Periodic Signal Research Articles

On the estimation of periodic signals in the diffusion process using a high-frequency scheme

Abstract The estimation of the frequency component is very interesting to study, considering its unique nature when these parameters are together in their amplitude. The periodicity of the frequency components is also thought to affect the convergence of these parameters. In this paper, we consider the problem of estimating the frequency component of a periodic continuous-time sinusoidal signal. Under the high-frequency sampling setting, we provide the frequency components’ consistency and asymptotic normality. It is observed that the convergence rate of the continuous-time sinusoidal signal of the diffusion process is the same as the continuous-time sinusoidal signal of the Ornstein–Uhlenbeck process, which is mentioned in [G. Pramesti, Parameter least-squares estimation for time-inhomogeneous Ornstein–Uhlenbeck process, Monte Carlo Methods Appl. 29 (2023), 1, 1–32]. The result of this study deduces that the convergence rate of the frequency is the same as long as the signal is periodic. In this case, the existence of the rate of reversion does not affect the convergence rate of the frequency components. Further, the result of the study, that is, the convergence rate of the frequency is ( n ⁢ h ) 3 \sqrt{(nh)^{3}} , also revised the previous one in [G. Pramesti, The least-squares estimator of sinusoidal signal of diffusion process for discrete observations, J. Math. Comput. Sci. 11 (2021), 5, 6433–6443], which mentioned ( n ⁢ h ) 3 ⁢ h \sqrt{(nh)^{3}h} . The proposed approach is demonstrated with a ten-minute sampling rate of real data on the energy consumption of light fixtures in one Belgium household.

Local electrical characteristic of memristor structure in a high-resistance state obtained using electrostatic force microscopy: Fractal and multifractal dynamics of surface

A heterostructure BiFeO3/TiO2(Nt)Ti (BFOT) was obtained by the atomic layer deposition (ALD) method. After thermal treatment, the redistribution of Fe/Ti atoms forms an Aurivillius intermediate layered phase, and local charge capture centers are formed in the sample. Due to cationic non-stoichiometry, the BFO film exhibits p-type conductivity, while the nanotubes exhibit n-type conductivity due to oxygen vacancies. It was observed that lateral displacement of the sample can lead to ferroelectric switching, which can, in turn, affect the transition of the memristive structure from high-resistance (HRS) to low-resistance states (LRS). The hysteresis suppression tends to transition to an ohmic character and depends on the amplitude, frequency, and duration of the periodic signal. It has been found that compensation of static charge during resistive switching can affect the transport properties of the material. Fractal dimension analysis showed an acceleration of structure restructuring with increasing voltage, possibly contributing to the transition from an insulator to a metal in certain areas of the film volume. The joint analysis of piezoresponse force microscopy (PFM), electrostatic force microscopy (EFM), and fractal/multifractal dynamics showed a correlation between surface static charge and piezopotential. The new methodology described in this work can help understand the resistive switching processes in ferroelectric/semiconductor memristive structures.

Metastable oscillations in an evolutionary game: Synchronization and control

Evolutionary games with a finite number of players may manifest transient oscillatory dynamics before reaching an absorbing state. Such oscillations could be prone to synchronization, however its details and specific properties are not known. Here, we investigate synchronization of metastable oscillations in the finite-dimensional evolutionary game “Battle of the Sexes”, as well as the possibility of controlling the properties of these oscillations by a multiplicative periodic signal. The appropriately generalized frequency and phase quantifiers demonstrate the possibility of synchronization, and the asymmetry of frequency range, induced by the finite size of population. Evolution of oscillations under strengthening periodic driving depends on whether synchronization is reached: in the synchronous regime the amplitude of oscillations grows, while their lifetime decreases, whereas in the asynchronous regime their amplitude decays to zero with the quasi-stationary distribution becoming unimodal.

Enhanced symplectic Ramanujan mode pursuit and its application in mechanical composite fault diagnosis

In practical engineering applications, traditional signal decomposition methods are often affected by various factors such as strong noise, alternating periods, etc. When signal mode analysis is conducted, it is often found that the decomposition results do not meet engineering requirements. To address these issues, Enhanced Symplectic Ramanujan Mode Pursuit (ESRMP) method is proposed in this paper, which aims to improve the accuracy and reliability of signal decomposition and period estimation. First, the cyclic symplectic geometry similarity transform is used to separate the components of different modes in the signal, and the anti-noise autocorrelation function is used to estimate the period of different components. Then, the rectangular length of the intercepted signal is determined based on the estimated period, and the periodic compensation is achieved through related detection and cubic spline interpolation. Finally, the reconstructed signal is projected onto the Ramanujan subspace to extract and enhance periodical pulses. The experimental results of multimodal composite fault signals show that the ESRMP method can accurately separate components of different modes, especially periodic pulse signals.

