Input Noise Amplitude Research Articles

Coherence Resonance in a Schmitt-Trigger Inverter with Delayed Feedback

We study the coherence resonance in a Schmitt-trigger inverter with a delayed feedback loop. The output of the system is analyzed changing the input noise amplitude and the delay time of the feedback loop. The regularity of the output shows resonance-like dependence on the input noise amplitude. At the optimum input noise amplitude, the system outputs well-regulated rectangular wave, and corresponding peaks in the output spectrum become large and sharp. This optimization of the system is accomplished when the period of the output rectangular wave almost coincides with the feedback delay time.

Theoretical and experimental study of stochastic effects on polarization rotation in a vectorial bistable laser

We investigate the two-dimensional optical rotor of a weakly modulated vectorial bistable laser submitted to a single or multiple stochastic perturbations. In the Langevin-type equation of the rotor the role of an even or odd input forcing function on the system dynamics is isolated. Through these two inputs of optical and magnetic natures we verify that the stochastic resonance exists only when the periodic modulation acts on the even parity optical input. When two mutually correlated noises are simultaneously submitted to the input functions of opposite parities, we find a critical regime of the noise interplay whereby one stable state becomes noise-free. In this case, the residence time of the light vector in the noise-free state diverges which leads to a collapse of the output signal-to-noise ratio. But, in this critical regime also obtained when one noise drives both the even and odd functions, if the system symmetry is broken through an independent lever control, we can recover the switching cycle due to a new response mechanism, namely, the dual stochastic response, with a specific output signal-to-noise ratio expression. Both the theoretical analysis and the experiment show that the signal-to-noise ratio now displays a robust behavior for a large rangemore » of the input noise amplitude, and a plateau with respect to the input signal amplitude. Furthermore, we isolate an original signature of this synchronization mechanism in the residence-time distribution leading to a broadband forcing frequency range. These noise interplay effects in a double well potential are of generic nature and could be found in other nonlinear systems.« less

Information gain in an optical bistable system by stochastic resonance

We have shown an experimental demonstration of information gain due to the stochastic resonance in an optical bistable system, that is, information hidden in the input wave form appears in the output of a nonlinear system when the input noise amplitude is adequate. The optical bistable system is a hybrid type comprising a LiNbO3 crystal with an electric feedback loop, and the input of the system is the sum of a binary bit series and a Gaussian colored noise. The information gain is proved to be prominent when the noise cutoff frequency is larger than the bit rate.

How much power does neural signal propagation need?

Two well known, biologically inspired non-dynamical models of stochastic resonance, the threshold-crossing model and the fluctuating rate model, are analyzed in terms of channel information capacity and dissipation of energy necessary for small-signal transduction. Using analogies to spike propagation in neurons we postulate the average output pulse rate as a measure of dissipation. The dissipation increases monotonically with the input noise. We find that for small dissipation both models give a close to linear dependence of the channel information capacity on dissipation. In both models the channel information capacity, as a function of dissipation, has a maximum at input noise amplitude that is different from that in the standard signal-to-noise ratio versus input noise plot. Though a direct comparison is not straightforward, for small signals the threshold model gives appreciably higher density of information per dissipation than the exponential fluctuating rate model. We show that a formal introduction of cooperativity in the rate fluctuating model permits us to imitate the response function of the threshold model and to enhance performance. This finding may have direct relevance to real neural spike generation where, due to a strong positive feedback, the ion channel currents add up in a synchronized way.

Signal-to-Noise Ratio of Arbitrary Power-Series Nonlinear Amplifier

A general analysis of the effect of an arbitrary power-series nonlinear amplifier followed by a coherent mixing device on signal-to-noise ratio (SNR) is performed. An expression is derived for the improvement factor which is defined as the logarithm of the ratio of the output SNR to the input SNR. This expression is applicable to the coherent amplitude detector and phase locked loop as well as noncoherent amplifier by appropriate selections of the detection angle. Moreover, the improvement factor can be obtained for noise with an arbitrary amplitude distribution. To demonstrate the applicability of this analysis, the improvement factors of the nonlinear amplifiers such as a power-law amplifier and a power-series amplifier with positive and negative discriminations are numerically calculated for the cases where the input noise amplitude distributions are Rician and triangular.

Signal-to-Noise Ratio of the nth Law Amplifier for Non-Gaussian Noise

The effects of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> th law amplifier on signal-to-noise ratio has not been represented as a function of the input signal-to-noise ratio when the input of the nonlinear device contains nonGaussian noise. In this paper, we analyze these effects and determine the improvement factor represented by the ratio of the output SNR to the input SNR. The results are illustrated by the calculation of the improvement factor for the cases where the input noise amplitude distributions are the uniform distribution, the triangle distribution, and the Rician distribution.

Unlock Characteristics of the Optimum Type II Phase-Locked Loop

This paper describes a study of the statistical unlock characteristics of the commonly used optimum type II phase-locked loop taking into account the nonlinearity of the phase detector. The unlock behavior is investigated by simulating the loop with random noise inputs on a digital computer. A criterion of loop unlock is evolved using the phase portrait of the loop and consists of crossing of separatrices by loop error and a measure of loop error rate. Approximately 100 statistically independent trials were made for each of a number of combinations of initial phase error, initial frequency error, and input noise amplitude. From these computer runs, cumulative frequency distributions of unlock time and curves of mean time to unlock were obtained and are presented. The phase portrait of the loop containing time information also is included in the paper, along with a plot of capture characteristics for large initial frequency offsets.