White Noise Signal Research Articles

Fast physical random bit generation using a millimeter-wave white noise source.

A broadband millimeter-wave (MMW) white noise signal generated by optical heterodyning of two Fabry-Perot laser diodes (FP-LDs) subject to optical feedback is demonstrated and employed for fast physical random bit generation with a simple least significant bits (LSBs) retaining method. Firstly, under suitable feedback conditions, two external-cavity feedback FP-LDs can be easily driven into chaotic states. In this process, the optical spectra of multi-longitudinal modes are significantly broadened. Then, two spectral broadening multi-longitudinal chaotic signals are mixed and converted into an MMW white noise signal through the heterodyne beating technique combined with a fast photodetector. With such an approach, a high dimensional broadband chaos with perfect characteristics of MMW white noise (3-dB bandwidth beyond 50 GHz without any time-delay signature) is experimentally achieved. Finally, taking the generated MMW white noise as the entropy source, 640 Gb/s physical random bit generation is realized by directly selecting 4-LSBs at 160 GS/s sampling rate after an 8-bit analog-digital-convertor.

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.

DFT-Based Frequency Estimation of Multiple Sinusoids

An accurate frequency estimation method of multi-component sinusoidal signal in additive white Gaussian noise (AWGN) is proposed. The algorithm is implemented in the frequency domain and based on discrete Fourier transform (DFT). The maximum DFT spectral line and two Discrete-Time Fourier Transform (DTFT) samples located on the same side of the maximum DFT spectral line are used to estimate the frequency of a sinusoidal component. And this algorithm is utilized in both the coarse estimation and the fine estimation. Simulation results show that compared with the competing estimators, the presented method is closer to the Cramer-Rao lower bound (CRLB). And it is almost independent of the frequency displacement. The numerical complexity of the presented method is similar with the competing DFT-based algorithms.

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.

An Optimized Zero-Attracting LMS Algorithm for the Identification of Sparse System

This paper introduces an optimized zero-attractor to improve the performance of least mean square (LMS)-based algorithms for the identification of sparse system. Compared with previous LMS-based algorithms for sparse system identification, the performance of the proposed optimized zero-attracting LMS (OZ-LMS) is much less sensitive to the tuning parameters and measurement noise power, and performs much better for sparse system. Comprehensive performance analysis of the mean-square deviation (MSD) of OZ-LMS is derived in detail. Moreover, the parameter selection rules for optimal steady-state MSD are discussed. Simulation results, using white Gaussian noise and speech input signals, show improved performance over existing methods. Furthermore, we show that the numerical results of OZ-LMS agree with the theoretical predictions.

Evaluation of quality of non-mydriatic fundus images obtained with non-contact TrueColor, confocal scanner during third phase of nationwide lockdown

Aims: This study aims to evaluate the non-mydriatic fundus image quality obtained with a confocal fundus device. Also, to evaluate the influence of non-mydriatic pupil size on image quality. Settings and Design: A cross-sectional study was conducted in the outpatient department of a high-volume tertiary eye care centre in South India during the third phase of the COVID-19 lockdown. Subjects and Methods: 831 consenting, consecutive patients (1539 eyes) were photographed from May 5 to May 17, 2020, and were graded excellent, fair, adequate, or inadequate; based on white noise, black noise, and image acquisition signals. Pupil diameters were obtained with light-emitting diode flash technology. Statistical Analysis: The collected data were analyzed using SPSS software. Descriptive statistics in the form of frequencies and percentages were calculated. Simple (univariate) linear regression analysis and adjusted regression analysis were used to establish the relationship between pupil size and fundus photo quality. Results: The quality of the fundus photo was excellent in 70.12% (n = 1079), fair in 15.72% (n = 242), adequate in 5.78% (n = 89), and inadequate in 8.38% (n = 129). Of the 1410 obtained images (subtracting the inadequate quality images), 87.66% (n = 1236) were normal and 12.34% (n = 174) were pathological. There was a positive linear relationship between pupil size and quality of retinal photograph; OS (R2 = 0.935) had a slightly better association than OD (R2 = 0.901). Conclusions: The majority of the confocal images were excellent in quality. Our four-point grading system serves as a reliable measure of non-mydriatic photograph quality. Pupil size is a significant predictor of image quality for non-mydriatic photographs in surveillance programs.

