Signals In White Gaussian Noise Research Articles

Stochastic resonance in time-delayed bistable coupled network systems driven by Gaussian white noise

In this paper, we study the stochastic resonance (SR) behavior of time-delayed bistable coupled network systems under the action of Gaussian white noise and periodic signal. The model consists of a finite number N of coupled oscillators interconnected with each other, where the oscillators interact to produce complex nonlinear behavior. The original system is reduced and approximated by using the mean field theory and the small delay approximation method, and the simplified model is obtained. Analytical expression for the signal-to-noise ratio (SNR) is derived in the adiabatic limit. Additionally, statistical complexity measure is also given to verify the validity of the SNR. The numerical results demonstrate that the coupled system exhibits SR. Then, the effect of system scale on time-delayed coupled systems is discussed. It is found that when the system scale increases to a certain extent, SNR curve evolves from single peak to double peak, indicating the occurrence of double SR in the system. And, the effects of time delay, system parameters and periodic signal parameters on SR and double SR behavior of the system are analyzed respectively. It is found that the effect of time delay on the system depends on the positive or negative of the time delay feedback strength. The influence of time delay on double SR in this system is weaker than its influence on single SR.

SignalFormer: Hybrid Transformer for Automatic Drone Identification Based on Drone RF Signals.

With the growing integration of drones into various civilian applications, the demand for effective automatic drone identification (ADI) technology has become essential to monitor malicious drone flights and mitigate potential threats. While numerous convolutional neural network (CNN)-based methods have been proposed for ADI tasks, the inherent local connectivity of the convolution operator in CNN models severely constrains RF signal identification performance. In this paper, we propose an innovative hybrid transformer model featuring a CNN-based tokenization method that is capable of generating T-F tokens enriched with significant local context information, and complemented by an efficient gated self-attention mechanism to capture global time/frequency correlations among these T-F tokens. Furthermore, we underscore the substantial impact of incorporating phase information into the input of the SignalFormer model. We evaluated the proposed method on two public datasets under Gaussian white noise and co-frequency signal interference conditions, The SignalFormer model achieved impressive identification accuracy of 97.57% and 98.03% for coarse-grained identification tasks, and 97.48% and 98.16% for fine-grained identification tasks. Furthermore, we introduced a class-incremental learning evaluation to demonstrate SignalFormer's competence in handling previously unseen categories of drone signals. The above results collectively demonstrate that the proposed method is a promising solution for supporting the ADI task in reliable ways.

The Reduced-Order Model for Droplet Drift of Aerial Spraying under Random Lateral Wind

The droplet drift during aerial spraying process of oilseed rape, which is induced by complex flow field including random lateral wind, is difficult to predict and suppress. In this study, the high-fidelity computational fluid dynamics (CFD) technique is employed to simulate the two-phase flow of droplets in the rotor flow field, and the influence of main operation parameters on spraying effect is investigated numerically. Furthermore, the mechanism of droplet deposition in various operation conditions is discussed according to the analysis of unsteady flow field characteristics. However, the simulation via CFD technique is time-consuming, and it is not suitable for multidisciplinary work and optimization design. To address such issue, a filter white Gaussian noise signal is used to mimic the random lateral wind, and the droplet drift distance is obtained numerically. Based on the input and output dataset of CFD, the recursive algorithm including nonlinear autoregressive exogenous model and surrogate-based recurrence framework and the deep learning method for time-series prediction called long short-term memory neural network are used to build the efficient reduced-order model, respectively. Numerical simulations show that the droplet drift distance can be predicted by measurable lateral wind speed via the reduced-order model approach, which agreed well with the results obtained via the CFD method. In addition, the reduced-order model could decrease computation cost by 6 orders of magnitude with an acceptable accuracy, which indicates that the proposed method could be used for the design of off-line closed-loop controller of a variable spraying system.

A Quantum Weak Signal Detection Method for Strengthening Target Signal Features under Strong White Gaussian Noise

As the noise power increases, the target signal features become less obvious, which leads to the failure of weak signal detection methods. To address this problem, a quantum weak signal detection method, Local Semi-Classical Signal Analysis-Singular Value Decomposition (LSCSA-SVD), for strengthening target signal features under strong white Gaussian noise is proposed. Firstly, the time domain weak signal is quantized by the Schrodinger operator and its discrete spectrum formula. Then, in the quantum domain, the later eigenvalues are used to reconstruct the time domain signal, which can protect and enhance the target signal features. Finally, the difference between signal and noise in the singular value vector is used to further extract the reconstruction signal features. In simulation, the LSCSA-SVD can accurately extract target signals from white Gaussian noise signals with a signal-to-noise ratio (SNR) of −30 dB, which is better than the comparison methods. In the experiment, the weak acceleration sensor signal and the weak signal of the test circuit are successfully extracted. The results show that the LSCSA-SVD can suppress strong noise and improve the SNR.

