Stable Noise Research Articles

Gene Regulation: Stable Noise

Transcriptional regulation is noisy, yet despite this variability, embryonic development reproducibly generates form and function. Recent work demonstrates that patterns of transcriptional activity in embryos are stably inherited through mitosis. These observations have implications for how accuracy arises in development.

A Robust and Adaptive Line Echo Canceller

In the actual communication system, the line echo is a frequent problem, so the line echo canceller is necessary. Traditionally, the cancellers are designed according to line noises based on the Gaussian noise model. However, the noises do not obey the Gaussian distribution; therefore the performances of algorithms decrease, even cannot be used. In order to solve this problem, this paper proposes a line echo canceller based on alpha stable distribution model. The Method in this line echo canceller has Robust and Adaptive. Alpha stable distribution modeling impulse noise, and under the rule of minimum average <i>p</i> norm, adaptive time delay estimator offsets the echo. This method can not only effectively offset the line echo with the Gaussian noise, but also to have the effect of good to echo with impulse noise. Theoretical analysis and computer simulation experiments show that it is very kind of the line echo canceller. It is robust to impulse noises and adaptive to echo cancellation.

Status of the EU-project ROSANNE

ROSANNE is a collaborative project in the Seventh EU Framework Programme which aims at developing/harmonising measurement methods for skid resistance, noise emission and rolling resistance of road pavements as a preparation for standardization. To achieve this, the project is following the recommendations of key predecessor projects like TYROSAFE, HERMES, SILVIA, SILENCE and MIRIAM as well as considering the ongoing work in CEN and ISO groups. Work package 1 deals with skid resistance and aims at the harmonization of skid resistance measurement following the TYROSAFE Roadmap, by deriving conversion factors for friction indices based on similar groups of devices, namely longitudinal and sideways skid resistance measurement devices. During the first project year a first round robin test was carried out in Nantes, ten different devices participated to the test. The results of this test are collected in report D1.2 “Analysis of data from the first round of tests and initial development of the common scale”. Work package 2 is dealing with the pavement influence on road traffic noise emission: the main objective of this work package is to combine the existing measurement methods of SPB (ISO 11819-1) and CPX (ISO/DIS 11819-2) into a stable and reliable harmonised pavement noise emission characterisation method. The project is validating procedure incorporating correction mechanisms for temperature influence and investigating its potential use for noise calculation methods like the one proposed by the CNOSSOS-EU project. Work package 3 is dealing with rolling resistance, where the ROSANNE project is mainly building on the results obtained in the MIRIAM project and is considering standardized trailer measurements of rolling resistance coefficients of road surfaces. After a first report D3.1 “State of the art on rolling resistance measurement devices including draft standard outline” the following main report was produced “Parameters influencing rolling resistance and possible correction procedures”. In the frame of work package 4 the project is also exploring the potential for developments in the measurement of surface texture in order to find out parameters that better reflect the physical process of tyre/road interaction and that may improve the understanding of how the texture influences noise emission, skid resistance and rolling resistance. In addition to that this work package is also investigating the performance of reference tyres and pavements which are necessary for the measurement of all three road surface properties. The present paper summarizes the project status after the first 18 project months.

Spectrum Sensing Based on Nonparametric Autocorrelation in Wireless Communication Systems under Alpha Stable Noise

Cognitive radio is regarded as a core technology to support wireless information systems. Spectrum sensing is one of the key steps to achieve cognitive radio technology. To address this problem in the presence of Alpha stable noise in wireless communication systems, we propose a nonparametric autocorrelation method, which takes advantages of the characteristics of signal autocorrelation and noise nonstationarity. The autocorrelated signal is distinguished from Alpha stable noise. As a result, the proposed method is immune from noise uncertainty. Simulation results show the validity of the proposed method under Alpha stable noise, for example, impulsive noise in wireless information systems.

Highly sensitive pseudo-differential ac-nanocalorimeter for the study of the glass transition.