Harmonic Detection for Active Power Filter Based on Two-Step Improved EEMD

The performance of active power filter (APF) mainly depends on its harmonic detection method. Empirical mode decomposition (EMD) is applied to APF because of its effectiveness for any complicated signal analysis. Ensemble empirical mode decomposition (EEMD) can suppress mode mixing caused by EMD to a certain extent, but the amplitude and energy of fundamental is severely attenuated. To solve this problem, in this article, the causes of attenuation are discussed from the perspective of intrinsic mode functions (IMFs) energy, and an approach based on two-step improved EEMD is proposed. The first improved step (FI-EEMD) is to suppress the mode mixing and fundamental attenuation by injecting white noise and analytical signal with determined parameters into the target signal. The parameters of the analytical signal are selected according to the power grid conditions and signal characteristics. The second improved step (SI-EEMD) puts forward a signal reconstruction method based on the distribution of IMF energy extreme points and the distinguishing law of signal and noise to reduce the influence of noise-dominated components. The results show that the two-step improved EEMD not only has high-quality extracted fundamental with low total harmonic distortion (THD) and energy attenuation, but also has good applicability to aperiodic and nonstationary signals, which greatly improve the harmonic detection accuracy of APF.

Active particle tracking microrheology using artificial thermal noise

Passive particle-tracking microrheology (PTM) uses inherent Brownian motion of colloidal probe particles to characterize the mechanical properties of materials at micrometer and submicrometer length scales. In higher modulus materials (G* > 101 Pa), the particle experiences restricted Brownian motion such that its displacements during reasonable observation time scales drop below the spatial resolution of a typical optical microscope (∼10 nm). Thus, the passive PTM technique is generally limited to low modulus materials (G* ∼ 100 Pa). To overcome this, we have developed a form of active microrheology using electromagnetic tweezers that induce an artificial thermal noise on a superparamagnetic particle in the form of a random white noise signal. This signal imparts stochastic forces that drive resolvable displacements, which are greater than what is observed from thermal energy (kT) alone. The main advantage of this technique over traditional active microrheological methods is that the induced random motion of the particle allows one to use hydrodynamic models to obtain material functions without needing to measure a defined strain field. We implement the artificial thermal noise approach with a 35.1 Pa s Newtonian fluid and measure viscosities that are an order of magnitude higher than the typical passive PTM limit (100 Pa s).

Determination of Cramer-Rao Lower Bound (CRLB) and Minimum Variance Unbiased Estimator of a DC Signal in AWGN Using Laplace Transform

This paper presents an alternative approach for the determination of Cramer-Rao Lower Bound (CRLB) and Minimum Variance Unbiased Estimator (MVUE) using Laplace transformation. In this work, a DC signal in Additive White Gaussian Noise (AWGN) was considered. During the investigation, a number of experiments were conducted to analyze different possible outputs under different conditions, and then the patterns of the outcomes were studied. Finally closed-form expressions for the CRLB and MVUE were deduced employing the Laplace transformation. The resulting expressions showed that the proposed method has almost the same number of steps as the existing method. However, the latter requires only the knowledge of algebra to arrive at the CRLB expressions contrary to the existing approach where a strong mathematical background is required and hence making it superior over the existing method, in that sense.
 Keywords: Additive White Gaussian Noise, Cramer-Rao Lower Bound, DC-Value, Laplace transform, and Minimum Variance Unbiased Estimator (MVUE).

Ivabradine increases the high frequency gain ratio in the vagal heart rate transfer function via an interaction with muscarinic potassium channels.