Component-scaled signal reconstruction for enhanced noise filtration

This research introduces a procedure for signal denoising based on linear combinations of intrinsic mode functions (IMFs) extracted using empirical mode decomposition (EMD). The method, termed component-scaled signal reconstruction, employs the standard EMD algorithm, with no enhancements to decompose the signal into a set of IMFs. The problem of mode mixing is leveraged for noise removal by constructing an optimal linear combination of the potentially mixed IMFs. The optimal linear combination is determined using an optimization routine with an objective function that maximizes and minimizes the information and noise, respectively, in the denoised signal. The method is demonstrated by applying it to a computer-generated voice sample and the displacement response of a cantilever beam with local stiffness nonlinearity. In the first application, the noise is introduced into the sample manually by adding a Gaussian white-noise signal to the signal. In the second application, the response of the entire beam is filmed using two 1-megapixel cameras, and the three-dimensional displacement field is extracted using digital image correlation. The noise in this application arises entirely from the images captured. The proposed method is compared to existing EMD, ensemble EMD, and LMD based denoising approaches and is found to perform better.

Current-to-Frequency Converter Based Photometer Circuit

In this article, the design of a photometer circuit based on a current-to-frequency converter is presented. This circuit is a piecewise linear circuit that makes the most of feedback to ensure a linear relationship between the input photocurrent and the output frequency. Here, Proteus simulations were used to verify the performance of the proposed circuit, and the electronic simulations and the experimental results were shown to be in total agreement. The experimental results showed that the proposed circuit rejected better additive white Gaussian noise signals than the classic photometer circuit based on the transimpedance amplifier. In addition, despite that the proposed circuit is more complex than the classic one, its high linearity, noise rejection, and easy implementation make it suitable for applications where measurement precision and noise rejection are of paramount importance.

Shear coefficient of spin viscosity estimation through velocity profiles of a ferrofluid under the effect of an external rotating magnetic field of low amplitude and frequency

The present article describes a numerical strategy for the estimation of the shear coefficient of spin viscosity for a ferrofluid sample confined to a cylindrical container and exposed to the effect of an external rotating magnetic field with a low amplitude and frequency. As far as we know, there are no experimental measurements of such coefficient. Furthermore, the few analytical values reported differ in several orders of magnitude. First, we describe briefly the mathematical model of the system and its numerical solution. Then, the definition of the direct and inverse problems is given as a part of the methodology for estimating such coefficient. Finally, we solve the inverse problem using simulated measurements and two global optimization algorithms. We generate this type of measurements by adding white Gaussian noise signals to the numerical solution of the ferrohydrodynamic mathematical model. Several noise levels in the range of 10 to 40 dB were used to increase the number of scenarios for validation purpose. Results showed an excellent agreement between the estimated values and those used in the numerical solution of the mathematical model. A statistical analysis revealed a normal distribution that was dependent on the noise level. This variation did not affect the results, but showed instead the validity of the proposed method. Additionally, this strategy stands as a computational tool for validating experimental results of the future in situ measurements. Tables 7, Figs 11, Refs 17.

A new physical parameter identification method for shear frame structures under limited inputs and outputs

A new physical parameter identification method with a name of EKPF-LS is proposed for shear frame structures under limited inputs and outputs by a combination of extended Kalman particle filter (EKPF) and least square (LS) algorithm. The basic principle of EKPF-LS is to establish the proposed distribution function of the particle filter through EKF-LS. In this method, EKPF is introduced to get rid of the restriction of Gaussian white noise model and reduce the linearization error caused by EKF. Meanwhile, LS is utilized to address the problem of unmeasured excitation estimations. The effectiveness and accuracy of the proposed EKPF-LS method is verified by a numerical example of a four-story hysteretic shear frame under an earthquake excitation and an experimental test of a four-story shear type frame using Gaussian white noise and sine sweep signal as excitations, respectively. Gaussian colored noises are then added to the solved and measured response signals in the numerical example and experimental test, respectively. The results demonstrate that the proposed method can identify the stiffness of shear frame structures effectively and is superior to the existed EKF-LS approach when the structural system is nonlinear structural system or Colored noise model.

