New Type of Spectral Nonlinear Resonance Enhances Identification of Weak Signals

Abstract

Some nonlinear systems possess innate capabilities of enhancing weak signal transmissions through a unique process called Stochastic Resonance (SR). However, existing SR mechanism suffers limited signal enhancement from inappropriate entraining signals. Here we propose a new and effective implementation, resulting in a new type of spectral resonance similar to SR but capable of achieving orders of magnitude higher signal enhancement than previously reported. By employing entraining frequency in the range of the weak signal, strong spectral resonances can be induced to facilitate nonlinear modulations and intermodulations, thereby strengthening the weak signal. The underlying physical mechanism governing the behavior of spectral resonances is examined, revealing the inherent advantages of the proposed spectral resonances over the existing implementation of SR. Wide range of parameters have been found for the optimal enhancement of any given weak signal and an analytical method is established to estimate these required parameters. A reliable algorithm is also developed for the identifications of weak signals using signal processing techniques. The present work can significantly improve existing SR performances and can have profound practical applications where SR is currently employed for its inherent technological advantages.

Figure 1

Fundamental mechanism of SR and signal extraction.

Figure 2

Current performances of SR with limited signal enhancement. (a) Signal-to-noise ratios from ref., results of experiment with crayfish mechanoreceptors (filled squares ▪) compared to the electronic Fitzhugh-Nagumo simulation (diamonds ◆) and the theoretical results (solid curve ^__). (b,c) Signal magnification factors with entraining signal being high frequency sinusoid, numerically reproduced from ref..

Figure 3

Magnification factors showing strong spectral resonances at different weak input and entraining signal parameters. (a) A = 0.001, ω = 0.17 and Ω = 0.10. (b) A = 0.0005, ω = 0.11 and Ω = 0.17. (c) A = 0.0005, ω = 0.17 and Ω = 0.19. (d) A = 0.001, ω = 0.07 and Ω = 0.13 (all parameters are non-dimensionalized).

Figure 4

Periodic response under sinusoidal entraining input and strong spectral resonance under combined signal and entraining inputs. (a) Entraining signal. (b) Response signal. (c) Spectrum of response signal in (b). (d) Combined signal and entrain inputs. (e) Response of stochastic resonance. (f) Spectrum of response signal in (e).

Figure 5

Magnification factors computed with different magnitudes of weak input signals, showing self-scaling characteristics of strong spectral resonances. (a) A = 0.025. (b) A = 0.005. (c) A = 0.001. (d) A = 0.0002.

Figure 6

Linearized characteristics of spectral resonator and the prediction of optimal entraining parameters. (a) Transfer function of the linearized bistable system. (b) Comparison of linearly predicted and actual responses showing strong spectral resonance region. c Predicted optimal entraining parameters. (d) Numerically computed entraining parameters at specific weak signal input of A = 0.001 and ω = 0.07.

Figure 7

Identification of signal frequency. (a) Time response of spectral resonance. (b) Spectrum of time response in (a) showing prominent frequencies as possible signal frequency. (c) Time response of spectral resonance when entraining signal changed to one of the suspected but incorrect frequencies. (d) Spectrum of time response in (c). (e) Time response of a periodic signal when entraining signal changed to one of the suspected but correct frequencies. (f) Spectrum of time response in (e).

Figure 8

Effect of noise on spectral resonance. (a) Weak input signal contaminated by substantial random noise. (b) Comparison of spectral resonance strengths with and without noise. (c) Time response of spectral resonance with input contaminated by noise showing increased irregularity in wave form. (d) Spectrum of time response in (c) showing low frequency noise spectrum.

Figure 9

Vibration response and spectrum with random noise but no weak signal input. (a) Vibration response. (b) Response spectrum showing all harmonic components and noise contamination.

Figure 10

Asymmetric response showing all harmonics and DC components. (a) Vibration response. (b) Response spectrum.

Figure 11

Asymmetric response and its response spectrum from dual-tone input excitation. (a) Vibration response. (b) Response spectrum.