Muscarinic potassium channels (I K,ACh) are thought to contribute to the high frequency (HF) dynamic heart rate (HR) response to vagal nerve stimulation (VNS) because they act faster than the pathway mediated by hyperpolarization‐activated cyclic nucleotide‐gated (HCN) channels. However, the interactions between the two pathways have not yet been fully elucidated. We previously demonstrated that HCN channel blockade by ivabradine (IVA) increased the HF gain ratio of the transfer function from VNS to HR. To test the hypothesis that IVA increases the HF gain ratio via an interaction with I K,ACh, we examined the dynamic HR response to VNS under conditions of control (CNT), I K,ACh blockade by tertiapin‐Q (TQ, 50 nM/kg), and TQ plus IVA (2 mg/kg) (TQ + IVA) in anesthetized rats (n = 8). In each condition, the right vagal nerve was stimulated for 10 min with binary white noise signals between 0–10, 0–20, and 0–40 Hz. On multiple regression analysis, the HF gain ratio positively correlated with the VNS rate with a coefficient of 1.691 ± 0.151 (×0.01) (p < 0.001). TQ had a negative effect on the HF gain ratio with a coefficient of −1.170 ± 0.214 (×0.01) (p < 0.001). IVA did not significantly increase the HF gain ratio in the presence of TQ. The HF gain ratio remained low under the TQ + IVA condition compared to controls. These results affirm that the IVA‐induced increase in the HF gain ratio is dependent on the untethering of the hyperpolarizing effect of I K,ACh.

Investigations on using white noise as a test signal for performing frequency response measurements on transformers

White noise is a random signal mathematically analogous to an impulse function in time and flat spectrum in frequency. Naturally, the white noise may be used as an alternative test signal for determining the frequency response analysis (FRA) of transformers. Such an attempt not only enhances the power of FRA testing but also enable development of an online diagnostic test method. At present, the concept of using white noise is well-defined, but the crucial knowledge of applying the same on a real-time power transformer is currently not available or at least in the public domain. The study attempts to bridge this gap between theoretical contribution and practical requirement. The mathematical concept, experimental illustrations, and onsite / field validation altogether provides a complete insight into the identified problem. In this regard, an experimental study that investigates on using white noise as a test signal in determining the frequency response of a two-winding transformer is initiated. First, the possibilities of application of theoretical and mathematical concepts of using white noise as a test signal for measuring the frequency response of winding-core assembly is verified. Following this, the white noise signal applied to the circuit model and the corresponding response is recorded and the arbitrary choice of data samples measured from the circuit model is ensured using brute-force approach. In this procedure, the number of samples are manually increased until the magnitude and natural frequencies of resonant peaks matches atleast within 2 % accuracy with conventional FRA measurements. This is performed to ensure the repeatability of the method. Later, the time and frequency dependent statistical properties of the measured signals are computed and the respective transfer function is obtained. Subsequently, the transfer function obtained from the white noise method and the respective natural frequency (tabulated) are compared with the values measured using conventional FRA method. Once this is accomplished, these findings are experimentally validated on an actual high voltage transformer.

A Hybrid WD-EEMD sEMG Feature Extraction Technique for Lower Limb Activity Recognition

Classification and analysis of surface EMG (sEMG) signals have been of particular interest due to their numerous applications in the biomedical field. They can be used for the diagnosis of neuromuscular diseases, kinesiological studies, and human-machine interaction. However, these signals are difficult to process due to their noisy nature. To overcome this problem, a hybrid of wavelet with ensemble empirical mode decomposition pre-processing technique called WD-EEMD is proposed for classifying lower limb activities based on sEMG signals in healthy and knee abnormal subjects. First, Wavelet De-noising is used for filtering out white Gaussian Noise (WGN) and unwanted signals (contribution of other muscle signals). Next, an Ensemble Empirical Mode Decomposition is used for filtering out power line interference (PLI) and baseline wandering (BW) noises, followed by extraction of a total of nine time-domain features. Finally, the performance parameters of the Linear Discriminant Analysis (LDA) classifier are calculated with a 3-fold cross-validation technique. This study involves 11 healthy and 11 individuals with a knee abnormality for three different activities: walking, flexion of the leg up (standing), and leg extension from sitting position (sitting). Different pre-processing techniques similar to that of WD-EEMD were compared. It was observed that the proposed method achieves an average classification accuracy of 90.69% and 97.45% for healthy subjects and knee abnormal subjects, respectively.