Noisy Galvanic Vestibular Stimulation (Stochastic Resonance) Changes Electroencephalography Activities and Postural Control in Patients with Bilateral Vestibular Hypofunction

Patients with bilateral vestibular hypofunction (BVH) often suffer from imbalance, gait problems, and oscillopsia. Noisy galvanic vestibular stimulation (GVS), a technique that non-invasively stimulates the vestibular afferents, has been shown to enhance postural and walking stability. However, no study has investigated how it affects stability and neural activities while standing and walking with a 2 Hz head yaw turning. Herein, we investigated this issue by comparing differences in neural activities during standing and walking with a 2 Hz head turning, before and after noisy GVS. We applied zero-mean gaussian white noise signal stimulations in the mastoid processes of 10 healthy individuals and seven patients with BVH, and simultaneously recorded electroencephalography (EEG) signals with 32 channels. We analyzed the root mean square (RMS) of the center of pressure (COP) sway during 30 s of standing, utilizing AMTI force plates (Advanced Mechanical Technology Inc., Watertown, MA, USA). Head rotation quality when walking with a 2 Hz head yaw, with and without GVS, was analyzed using a VICON system (Vicon Motion Systems Ltd., Oxford, UK) to evaluate GVS effects on static and dynamic postural control. The RMS of COP sway was significantly reduced during GVS while standing, for both patients and healthy subjects. During walking, 2 Hz head yaw movements was significantly improved by noisy GVS in both groups. Accordingly, the EEG power of theta, alpha, beta, and gamma bands significantly increased in the left parietal lobe after noisy GVS during walking and standing in both groups. GVS post-stimulation effect changed EEG activities in the left and right precentral gyrus, and the right parietal lobe. After stimulation, EEG activity changes were greater in healthy subjects than in patients. Our findings reveal noisy GVS as a non-invasive therapeutic alternative to improve postural stability in patients with BVH. This novel approach provides insight to clinicians and researchers on brain activities during noisy GVS in standing and walking conditions in both healthy and BVH patients.

On Asymptotically Minimax Nonparametric Detection of Signal in Gaussian White Noise

For the problem of nonparametric detection of signal in Gaussian white noise, strong asymptotically minimax tests are found. The sets of alternatives are balls in the Besov space 𝔹 $$ {{}_2^{\mathrm{s}}}_{\infty } $$ with “small” balls in 𝕃2 removed. The balls in the Besov space are defined in terms of orthogonal expansions of functions in trigonometrical basis. Similar result is also obtained for nonparametric hypothesis testing on a solution of ill-posed linear inverse problem with Gaussian random noise. Bibliography: 19 titles.

Minimax Nonparametric Estimation on Maxisets

We study nonparametric estimation of a signal in Gaussian white noise on maxisets. We point out minimax estimators in the class of all linear estimators and strong asymptotically minimax estimators in the class of all estimators. We show that balls in Sobolev spaces are maxisets for the Pinsker estimators.

Contrasting open-loop dynamic characteristics of sympathetic and vagal systems during baroreflex-mediated heart rate control in rats.

Although heart rate (HR) is governed by the sympathetic and parasympathetic nervous systems, a head-to-head comparison of the open-loop dynamic characteristics of the total arc from a baroreceptor pressure input to the HR response has yet to be performed. We estimated the transfer function from carotid sinus pressure input to the HR response (HCSP→HR) before and after bilateral vagotomy (n = 7) as well as before and after the administration of a β-blocker propranolol (n = 8) in anesthetized male Wistar-Kyoto rats. The carotid sinus pressure was perturbed according to a Gaussian white noise signal so that the input power spectra were relatively flat between 0.01 and 1 Hz. The gain plot of HCSP→HR was V-shaped. Vagotomy reduced the dynamic gain at 1 Hz (0.0598 ± 0.0065 to 0.0025 ± 0.0004 beats·min-1·mmHg-1, P < 0.001) but not at 0.01 or 0.1 Hz. β-Blockade reduced the dynamic gain at 0.01 Hz (0.247 ± 0.069 to 0.077 ± 0.017 beats·min-1·mmHg-1, P = 0.020) but not at 0.1 or 1 Hz. We also estimated the efferent limb transfer function from electrical vagal efferent stimulation to the HR response (HVN→HR) under β-blockade conditions. We associated the model parameters of HVN→HR with the mean HR and the standard deviation of HR so that HVN→HR could be estimated based only on the HR data. We finally estimated the neural arc transfer function from a pressure input to efferent vagal nerve activity by dividing HCSP→HR by HVN→HR. The mathematically determined vagal neural arc showed derivative characteristics with its phase near zero radians at the lowest frequency.

