Proc. SPIE. 6600, Noise and Fluctuations in Circuits, Devices, and Materials
KEYWORDS: Target detection, Detection and tracking algorithms, Control systems, Laser stabilization, Microcontrollers, Error control coding, Signal detection, Pulsed laser operation, Stochastic processes, Laser systems engineering
We present a laser delay control system based on adaptive averaging which utilises the jitter noise of the laser
to stabilise the delay more precisely. The system contains delay lines to measure and control the laser delay and
a microcontroller that runs our control algorithm. The algorithm regulates the laser delay on the basis of the
average of detected delay values, wherein the steps with which the delay is varied and the averaging length are
chosen adaptively, depending on the distance from the target delay. Our complementary numerical simulations
show that the jitter of the laser may play a beneficial role here: the error of the delay has a distinct minimum
at a non-zero noise level. In a way similar to the dithering principle applied in analogue-to-digital conversion,
averaging the noise-modulated detection instances yields a precision in setting the delay that is well beyond the
resolution provided by detection time windows, and is close to the theoretical limit determined by the step size
of the delay line we applied.
Proc. SPIE. 5845, Noise in Complex Systems and Stochastic Dynamics III
KEYWORDS: Signal to noise ratio, Digital signal processing, Digital filtering, Interference (communication), Signal processing, Information theory, Signal analyzers, Detection theory, Stochastic processes, Systems modeling
We consider two bistable systems, the double-well potential and the Schmitt-trigger, and examine whether the stochastic resonance occurring in these systems may produce output signals less noisy than the input. We apply cross-spectrum and cross-correlation based generalised measures to quantify noise content in the input and output, which enables us to use aperiodic or random sequences as input signals. We show that input-output signal improvement occurs even for these types of input.
KEYWORDS: Human-machine interfaces, Optical filters, Digital signal processing, Clocks, Digital filtering, Interference (communication), Numerical simulations, Control systems, Signal processing, Analog filtering
1/f noise is present in several natural and artificial systems, and even though it was discovered several years ago, it is still not completely understood. Due to the lack of an universal model, the main methods of investigating a system where 1/f noise is present are numerical simulations and real measurements. The second method can lead to more adequate results, since it is free from numerical artifacts. In the case of real measurements, we need reliable, wide-band noise generators. Many ways of generating noise are known; most of them have several limitations on the frequency bandwidth or on spectral properties. We wanted to create a device which is easy to use, which can generate any kind of 1/fα noise and whose bandwidth is wide enough to make our investigations. We used a DSP (ADSP2181) to numerically generate the desired noise, and a D/A converter to convert it to an analogue signal. The noise generation algorithm was based on the known method of filtering a Gaussian white noise with a series of first-order digital filters. We enhanced this method to get a better spectral shape and to compensate for the side effects of the digital-to-analogue conversion.
We studied two non-dynamical stochastic resonators, the level-crossing detector (LCD) and the Schmitt trigger, driven by a periodic pulse train plus 1/fκ-type coloured noises, and we have examined the dependence of the SNR gain maxima on the spectral exponent κ of the random excitation. We have found, in accordance with what previous studies predict for the output SNR in non-dynamical systems, that the correlation only degrades the SNR gain: greater noise amplitudes are required for the gain to peak if we increase the spectral exponent. We have observed that the two different kinds of SNR gains we used, the narrow-band and the wide-band gain, describe the behaviour of these systems rather differently: while the maximum of the wide-band gain decreases monotonically with the spectral exponent κ, the narrow-band gain is optimal at a certain κ. We have also surveyed how the value of the optimal κ depends on the frequency conditions.
In the last few years, several papers have been published that reported high signal-to-noise ratio (SNR) gains in systems showing stochastic resonance. In the present work, we consider a level-crossing detector driven by a periodic pulse train plus Gaussian band-limited white noise, and provide analytical formulae for the dependence of the SNR gain on the relevant parameters of the input (the amplitude and the cut-off frequency of noise, the duty cycle of the deterministic signal and the distance between the threshold and the amplitude of the signal). Our results are valid in the input parameter range wherein high gains are expected, that is, wherein the probabilities of missing and, especially, extra output peaks are very low. We also include numerical simulation results that support the theory, along with illustrations of cases which are outside the validity of our theory.
It has been recently shown that the amplitude truncation of Gaussian 1/f noise does not change the shape of the power spectral density under rather general conditions, including the case when a Heaviside transformation results in a dichotomous noise. This invariance of 1/f noise seems to be an important addition to the knowledge about this kind of noise and may be promising in understanding dichotomous 1/f noise, noise-driven switching and stepping. Probably the most important application is the explanation of ion channel currents in biomembranes. In this work we have extended our investigations, especially concerning the level crossing properties of 1/f noises. We determined the level crossing time statistics for 1/fα noises (0<α<2) and found an empirical formula for the level-crossing time distribution. The correlation properties of successive level crossing intervals are also explored by measurements and numerical simulations and it is shown that the case α=1 is unique in the range from 0 to 2. These time structure related additions to the knowledge about 1/f noise further emphasize the uniqueness of this kind of noise. These results may help to understand 1/f noises better and are strongly relevant to 1/f noise driven switching, dichotomous noises such as the case of ion channel current fluctuations.