution of Eq. (5) is available for the special case of a piecewise constant (rectangular well) potential 137138
    • Several techniques have been envisaged to solve Eq. (5). The problem was recast in 129 in terms of a master equation for the stable-well populations, which was solved under the weak-signal and adiabatic approximations. The original master-equation adiabatic approach 129 was subsequently extended to the nonlinear (and/or weak noise) case in 130131. Time-dependent perturbation-expansion-based approximate solutions were worked out in 132133. A rigorous approach, based on Floquet theory, was developed by P. Jung and co-workers 134135136. More recently, an efficient path-integral solution technique was applied in 106. An exact solution of Eq. (5) is available for the special case of a piecewise constant (rectangular well) potential 137138.
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    • The [formula presented] estimate (7) is exactly twice that introduced by Benzi 1. The latter, however, provides a good approximation only in the high-barrier asymptotic limit [formula presented] For finite ε, the first-order correction is available 140. It can be verified that Eq. (7) provides a good trade-off between ease and accuracy in the (finite) potential barrier height range of interest
    • The TK estimate (7) is exactly twice that introduced by Benzi 1. The latter, however, provides a good approximation only in the high-barrier asymptotic limit ε→0. For finite ε, the first-order correction is available 140. It can be verified that Eq. (7) provides a good trade-off between ease and accuracy in the (finite) potential barrier height range of interest.
  • 150
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    • the presence of noise only, the random variables [formula presented] have the same distribution as the [formula presented]
    • In the presence of noise only, the random variables xk have the same distribution as the x(tk).
  • 151
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    • We checked via numerical simulations that the correlation is negligible in the parameter range of interest
    • We checked via numerical simulations that the correlation is negligible in the parameter range of interest.
  • 154
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    • L. Gammaitoni et al., http://www.pg.infn.it.sr
    • L. Gammaitoni et al., http://www.pg.infn.it.sr


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.