Stabilizing breathing pattern using local mechanical vibrations: comparison of deterministic and stochastic stimulations in rodent models of apnea of prematurity.

Mechanical stimulation has been shown to reduce apnea of prematurity (AOP), a major concern in preterm infants. Previous work suggested that the underlying mechanism is stochastic resonance, amplification of a subthreshold signal by stochastic stimulation. We hypothesized that the mechanism behind the reduction of apnea length may not be a solely stochastic phenomenon, and suggest that a purely deterministic, non-random mechanical stimulation could be equally as effective. Mice and rats were anesthetized, tracheostomized, and mechanically ventilated to halt spontaneous breathing. Two miniature motors controlled by a microcontroller were attached around the abdomen. Ventilation was paused, stimulations were applied, and the time to the rodent’s first spontaneous breath (T) was measured. Six spectrally different signals were compared to one another and the no-stimulation control in mice. The most successful deterministic stimulation (D) at reducing apnea was then compared to a pseudo-random noise (PRN) signal of comparable amplitude and frequency. CO2%, CO2 stabilization time (Ts), O2 saturation (SpO2%), and T were also measured. D significantly reduced T compared to no stimulation for medium and high amplitudes. PRN also reduced T, without a difference between D and PRN. Furthermore, both stimulations significantly reduced Ts with no significant differences between the respective stimulations. However, there was no effect of D or PRN on SpO2%. The lack of differences between D and PRN led to an additional series of experiment comparing the same D to a band-limited white noise (WN) signal in young rats. Both D and WN were shown to significantly reduce T, with D showing statistical superiority in reduction of apnea. We further speculate that both deterministic and stochastic mechanical stimulations induce some form of mechanotransduction which is responsible for their efficacy, and our findings suggest that mechanical stimulation may be effective in treating AOP.Supplementary InformationThe online version contains supplementary material available at 10.1007/s13534-021-00203-x.

Exponential Stability of Impulsive Stochastic Delay System Based on Razumikhin Method and Its Application to Chaos Control

In this paper, the exponential stability of a stochastic delay system with impulsive signal is considered, and stability theorem of this system is proposed based on the Lyapunov–Razumikhin method; the convergence rate is also given, which gives theoretical foundation to chaos control and synchronization using the impulsive method. Finally, the classic delay chaos system with white noise and impulsive signal is employed to verify the feasibility and effectiveness of our theorem.

Determination of CRLB and Minimum Variance Unbiased Estimator of a DC Signal in AWGN Using Laplace Transform

This paper presents an alternative approach for the determination of Cramer-Rao Lower Bound (CRLB) and Minimum Variance Unbiased Estimator (MVUE) using Laplace transformation. In this work, a DC signal in Additive White Gaussian Noise (AWGN) was considered. During the investigation, a number of experiments were conducted to analyze different possible outputs under different conditions, and then the patterns of the outcomes were studied. Finally closed-form expressions for the CRLB and MVUE were deduced employing the Laplace transformation. The resulting expressions show that the proposed method has almost the same number of steps as the existing method. However, the later requires only the knowledge of algebra to arrive at the CRLB expressions contrary to the existing approach where a strong mathematical background is required and hence making it superior over the existing method, in that sense.

3.25 kW all-fiberized and polarization-maintained Yb-doped amplifier with a 20 GHz linewidth and near-diffraction-limited beam quality.

In this paper, we demonstrate a high-power, narrow-linewidth, polarization-maintaining fiber amplifier with near-diffraction-limited beam quality. By optimizing the phase modulation signal, a nearly top-hat-shaped spectrum was generated for self-pulsing suppressing. That results in doubling the self-pulsing threshold we got from conventional white noise signal phase modulation with the same optical linewidth. Based on an optimized signal and a high power, polarization-maintaining, counter-pumped fiber amplifier, we obtain a 3.25 kW narrow-linewidth linearly polarized laser output with a linewidth of ∼20GHz, the polarization extinction ratio is about 15 dB, and the M2 is less than 1.22 at the maximum output power. To the best of our knowledge, this is the first demonstration of a narrow-linewidth, linear polarization, all-fiber amplifier with 3.25 kW laser output.

