Quasi-periodic Signals Research Articles

Investigation of quasi periodic signals of X-Ray bursts from neutron star AXP 1E2259+586 using Fourier analysis techniques

Investigation of quasi periodic signals of X-Ray bursts from neutron star AXP 1E2259+586 using Fourier analysis techniques

Investigation of quasi periodic signals of X-Ray bursts from neutron star AXP 1E2259+586 using Fourier analysis techniques

Investigation of Quasi Periodic Oscillations (QPOs) in the spacecraft instrument signals provides significant insights towards understanding the physical processes that are taking place in the emissions of X-rays. The QPOs are the frequency oscillations which give us more and detailed information about the science of stars. Since astronomy is an observational and not experimental science; the physics of stars cannot be studied by traditional methods of changing variables. In this paper, we present how the Fourier analysis and its computational algorithm of Fast Fourier Transform (FFT) can be applied towards detection of the QPOs by generating the power-frequency curves of various x-ray bursts.To undertake this study, the science of High Energy Astrophysics (HEA) has been applied in parallel with exploration of the digital observational data from Rossi X-ray Timing Explorer (RXTE) spacecraft databases which are freely made available from NASA & ESA electronic archives. The sample data used are those of the neutron star Anomalous X-Ray Pulsar (AXP) 1E2259+586. The study involved intense computer programming using tools such as UBUNTU 10.04 OS, MATLAB 2010a UBUNTU compatible version for data visualization, HEASOFT-6.10 package with FTools and IDL software for processing of the science events.A timing analysis of QPOs has been accomplished through applying computational technique of FFT algorithm.The study reveals that FFT is a strong mathematical tool in finding QPOs of the X-ray bursts. The FFT applied on the light curve with the highest time resolution can manage to remove the background noise and detect a QPO’s signal. To detect a QPO event, the FFT must show the high power peaks above f = 100 Hz or through the 3 sigma level of normalized FFT plots which indicates a QPO when its power level is of high value. The statistical significance of QPOs can be established by fitting with a Gaussian function to determine the width and central frequency and to assess the Fourier Analysis method using a probabilistic approach of the Monte Carlo Simulation (MCS) by running random number of simulations in MATLAB computing language.The main contribution of this work is to demonstrate the strength of Fourier analysis in Digital Signal Processing (DSP) and show the extent on which it can be applied in analyzing spacecraft data. The software and technical challenges have been raised to promote support for researchers in developing countries.Keywords: Fourier Analysis, FFT, QPO,X-Ray:burst,Star: neutron, Pulsar: AXP 1E2259+586

Arterial blood pressure monitoring by active sensors based on heart rate estimation and pulse wave pattern prediction

This paper presents the results of development of a novel method for measuring nonstationary quasi-periodic biomedical signals, in particular, the arterial blood pressure pulse signal. It has been demonstrated that the proposed method for compensation tracing of dynamic signals suggests not only smart, but also active sensors. In connection with this, a major part of the introduction is devoted to expanding the conception of smart sensors to the paradigm of active sensors. Further, following the introduction on the background of the question, a brief description of the functioning principles and some design features of the active sensor developed by us are given. The results of the sensor test and calibration are discussed, and the necessity of its complicated control is substantiated. The remaining part of the paper is devoted to possible ways of development of this control and the way that we have chosen to control the active sensor of arterial blood pressure. The principle of controlling compensation of a pulse pressure based on prediction of pulse wave patterns is discussed and substantiated. The final part is devoted to technical matters of formation of dynamic patterns using multiscale correlation analysis of a current local period of heart contractions.

Testing Rayleigh–Schuster hodographs using time series models and earthquake flows

The paper considers features and peculiarities of Rayleigh−Schuster hodographs designed for detailed investigation of changes in the phase of quasiperiodic signals in time series. The method allows a researcher to estimate the statistical significance of analyzed periodicities and visualize a change in the signal phase. The method is tested using various models, in particular, flows of random events, earthquake flows, periodic signals, and noise-contaminated periodic signals of earthquake flows. The equations for estimating errors in the resulting vector phase are given. It is clearly demonstrated that the hodographs of random signals can in some cases be similar to nonrandom ones. This effect contradicts intuitive concepts and creates the illusion of nonrandom signals. Possible causes of the phenomenon are discussed. A methodology for hodograph analysis ensuring a more feasible interpretation is proposed.