Efficient determination of local defect resonance frequencies from bicoherence plots using double excitations

Abstract In recent years, a lot of developments can be seen in the field of local defect resonance (LDR) based thermosonics which provide thermal image of a defect by exciting the structure at particular defect frequencies. LDR based thermosonics is found to be more promising compared to traditional thermosonics due to its high reproducibility and low power usage. However, fast and accurate detection of these LDR frequencies is a challenging task. In this context, this paper addresses a fast and reliable method of LDR frequency determination using bicoherence plots. Two exciters and one receiver PZTs (lead zirconate titanate) are used for the experiment. One exciter PZT is provided with chirp or Gaussian white noise signal input while a fixed frequency signal is given to the second exciter PZT. Intermodulation of LDR and excitation frequencies can be observed in frequency plots. LDR frequencies can be easily detected from bicoherence plots, while its detection from frequency plots is found to be cumbersome. The efficacy of bicoherence analysis in detection of LDR frequency is shown using an aluminium plate with flat bottom hole and three delaminated glass fibre reinforced composite (GFRP) plates. Second harmonic of LDR frequencies are evaluated from the bicoherence plots which can be used later for defect imaging.

Detection of Array Signal Number With Multiple Sensors Based on Transfer Component Analysis

The conventional algorithms for estimating number of array signals are only suitable for the background of Gaussian white noise, and need many snapshots, but their performance will reduce seriously in the circumstance of impulse noise and small samples. Therefore, a new method of detecting array signal number with multiple sensors based on transfer component analysis is proposed in this paper. First, the array signals in Gaussian white and impulse noise are respectively modeled. Then the received array data are transformed into a common hidden space by the mapping function, thus, data in the hidden space have the same distribution, and most initial characteristics are retained. Finally, a support vector machine or K-means clustering are used for classifying the mapped data into two categories, on this basis, the array signal number can be estimated.

Best Linear Approximation of Wiener Systems Using Multilevel Signals: Theory and Experiments

The problem of measuring the best linear approximation (BLA) of a nonlinear system by means of multilevel excitation sequences is analyzed. A comparison between different types of sequences applied at the input of Wiener systems is provided by numerical simulations and by experiments on a practical circuit, including an analog filter and a clipping nonlinearity. The performance of the sequences is compared with a white Gaussian noise signal for reference purposes. The theoretical characterization of the BLA when using randomized constrained sequences is derived analytically for the cubic nonlinearity case. Numerical and experimental results show that the randomized constrained approach for designing ternary sequences has a low sensitivity to both even- and odd-order nonlinearities, resulting in a response close to the actual response of the underlying linear system.

On misspecifications in regularity and properties of estimators

The problem of parameter estimation by the continuous time observations of a deterministic signal in white Gaussian noise is considered. The asymptotic properties of the maximum likelihood estimator are described in the asymptotic of small noise (large signal-to-noise ratio). We are interested in the situation when there is a misspecification in the regularity conditions. In particular it is supposed that the statistician uses a discontinuous (change-point type) model of signal, when the true signal is continuously differentiable function of the unknown parameter.

Stochastic Resonance in Second-Order Underdamped System With Exponential Bistable Potential for Bearing Fault Diagnosis

Stochastic resonance (SR) as effective approach for weak signal detection has been widely used in bearing fault signal diagnosis. In this paper, a new method was proposed to detect fault signals, which consists of an exponential bistable potential model generalized by using a harmonic Potential (HP) model, a Gaussian potential (GP) model and second-order underdamped system. As the classical bistable SR (CBSR) has the disadvantage of output saturation, which will suppress the optimal signal-to-noise ratio (SNR) of the system, therefore, underdamped SR with exponential potential (UESR) and underdamped SR with classical bistable potential (UCSR) are applied to detect fault signal, respectively. Under the adiabatic condition, the analytical expression of the SNR is calculated for the UESR system driven by Gaussian white noise and periodic signal. Then, the effects of system parameters and the damping factor on analytical expression of SNR as a function of noise intensity for different parameters are studied, respectively. Finally, the proposed method is applied to detect simulated fault signals and actual bearing fault signals. The experimental results show that the proposed UESR method is superior to the UCSR method in fault signal diagnosis, such as larger output SNR and higher spectrum peaks at fault characteristic frequencies.