We present a nanocalorimeter designed for the measurement of the dynamic heat capacity of thin films. The microfabricated sensor, the thermal conditioning of the sensor, as well as the highly stable and low noise electronic chain allow measurements of the real and imaginary parts of the complex specific heat with a resolution Δ C/C of about 10(-5). The performances of this quasi-differential nanocalorimeter were tested on a model of polymeric glass-former, the polyvinyl acetate (PVAc). The high stability and low noise of the device are essential for accurate studies on non-equilibrium slow relaxing systems such as glasses.

Power-law statistics from nonlinear stochastic differential equations driven by Lévy stable noise

Anomalous diffusion occurring in complex dynamical systems can often be described by Langevin equations driven by Lévy stable noise. Nonlinear stochastic differential equations yielding power-law steady state distribution and generating signals with 1/f power spectral density can be generalized by replacing the Gaussian noise with a more general Lévy stable noise. These nonlinear equations can generate signals exhibiting anomalous diffusion: either sub-diffusion or super-diffusion. In a special case when stability index is α=2, we retain the equations with the Gaussian noise. We investigate numerically the frequency range where the spectrum has 1/f form and demonstrate that this frequency range depends on power-law exponent in steady state distribution as well as on the index of stability α. We expect that this generalization may be useful for describing 1/f fluctuations in the complex systems exhibiting anomalous diffusion.

Blind source separation based x-ray image denoising from an image sequence.

Blind source separation (BSS) based x-ray image denoising from an image sequence is proposed. Without priori knowledge, the useful image signal can be separated from an x-ray image sequence, for original images are supposed as different combinations of stable image signal and random image noise. The BSS algorithms such as fixed-point independent component analysis and second-order statistics singular value decomposition are used and compared with multi-frame averaging which is a common algorithm for improving image's signal-to-noise ratio (SNR). Denoising performance is evaluated in SNR, standard deviation, entropy, and runtime. Analysis indicates that BSS is applicable to image denoising; the denoised image's quality will get better when more frames are included in an x-ray image sequence, but it will cost more time; there should be trade-off between denoising performance and runtime, which means that the number of frames included in an image sequence is enough.

Variability of the coherent arrivals extracted from low-frequency deep-ocean ambient noise correlations

Correlation processing of ocean noise can be used to develop totally passive ocean monitoring methods. Using various hydrophone pair orientations, this study investigates the frequency dependence, seasonal variability, and emergence rate of coherent arrivals from cross-correlations of low frequency ambient noise (f < 40 Hz) recorded on triangular hydrophones arrays. These arrays are located at five existing hydroacoustic stations of the International Monitoring System (IMS), situated in the deep-sound channel, and distributed across the Atlantic, Pacific, and Indian Ocean basins. For the majority of studied sites, persistent and fast-emerging coherent arrivals are reliably obtained if the axis connecting the selected hydrophone pair has a direct line-of-sight with regions of the globe containing stable and diffuse noise sources (e.g., polar-ice or seismic noise). Furthermore, for this favorable orientation, the emergence rate of coherent arrivals extracted between hydrophone pairs separated by long ranges (here ∼130 km) can be approximated based on measurements made between hydrophone pairs separated by short ranges (∼2 km) in the Atlantic Ocean. Hence, results from this study, obtained using existing hydrophone configurations of the IMS hydroacoustic stations, could be used to guide the placement of other hydrophone arrays over the globe for future long-range passive ocean monitoring experiments.

Research on Parameter Estimation Methods for Alpha Stable Noise in a Laser Gyroscope's Random Error.

Alpha stable noise, determined by four parameters, has been found in the random error of a laser gyroscope. Accurate estimation of the four parameters is the key process for analyzing the properties of alpha stable noise. Three widely used estimation methods—quantile, empirical characteristic function (ECF) and logarithmic moment method—are analyzed in contrast with Monte Carlo simulation in this paper. The estimation accuracy and the application conditions of all methods, as well as the causes of poor estimation accuracy, are illustrated. Finally, the highest precision method, ECF, is applied to 27 groups of experimental data to estimate the parameters of alpha stable noise in a laser gyroscope’s random error. The cumulative probability density curve of the experimental data fitted by an alpha stable distribution is better than that by a Gaussian distribution, which verifies the existence of alpha stable noise in a laser gyroscope’s random error.