Detecting a periodic signal by a population of spiking neurons in the weakly nonlinear response regime

Motivated by experimental observations, we investigate a variant of the cocktail party problem: the detection of a weak periodic stimulus in the presence of fluctuations and another periodic stimulus which is stronger than the periodic signal to be detected. Specifically, we study the response of a population of stochastic leaky integrate-and-fire (LIF) neurons to two periodic signals and focus in particular on the question, whether the presence of one of the stimuli can be detected from the population activity. As a detection criterion, we use a simple threshold-crossing of the population activity over a certain time window. We show by means of the receiver operating characteristics (ROC) that the detectability depends only weakly on the time window of observation but rather strongly on the stimulus amplitude. Counterintuitively, the detection of the weak periodic signal can be facilitated by the presence of a strong periodic input current depending on the frequencies of the two signals and on the dynamical regime in which the neurons operate. Beside numerical simulations of the model, we present an analytical approximation for the ROC curve that is based on the weakly nonlinear response theory for a stochastic LIF neuron.Graphic abstract

A combination of annual and nonannual forces drive respiratory disease in the tropics

IntroductionIt is well known that influenza and other respiratory viruses are wintertime-seasonal in temperate regions. However, respiratory disease seasonality in the tropics is less well understood. In this study, we...

A Lack of 9 s Periodicity in the Follow-up NuSTAR Observation of LS 5039

The Nuclear Spectroscopic Array (NuSTAR) observed the gamma-ray binary LS 5039 for a second time in order to check for the presence of a periodic signal candidate found in the data from the previous NuSTAR observation. We do not detect the candidate signal in the vicinity of its previously reported frequency, assuming the same orbital ephemeris as in our previous paper. This implies that the previously reported periodic signal candidate was a noise fluctuation. We also perform a comparison of the lightcurves from the two NuSTAR observations and the joint spectral fitting. Our spectral analysis confirms the phase dependence found from a single NuSTAR observation at a higher significance level.

Analytic and directional wavelet packets in the space of periodic signals

Analytic and directional wavelet packets in the space of periodic signals

A Universal Digital Lock-in Amplifier Design for Calibrating the Photo-Detector Responses with Standard Black-Bodies.

The lock-in amplifier (LIA) is widely utilized to detect ultra-weak optical periodic signals based on the phase-sensitive and enhanced detecting theory. In this paper, we present an all-digital and universal embedded LIA platform that accurately and conveniently describes the spectrum generated by standard black bodies at various temperatures with different optical detectors. The proposed design significantly reduces the complexity and cost of traditional analog LIAs while maintaining accuracy. The LIA components are implemented using a single field programmable gate array (FPGA), offering flexibility to modify parameters for different situations. The normalized mean-square error (NMSE) of the captured spectra in the experiments is within 0.9% compared the theoretical values.

Analysis and Synthesis of Guitar Sounds with Hammer on Strumming Technique

This research aims to analyze and synthesize periodic signals derived from guitar string plucking with hammer-on technique. This research has three stages, namely the data collection stage, the analysis stage, and the synthesis stage. The guitar string was plucked with a tension of 2.5 N and recorded using a sound sensor connected to PASCO Capstone software. The data used has two variations, namely the sound signal of a hammer-on pluck with a half tone increase and a one tone increase. Data analysis was carried out using MATLAB software to obtain deviation graphs as a function of frequency, damping coefficient values, and frequency spectra. The results showed that after hammer-on the amplitude of the tone decreased drastically as the mass per unit length of the string decreased. The initial tone before the hammer-on will appear in the tone after the hammer-on with a lower amplitude as the mass per unit length of the string increases. The synthesis of guitar sounds with this technique is done by combining the individual tones obtained and adjusting the time interval and amplitude according to the literature data

Improved sliding mode observer based repetitive control for linear systems with time‐varying input and state delays

SummaryControl systems are frequently subject to the negative effects of time delays and disturbances, which diminish the systems' tracking performance. In response to these challenges, this paper presents a novel approach, that is, the improved sliding mode observer based repetitive control (ISMO‐RC), to enhance the system's periodic signal tracking in the presence of the input and state time delays and the input disturbances. The design takes the advantages of RC and ISMO, in which RC effectively compensates periodic signals, while ISMO compensates both aperiodic disturbances and the time‐varying input and state delays. The stability of the whole system is guaranteed via the linear matrix inequality (LMI) and the Lyapunov–Krasovskii functional analysis. The proposed controller is evaluated through extensive simulations and experiments, which demonstrate its superiority over comparative control methods.