Tonic aortic depressor nerve stimulation does not impede baroreflex dynamic characteristics concomitantly mediated by the stimulated nerve.

Although electrical activation of the carotid sinus baroreflex (baroreflex activation therapy) is being explored as a device therapy for resistant hypertension, possible effects on baroreflex dynamic characteristics of interaction between electrical stimulation and pressure inputs are not fully elucidated. To examine whether the electrical stimulation of the baroreceptor afferent nerve impedes normal short-term arterial pressure (AP) regulation mediated by the stimulated nerve, we electrically stimulated the right aortic depressor nerve (ADN) while estimating the baroreflex dynamic characteristics by imposing pressure inputs to the isolated baroreceptor region of the right ADN in nine anesthetized rats. A Gaussian white noise signal with a mean of 120 mmHg and standard deviation of 20 mmHg was used for the pressure perturbation. A tonic ADN stimulation (2 or 5 Hz, 10 V, 0.1-ms pulse width) decreased mean sympathetic nerve activity (367.0 ± 70.9 vs. 247.3 ± 47.2 arbitrary units, P < 0.01) and mean AP (98.4 ± 7.8 vs. 89.2 ± 4.5 mmHg, P < 0.01) during dynamic pressure perturbation. The ADN stimulation did not affect the slope of dynamic gain in the neural arc transfer function from pressure perturbation to sympathetic nerve activity (16.9 ± 1.0 vs. 14.7 ± 1.6 dB/decade, not significant). These results indicate that electrical stimulation of the baroreceptor afferent nerve does not significantly impede the dynamic characteristics of the arterial baroreflex concomitantly mediated by the stimulated nerve. Short-term AP regulation by the arterial baroreflex may be preserved during the baroreflex activation therapy.

Suppressing the discrete spectral interference of the partial discharge signal based on bivariate empirical mode decomposition

Summary In the present study, a discrete spectral interference (DSI) suppressing method based on bivariate empirical decomposition mode (BEMD) related to partial discharge measurements is presented. PD complex-valued signals are generated first, whose real part is DSI polluting PD signals and imaginary part is zero mean white Gaussian noise (WGN) signals. PD complex-valued signals are decomposed based on BEMD, and intrinsic mode functions (IMFs) can be sifted by this decomposition. The real part of IMFs (RIMFs) are decomposition results of DSI polluting signals and imaginary part of IMFs (IIMFs) are decomposition results of zero mean WGN signals. With the assistance of WGN signals, the mode mixing effect in RIMFs can be alleviated. Besides, RIMFs are free from the influence of WGN signals, which will avoid the disadvantage of long-time computing for ensemble empirical mode decomposition (EEMD) and satisfy the request of PD online monitoring. The goal for suppressing DSI of PD signals can be achieved by reconstructing RIMFs based on sine amplitude judgment method proposed in this study. The DSI suppressing method presented in this article was applied on the simulated and measured PD signals, and the obtained denoising results mainly based on EEMD, BEMD, and wavelet transform (WT) were compared and analyzed to verify the effectiveness of the proposed method. Besides, assessment indices including signal to noise ratio (SNR), amplitude relative error (ARE), root mean square error (RMSE), and normalized correlation coefficient (NCC) were used as objective evaluation criteria for denoising effect, and the results show that the presented method is superior to traditional EEMD methods and WT methods, which has less amplitude error as well as less waveform destination.

KHz-order linewidth controllable 1550 nm single-frequency fiber laser for coherent optical communication.

A kHz-order linewidth controllable 1550 nm single-frequency fiber laser (SFFL) is demonstrated for the first time to our best knowledge. The control of the linewidth is realized by using a low-pass filtered white Gaussian noise (WGN) signal applied on a fiber stretcher in an optical feedback loop. Utilizing WGN signals with different signal amplitudes An and different cutoff frequencies fc, the linewidths are availably controlled in a wide range from 0.8 to 353 kHz. The obtained optical signal-to-noise ratio (OSNR) is more than 72.0 dB, and the relative intensity noise (RIN) at frequency greater than 40 MHz reaches -148.5 dB/Hz which approaches the shot noise limit (-152.9 dB/Hz). This kHz-order linewidth controllable SFFL is meaningful and valuable, for optimizing the receiver sensitivity and bit error rate (BER) performance of the coherent optical communication system based on high-order quadrature amplitude modulation (QAM).