New application of wavelets in magnetotelluric data processing: reducing impedance bias

Magnetotelluric (MT) data consist of the sum of several types of natural sources including transient and quasiperiodic signals and noise sources (instrumental, anthropogenic) whose nature has to be taken into account in MT data processing. Most processing techniques are based on a Fourier transform of MT time series, and robust statistics at a fixed frequency are used to compute the MT response functions, but only a few take into account the nature of the sources. Moreover, to reduce the influence of noise in the inversion of the response functions, one often sets up another MT station called a remote station. However, even careful setup of this remote station cannot prevent its failure in some cases. Here, we propose the use of the continuous wavelet transform on magnetotelluric time series to reduce the influence of noise even for single site processing. We use two different types of wavelets, Cauchy and Morlet, according to the shape of observed geomagnetic events. We show that by using wavelet coefficients at clearly identified geomagnetic events, we are able to recover the unbiased response function obtained through robust remote processing algorithms. This makes it possible to process even single station sites and increase the confidence in data interpretation.

A numerical method for computing initial conditions of Lagrangian invariant tori using the frequency map

We present a numerical method for computing initial conditions of Lagrangian quasi-periodic invariant tori of Hamiltonian systems and symplectic maps. Such initial conditions are found by solving, using the Newton method, a nonlinear system obtained by imposing suitable conditions on the frequency map. The basic tool is a newly developed methodology to perform the frequency analysis of a discrete quasi-periodic signal, allowing to compute frequencies and their derivatives with respect to parameters. Roughly speaking, this method consists in computing suitable weighted averages of the iterates of the signal and using the Richardson extrapolation method. The proposed approach performs with high accuracy at a moderate computational cost. We illustrate the method by considering a discrete FPU model and the vicinity of the point L4 in a RTBP.

A Unified Approach to the Sensitivity and Variability Physics-Based Modeling of Semiconductor Devices Operated in Dynamic Conditions—Part I: Large-Signal Sensitivity

We present here and in the companion paper (Part II) a general framework for the modeling of semiconductor device variability through the physics-based analysis of the small-change sensitivity. We consider a very general class of dynamic device operation, i.e., the periodic or quasi-periodic large signal (LS) time-varying regime, and we evaluate the sensitivity of both dc and harmonic components of the device dynamic working point with respect to process or physical device parameters. The proposed technique is based on the linearization of the physics-based device model around a nominal parameter, and extends to the dynamic case the already established Green’s function approach to the numerically efficient dc sensitivity analysis. As an example of application, we consider a class A GaAs MESFET microwave power amplifier; the sensitivity of the LS working point with respect to doping and gate work function variations is evaluated through the proposed approach and compared with the result of repeated LS amplifier analyses, showing that the numerically efficient small-change sensitivity approach provides reliable predictions for parameter variations up to 10% of the nominal value.

Studying dynamic chaos in microwave ring generators based on normally magnetized ferromagnetic film

We present results of an experimental investigation of the transition to a microwave dynamic chaos regime in ring oscillators based on normally magnetized yttrium iron garnet (YIG) films. It is established that an increase in the ring gain leads to the sequential generation of monochromatic, periodic, quasi-periodic, and chaotic signals. The quasi-periodic regime is characterized by the appearance of secondary modulation of the signal amplitude. In the regime of dynamic chaos generation, the parameters can be controlled by gain of the ring.

Theoretical model and simulation of ship underwater radiated noise

Ship underwater radiated noise is one of the most important ocean ambient noise sources, and building a reasonable model for the ship underwater radiated noise is helpful for understanding the physical mechanism and reducing research cost of ship underwater radiated noise. The quasi-periodic random sound pulse sequence signals act well in explaining the rhythm and the power spectrum variation of the ship underwater radiated noise, and reveal that there are not any real sinusoidal components in ship radiated noise signals, which come from the non-linear transformation of the signals, and the analysis of some representative experimental data of ship radiated noise also supports this idea. Based on this, the explosion-type cosine pulses are used as the units of quasi-periodic random sound pulse sequences. This model can generate the power spectrum with a peak, and the peak location can change with ship velocity or ship type. The power spectrum variation characteristics of quasi-periodic random sound pulse sequences consisting of the explosion-type cosine pulses are in good agreement with the measured ship underwater radiated noise data, which shows that this model is of important practical value.

Improvement of robustness and stability in estimating Rayleigh–Schuster’s hodograph parameters using different procedures of vector normalization

This paper deals with Rayleigh–Schuster’s hodographs, intended for the detailed investigation of changes in the phase of quasiperiodic signals in time series. The hodographs are also known as the phasor-walkout method. A procedure of conditional vector normalization is proposed: it takes into account the vector amplitude for each period under consideration. The procedure considerably improves the robustness and stability of the hodograph approach to changes in the character of the processed data distributions and to various defects in the data. For example, when analyzing the earthquake catalog, the procedure strongly diminishes the influence of the event clustering caused, in particular, by swarms of earthquakes with comparable magnitude and the aftershock sequences of strong earthquakes. At the first stage, we calculate the vector sums (resulting vectors) for each period under investigation throughout the time series duration. For example, investigating diurnal periodicity of earthquakes, we first calculate the resulting vectors for each day of the observation. The further analysis of resulting vectors for each period throughout the time series duration can be performed with different procedures. We compare three procedures for normalization of the obtained resulting vectors, which are as follows: (1) th traditional one, preserving the real signal amplitude; (2) that with reduction of the obtained resulting vectors to the unit vector (phasor); and (3) that with conditional vector normalization, taking into account the amplitude of resulting vectors for each period throughout the time series duration. The third procedure diminishes the possible instability in some special distributions of the investigated data when the resulting vector for a period is close to zero. The procedures are compared using model signals and samples from real earthquake catalogs. All the procedures used give close results when processing random time series.