ECL-Based SiC Logic Circuits for Extreme Temperatures

Integrated digital circuits, fabricated in a bipolar SiC technology, have been successfully tested up to 600 °C. Operated with-15 V supply voltage from 27 up to 600 °C OR-NOR gates exhibit stable noise margins of about 1 or 1.5 V depending on the gate design, and increasing delay-power consumption product in the range 100 - 200 nJ. In the same temperature range an oscillation frequency of about 1 MHz is also reported for an 11-stage ring oscillator.

Application of a new passive acoustic leak detection approach to recordings from the Dounreay prototype fast reactor

A new approach for passive acoustic leak detection in sodium fast reactors without using a priori knowledge on the leak noise is introduced. The new approach is tested on recordings of argon and water injections from the Dounreay prototype fast reactor under digital mixing with two types of additional noise. It is estimated that the new approach is able to detect injection of argon into sodium in a stable background noise at signal to noise ratios between -9 and -17dB with a low false alarm rate and with few free parameters in the signal processing. For detection of water into sodium injection the corresponding signal to noise ratios range from -9 to -18dB.

Stable low noise 1.5 µm laser generated by a singly resonant optical parametric oscillator

We present a stable low noise continuous wave (CW) single frequency 1.5 µm laser generated by an output-coupled singly resonant optical parametric oscillator based on a periodically poled lithium niobate (PPLN) and a home-made CW single frequency Nd:YVO4 laser at 1.064 µm as the pump source. A maximum signal power of 5.3 W can be obtained at a pump power of 16 W. The long-term power stability is better than ±0.9% in a given two hours and the intensity noise reaches the shot noise limit for frequencies above 3 MHz. The signal wavelength can be tuned from 1.560 to 1.592 µm with PPLN temperature controlled from 120 to 180 °C. This kind of laser source can be used in quantum information processing research.

Novel &lt;inline-formula&gt; &lt;tex-math notation="TeX"&gt;${\rm S}\alpha{\rm S} $&lt;/tex-math&gt;&lt;/inline-formula&gt; PDF Approximations and Their Applications in Wireless Signal Detection

Three new approximations to the probability density function (PDF) of the symmetric alpha stable $({\rm S}\alpha{\rm S} ) $ distribution are proposed. The first two approximations use rational functions while the third approximation uses power functions. Using these approximations, new detectors for signals in symmetric alpha stable noise are also derived. Numerical results show that all these new approximations have good accuracies. Numerical results also show that the new detectors based on these approximations outperform the existing detectors, especially when the characteristic exponent of the symmetric alpha stable distribution is small.

Stochastic resonance of asymmetric bistable system with α stable noise

In this paper we take the asymmetric bistable system excited by weak periodic signal as a model and regard signal-to-noise ratio gain as an index to investigate the stochastic resonance phenomenon stimulated by additive and multiplicative α stable noise. Stochastic resonance phenomenon stimulated by only additive α stable noise is also investigated here. The laws for the resonance system parameters a, b, asymmetric skewness r and intensity amplification factor Q or D of α stable noise to act on the resonant output are explored under different stability index α and skewness parameter β of α stable noise. The results show that no matter whether under the joint action of additive and multiplicative α stable noise or under the action of only additive α stable noise, weak signal detection can be realized by tuning the system parameters a, b and r. The intervals of a, b and r which can induce stochastic resonances are multiple, and do not change with α nor β. Moreover, when investigating the noise-induced stochastic resonance, it is found that stochastic resonance can also be realized by tuning the intensity amplification factor of α stable noise. And the interval of D does not change with α nor β. The results will contribute to a reasonable selection of parameter-induced stochastic resonance system parameters and noise intensity of noise-induced stochastic resonance under α stable noise.