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.

Paths to caustic formation in turbulent aerosols

The dynamics of small, yet heavy, identical particles in turbulence exhibits singularities, called caustics, that lead to large fluctuations in the spatial particle-number density, and in collision velocities. For large particle, inertia the fluid velocity at the particle position is essentially a white-noise signal and caustic formation is analogous to Kramers escape. Here we show that caustic formation at small particle inertia is different. Caustics tend to form in the vicinity of particle trajectories that experience a specific history of fluid-velocity gradients, characterised by low vorticity and a violent strain exceeding a large threshold. We develop a theory that explains our findings in terms of an optimal path to caustic formation that is approached in the small inertia limit.

Shear deformation detection in smart rubber bearing (SRB) using active sensing method

Rubber bearings are one of the key components of base-isolated structures. Therefore, it is important to monitor the state in rubber bearing effectively. Based on the Smart Rubber Bearing (SRB) proposed in the previous study, this paper studied the feasibility of SRB in shear deformation detection. Theoretical analysis revealed that the SRB has considerable potential in shear deformation detection while dose not affect its original horizontal stiffness. Detection tests were carried out on a full-scale SRB with different shear deformations, and a swept signal and white noise signal were used as the detection signals. A wavelet-packet-based shear deformation index is proposed based on the tests. The test result shows that the proposed shear deformation index can accurately represent the shear deformation in SRB when the transducers are installed on the same vertical axis, and the shear deformation index decreases approximately linearly with the increase of the shear deformation in SRB.

Ivabradine augments high-frequency dynamic gain of the heart rate response to low- and moderate-intensity vagal nerve stimulation under β-blockade.

Our previous study indicated that intravenously administered ivabradine (IVA) augmented the dynamic heart rate (HR) response to moderate-intensity vagal nerve stimulation (VNS). Considering an accentuated antagonism, the results were somewhat paradoxical; i.e., the accentuated antagonism indicates that an activation of hyperpolarization-activated cyclic nucleotide-gated (HCN) channels via the accumulation of intracellular cyclic adenosine monophosphate (cAMP) augments the HR response to VNS, whereas the inhibition of HCN channels by IVA also augmented the HR response to VNS. To remove the possible influence from the accentuated antagonism, we examined the effects of IVA on the dynamic vagal control of HR under β-blockade. In anesthetized rats (n = 7), the right vagal nerve was stimulated for 10 min according to binary white noise signals between 0 and 10 Hz (V0-10), between 0 and 20 Hz (V0-20), and between 0 and 40 Hz (V0-40). The transfer function from VNS to HR was estimated. Under β-blockade (propranolol, 2 mg/kg iv), IVA (2 mg/kg iv) did not augment the asymptotic low-frequency gain but increased the asymptotic high-frequency gain in V0-10 (0.53 ± 0.10 vs. 1.74 ± 0.40 beats/min/Hz, P < 0.01) and V0-20 (0.79 ± 0.14 vs. 2.06 ± 0.47 beats/min/Hz, P < 0.001). These changes, which were observed under a minimal influence from sympathetic background tone, may reflect an increased contribution of the acetylcholine-sensitive potassium channel (IK,ACh) pathway after IVA, because the HR control via the IK,ACh pathway is faster and acts in the frequency range higher than the cAMP-mediated pathway.NEW & NOTEWORTHY Since ivabradine (IVA) inhibits hyperpolarization-activated cyclic nucleotide-gated channels, interactions among the sympathetic effect, vagal effect, and IVA can occur in the control of heart rate (HR). To remove the sympathetic effect, we estimated the transfer function from vagal nerve stimulation to HR under β-blockade in anesthetized rats. IVA augmented the high-frequency dynamic gain during low- and moderate-intensity vagal nerve stimulation. Untethering the hyperpolarizing effect of acetylcholine-sensitive potassium channels after IVA may be a possible underlying mechanism.