Implementation of [formula omitted]-Interval fourier transform analysis - Application to compound action potentials

N-Interval Fourier Transform Analysis (N-FTA) allows for spectral separation of a periodic target signal from uncorrelated background interference. A N-FTA pseudo-code is presented. The spectral resolution is defined by the repetition rate of the near periodic signal. Acceptance criteria for spectral targets were defined such that the probability of accepting false positives is less than 1500. Simulated and recorded neural compound action potentials (CAPs) were investigated. Simulated data allowed for comparison with reference solutions demonstrating the stability of N-FTA at conditions being comparable to real world data. Background activity was assessed with small errors. Evoked target components were assessed down to power spectral density being approximately N times below the background level. Validation was completed investigating a measured CAP. In neurophysiological recordings, this approach allows for accurate separation of near periodic evoked activity from uncorrelated background activities for frequencies below 1kHz.•N-FTA allows for spectral separation of a periodic target signal from uncorrelated interference by analyzing a segment containing N target signal repetitions.•A MATLAB implementation of the algorithm is provided along with simulated and recorded data.•N-FTA was successfully validated using simulated and measured data for CAPs.

A Fourier-based explanation of 1D-CNNs for machine condition monitoring applications

Neural networks (NN) have generated extensive interest in the field of machine condition monitoring (MCM). Many applications are however adapting structures and approaches from fields where NNs are highly established (e.g., image classification). This is done despite many neural network layers presenting strong similarities to signal processing steps that are well established in MCM. This paper aims at providing a mathematical analysis of typical NN architectures and layers, with specific attention to similarities to common signal processing steps such as filtering, downsampling, and enveloping. The set of strong analogies between NN and traditional MCM tools enables this work to provide MCM-specific guidelines for the design and tuning of NN architectures for MCM-specific applications. Most MCM applications are often characterised by periodic and cyclostationary signals, a situation not frequently encountered in many other NN applications. Hence, the Fourier-based explanation of the typical NN layers will be specific to the solution of typical MCM problems (e.g., diagnostics of gears and bearings). The study is aligned with the current trends of explainable AI and physics informed neural networks (PINN), in the sense that it aims at producing mathematical rules for a rational design of the network, drawing on the expertise accumulated in decades of signal processing for MCM. This is however done without upsetting traditional NN architectures, but rather trying to provide clear reasons for the setting of network parameters. The analytical work will be verified with numerical tests, which will also enable practical considerations, and by application of the suggested guidelines to the popular Case Western Reserve University (CWRU) experimental dataset.

Solaris photometric survey: Search for circumbinary companions using eclipse timing variations

ABSTRACT Eclipse timing variations (ETVs) have been a successful tool for detecting circumbinary companions to eclipsing binaries (EBs). While TESS and Kepler have been prolific for ETV searches, they sometimes can be limited by time and sky coverage, a limitation that can be addressed by specialized ground-based ETV surveys. We present the initial results from the Solaris photometric survey, which uses four 0.5-m robotic telescopes in the Southern hemisphere to look for circumbinary companions. We present the method of light-curve extraction, detrending, and EB modelling using observations from the Solaris network. Using these light curves, we extract precise eclipse timings for seven EBs and look for companions using a Lomb–Scargle periodogram search. We find two possible periodic signals for the target GSC 08814–01026. With the system having strong activity, we check for the feasibility of orbital solutions at these two periods. We find that the 245 ± 1 d period is due to an M dwarf-mass companion. This makes GSC 08814–01026 a candidate compact hierarchical triple system. The other periodic signal at 146 ± 1 d is an artefact of stellar activity.

Search for periodic signals in the dielectron and diphoton invariant mass spectra using 139 fb−1 of pp collisions at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV with the ATLAS detector

A search for physics beyond the Standard Model inducing periodic signals in the dielectron and diphoton invariant mass spectra is presented using 139 fb−1 of s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV pp collision data collected by the ATLAS experiment at the LHC. Novel search techniques based on continuous wavelet transforms are used to infer the frequency of periodic signals from the invariant mass spectra and neural network classifiers are used to enhance the sensitivity to periodic resonances. In the absence of a signal, exclusion limits are placed at the 95% confidence level in the two-dimensional parameter space of the clockwork gravity model. Model-independent searches for deviations from the background-only hypothesis are also performed.