Stochastic Averaging of Dynamical Systems with Multiple Time Scales Forced with $\alpha$-Stable Noise

Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze variables evolving on the slow time scale. These procedures have been studied extensively for systems driven by Gaussian noise, but very little attention has been given to the case of $\alpha$-stable noise forcing which arises naturally from heavy-tailed stochastic perturbations. In this paper, we study nonlinear fast-slow stochastic dynamical systems in which the fast variables are driven by additive $\alpha$-stable noise perturbations and the slow variables depend linearly on the fast variables. Using a combination of perturbation methods and Fourier analysis, we derive stochastic averaging approximations for the statistical contributions of the fast variables to the slow variables. In the case that the diffusion term of the reduced model depends on the state of the slow variable, we show that this term is interpreted in terms of the Marcus calculus. For the case $\alpha = 2$, which corresponds to Gaussian noise, the results are consistent with previous results for stochastic averaging in the Gaussian case. Although the main results are derived analytically for $1 < \alpha < 2$, we provide evidence of their validity for $\alpha < 1$ with numerical examples. We numerically simulate both linear and nonlinear systems and the corresponding reduced models, demonstrating good agreement for their stationary distributions and temporal dependence properties.

Beamspace time-frequency analysis for identification of underwater tone noise sources

The noise emitted by an underwater vehicle consists of several strong tones superimposed on a broad-band radiated noise component. Among them, the stable low-frequency tone noise induced by the reciprocating movements of the auxiliary machines in the underwater vehicle, carries characteristic information of the vehicle and is necessary for long-distance detection. Therefore, identification of the tone noise sources of an underwater vehicle is significant for noise reduction. On the basis of the joint information of space-time-frequency, beamspace time-frequency analysis (TFA) scheme is proposed for identification of low-frequency tone noise sources of underwater moving vehicle. First, the Doppler signals formed when the tone noise sources pass through the closest point of approach (CPA) are separated in time domain, by using superdirectivity beamforming of a small aperture circular array. The output signals can be approximated in linear form, i. e., LFM signal. After the LFM signals from the narrow beam are processed by two TFA methods of pseudo Wigner - Ville distribution and chirplet transform (CT), the time-frequency images of the noise signals are obtained. Then, the CPA time of each tone noise sources can be estimated by using peak search of the time-frequency images. At last, by converting the time coordinate to space coordinate and comparing with a reference source whose CPA time and position are known in advance, the positions of the low-frequency tone noise sources on the underwater vehicle are identified. The proposed scheme is different from the focused beamforming method, which scans the beam angle after eliminating the Doppler effect. Besides, due to no need of decorrelation usually used in the focused beamforming method, beamspace TFA scheme resolves the problem that array aperture is limited for identification of coherent noise sources of an underwater vehicle. The aperture of the used array can be reduced to meter-scale even when the frequencies of the tone noise are low. Although the array gain of superdirectivity beamforming decreases in nonisotropic noise field, the main lobe of the beam still keeps the same shape. Therefore, the performance of the proposed scheme is robust. Simulation analysis shows the following results: (1) Both the two beamspace TFA methods can precisely identify the underwater tone noise sources through a small aperture circular array, the radius of which is equal to 1.6 m, and the localization errors are less than 1 m when the signal-to-noise ratios are moderate; (2) The higher the frequencies of the tone noises are, the better the localization accuracy of beamspace TFA methods obtain; (3) The proposed scheme is less sensitive to the velocity of the underwater moving vehicle, and the localization results just have very small difference under various velocities; (4) The localization accuracy is related to distance, and decade meters is a reasonable choose for actual noise measurement; (5) Beamspace CT has better resolving accuracy when the information of measurement system is given, so the choice of the two beamspace TFA methods can be decided according to the actual measurement condition.

Noise-benefit forbidden-interval theorems for threshold signal detectors based on cross correlations.