RECOGNITION OF REFERENCE SIGNALS AND DETERMINATION OF THEIR WEIGHTING COEFFICIENTS IF AN ADDITIVE INTERFERENCE PRESENTS

Context. The subject matter of the article is the recognition of a reference signal in the presence of additive interference.
 Objective. The recognition of the reference signal by the obtained value of its weighting factor in conditions where additive interference is imposed on the spectrum of the reference signal at unknown random frequencies. The task is the development of a method for recognizing a reference signal for the case when the interference consists of an unknown periodic signal that can be represented by a finite sum of basis functions. In addition, interference may also include deterministic signals from a given set with unknown weighting coefficients, which are simultaneously transmitted over the communication channel with the reference signal.
 Method. The method of approximating the unknown periodic component of the interference by the sum of basis functions is used. The current number of values of the signal that enters the recognition system depends on the number of basis functions. This signal is the sum of the basis functions and the reference signal with unknown weighting coefficients. To obtain the values of these coefficients, the method based on the properties of the disproportion functions is used. The recognition process is reduced to the calculation of the weight coefficient of the reference signal. If it is zero, it indicates that the reference signal is not part of the signal being analyzed. The recognition system is multi-level. The number of levels depends on the number of basis functions.
 Results. The obtained results show that, provided that the reference signal differs by at least one component from the given set of basis functions, the recognition is successful. The given examples show that the system recognizes the reference signal even in conditions where the weighting coefficient of the interference is almost 1000 times greater than the coefficient for the reference signal. The recognition system also works successfully in conditions where the interference includes the sum of deterministic signals from a given set, which are simultaneously transmitted over the communication channel.
 Conclusions. The scientific novelty of the obtained results is that a method for recognizing the reference signal has been developed in conditions where only an upper estimate of its maximum frequency is known for the periodic component of the interference. Also, recognition occurs when, in addition to unknown periodic interference, the signals from a given set with unknown weighting coefficients are superimposed on the reference signal. In the process of recognition, in addition to the weighting factor for the reference signal, the factors for the interference components are also obtained.

Research and application of composite stochastic resonance in enhancement detection

Aiming at the problem that the intermediate potential part of the traditional bistable stochastic resonance model cannot be adjusted independently, a new composite stochastic resonance (NCSR) model is proposed by combining the Woods–Saxon (WS) model and the improved piecewise bistable model. The model retains the characteristics of the independent parameters of WS model and the improved piecewise model has no output saturation, all the parameters in the new model have no coupling characteristics. Under α stable noise environment, the new model is used to detect periodic signal and aperiodic signal, the detection results indicate that the new model has higher noise utilization and better detection effect. Finally, the new model is applied to image denoising, the results showed that under the same conditions, the output peak signal-to-noise ratio (PSNR) and the correlation number of NCSR method is higher than that of other commonly used linear denoising methods and improved piecewise SR methods, the effectiveness of the new model is verified.

Probable low-frequency quasi-periodic oscillations in blazars from the ZTF survey

ABSTRACT We investigate the possible presence of quasi-periodic oscillation (QPO) signals in 2103 blazars from the Zwicky Transient Facility (ZTF) time-domain survey. We detect a low-frequency QPO signal in five blazars observed over these 3.8-yr-long optical r-band ZTF light curves. These periods range from 144 to 196 d detected at ≳4σ significance levels in both the Lomb–Scargle periodogram and weighted wavelet Z-transform analyses. We find consistent results using the phase dispersion minimization technique. A similar peak is detected in the g-band light curves at a slightly lower significance of 3σ. Such nearly periodic signals on these time-scales in optical wavebands most likely originate from a precessing jet with high Lorentz factor, closely aligned to the observer’s line of sight or the movement of plasma blobs along a helical structure in the jet.

Impact of Non-Gaussian Noise and Time Delay on Stability and Stochastic Resonance for a FitzHugh-Nagumo Neural System Subjected to a Multiplicative Periodic Signal

In this paper, we focus on the investigations on the stochastic stability and the stochastic resonance (SR) phenomena for a FitzHugh-Nagumo system with time delay induced by a multiplicative non-Gaussian colored noise and an additive Gaussian colored noise. By use of the fast descent method, the unified colored noise approximation and the two-state theory for the SR, the stationary probability density function (SPDF) and the signal-to-noise ratio (SNR) caused by different noise terms and time delay are explored. The investigation results indicate that the two noise intensities, time delay and the departure parameter from the Gaussian noise can all reduce the probability density around the two stable states and destroy the stability of the neural system; while the two noise correlation times [Formula: see text] and [Formula: see text] can both improve the probability density around both stable states and reinforce the biological stability of the neural system. As regards the SNR, it is found that the two noise intensities and the departure coefficient can all weaken the SR effect, while time delay [Formula: see text] and the correlation time [Formula: see text] of the multiplicative noise will always magnify the SR phenomenon. It is worth to mention that the correlation time [Formula: see text] of the additive noise can stimulate the SR effect, but not alter the maximum of the SNR.

Disturbance attenuation for neutral Markovian jump systems with multiple delays

The work explores the study of a neutral Markovian jump system that contains multiple delays, external disturbances, and unknown non-linear uncertainties. To overcome the tracking problem, a modified repetitive controller infused with the higher equivalent-input-disturbance approach and the extended Smith predictor approach is suggested. To guarantee the mean-square asymptotic stability of the system, an appropriate mode-dependent loop-based Lyapunov–Krasovskii functional is used. The proposed controller explicitly forces the system output and accurately follows any supplied periodic reference signal. Subsequently, the efficiency of the recommended technique is demonstrated with the simulations that validate the outcomes by comparing them to the existing results.