We show that the main forbidden interval theorems of stochastic resonance hold for a correlation performance measure. Earlier theorems held only for performance measures based on mutual information or the probability of error detection. Forbidden interval theorems ensure that a threshold signal detector benefits from deliberately added noise if the average noise does not lie in an interval that depends on the threshold value. We first show that this result holds for correlation for all finite-variance noise and for all forms of infinite-variance stable noise. A second forbidden-interval theorem gives necessary and sufficient conditions for a local noise benefit in a bipolar signal system when the noise comes from a location-scale family. A third theorem gives a general condition for a local noise benefit for arbitrary signals with finite second moments and for location-scale noise. This result also extends forbidden intervals to forbidden bands of parameters. A fourth theorem gives necessary and sufficient conditions for a local noise benefit when both the independent signal and noise are normal. A final theorem derives necessary and sufficient conditions for forbidden bands when using arrays of threshold detectors for arbitrary signals and location-scale noise.

Polynomial‐approximation‐based locally optimum detector for signals with symmetric alpha stable noise

Rational approximation to the non-linear score function used in the locally optimum detector is derived for signals corrupted by the impulsive symmetric alpha stable noise. The new approximation uses a third-order polynomial in the numerator and a fourth-order polynomial in the denominator, compared with the existing approximation that uses a first-order polynomial in the numerator and a second-order polynomial in the denominator. The parameters of the polynomials are derived using non-linear least squares curve fitting. The relationships between the polynomial parameters and the value of the characteristic exponent are also obtained. Numerical results show that the proposed approximation has superior accuracy to the existing approximations. The proposed new approximation is then applied to the locally optimum detector by replacing the score function in the decision variable. Numerical results show that the proposed detector, optimised according to a curve-fitting approach, outperforms previous approximations of the locally optimum detector, also optimised according to a curve-fitting approach, for binary phase shift keying signals and in some cases for on–off keying signals.

On Single-Carrier Communication in Additive White Symmetric Alpha-Stable Noise

In this paper we analyze design aspects of a single-carrier digital communications receiver in the presence of impulsive noise. We use the additive white symmetric $\alpha$ -stable noise $(\hbox{AWS}\alpha\hbox{SN})$ to model the channel noise. By introducing passband sampling, efficient constellations and suitable baseband detectors, we show that the uncoded error performance of the conventional (linear) receiver can be enhanced given the real and imaginary components of the transmitted symbol are decoded separately. The performance may be improved further by sacrificing the linearity of the system. Various non-linear estimation and joint-detection schemes are discussed and their error performance analyzed. It is shown that if the receiver bandwidth is large enough, impulsive noise may be effectively countered in a single-carrier communications system.

Image-guided sonothrombolysis in a stroke model with a cavitation delivery and monitoring system

Microbubbles (MB) and ultrasound (US) can dissolve intra-arterial thrombi. In order to reproducibly deliver the correct cavitation dose and ensure treatment efficacy and safety, we designed a therapeutic US mode with cavitation monitoring. Therapy delivery and recording of the MB signal are achieved with a sector imaging probe. Monitoring is achieved by spectrally analyzing the MB signal: ultraharmonics are a marker of stable cavitation (SC) and broadband noise characterizes inertial cavitation (IC). We used the system in a pig model. Thrombotic occlusions were created by injecting 4-hour old clots bilaterally into the internal carotids. Forty pigs were randomized to either 2.4 MI, 5 μs pulses with MBs; 1.7 MI, 20 μs pulses with MBs; and 2.4 MI, 5 μs pulses without MBs. Angiographic recanalization rates were compared. Cavitation as a function of MI was estimated in vivo. Dominant SC started at an applied MI of 0.6 (0.3MI in situ after derating by skull attenuation). Dominant IC was estimated to start at an applied MI of 0.9 (0.6 in situ). Thus, all therapy settings were in the IC regime. The 2.4MI + MB setting was the most effective (100% recanalization) vs 38% for the 1.7MI + MB and 50% for 2.4 MI without MBs (both p<0.05 compared to 2.4MI + MB). No signs of hemorrhage were found in any animal. In conclusion, higher IC levels are most effective for thrombus dissolution. Spectral analysis techniques can be used to plan and monitor the therapy.