Coherent network analysis of gravitational waves from three-dimensional core-collapse supernova models

Using predictions from three-dimensional (3D) hydrodynamics simulations of core-collapse supernovae (CCSNe), we present a coherent network analysis to detection, reconstruction, and the source localization of the gravitational-wave (GW) signals. We use the {\tt RIDGE} pipeline for the analysis, in which the network of LIGO Hanford, LIGO Livingston, VIRGO, and KAGRA is considered. By combining with a GW spectrogram analysis, we show that several important hydrodynamics features in the original waveforms persist in the waveforms of the reconstructed signals. The characteristic excess in the spectrograms originates not only from rotating core-collapse, bounce and the subsequent ring down of the proto-neutron star (PNS) as previously identified, but also from the formation of magnetohydrodynamics jets and non-axisymmetric instabilities in the vicinity of the PNS. Regarding the GW signals emitted near at the rotating core bounce, the horizon distance extends up to $\sim$ 18 kpc for the most rapidly rotating 3D model in this work. Following the rotating core bounce, the dominant source of the GW emission shifts to the non-axisymmetric instabilities. The horizon distances extend maximally up to $\sim$ 40 kpc seen from the spin axis. With an increasing number of 3D models trending towards explosion recently, our results suggest that in addition to the best studied GW signals due to rotating core-collapse and bounce, the time is ripe to consider how we can do science from GWs of CCSNe much more seriously than before. Particularly the quasi-periodic signals due to the non-axisymmetric instabilities and the detectability should deserve further investigation to elucidate the inner-working of the rapidly rotating CCSNe.

Averaging of nonlinearly aligned signal cycles for noise suppression

Abstract Averaging of nonlinearly aligned (time-warped) signal cycles is an important method for suppressing noise of quasi-periodical or event related signals. However, in the paper we show that the operation of time warping introduces unfavorable violation of the requirements that should be satisfied for effective averaging and, as a result, it causes poor suppression of noise. To limit these effects, we redefine the matrix of the alignment costs. To improve results of averaging in cases of variable energy noise, we apply weighting of the summed signal samples. The derived formula gives smaller weights for more noisy signal cycles and this way limits their influence on the constructed template. The proposed modifications caused a significant increase of the Noise Reduction Factor (NRF) in the experiments on the simulated evoked potentials. Whereas the greatest NRF obtained by the reference methods in nonstationary white noise environment was equal to 1.55, for the new method proposed we achieved a value of 4.44. For non-stationary colored noise, the corresponding values were 1.44 and 2.99. Moreover, application of the developed method to ECG signal processing, prior to the measurements of the QT interval, significantly improved the measurements immunity to noise.

Hilbert–Huang Transform Approach to Lorenz Signal Separation

This study uses the Hilbert–Huang transform (HHT), a signal analysis method for nonlinear and non-stationary processes, to separate signals of varying frequencies in a nonlinear system governed by the Lorenz equations. Similar to the Fourier series expansion, HHT decomposes a data time series into a sum of intrinsic mode functions (IMFs) using empirical mode decomposition (EMD). Unlike an infinite number of Fourier series terms, the EMD always yields a finite number of IMFs, whose sum is equal to the original time series exactly. Using the HHT approach, the properties of the Lorenz attractor are interpreted in a time–frequency frame. This frame shows that: (i) the attractor is symmetric for [Formula: see text] (i.e. invariant for [Formula: see text]), even though the signs on [Formula: see text] and [Formula: see text] are changed; (ii) the attractor is sensitive to initial conditions even by a small perturbation, measured by the divergence of the trajectories over time; (iii) the Lorenz system goes through “windows” of chaos and periodicity; and (iv) at times, a system can be both chaotic and periodic for a given [Formula: see text] value. IMFs are a finite collection of decomposed quasi-periodic signals, starting from the highest to lowest frequencies, providing detection of the lower frequency signals that may have otherwise been “hidden” by their higher frequency counterparts. EMD decomposes the original signal into a family of distinct IMF signals, the Hilbert spectra are a “family portrait” of time–frequency–amplitude interplay of all IMF members. Together with viewing the IMF energy, it is easy to discern where each IMF resides in the spectra in relation to one another. In this study, the majority of high amplitude signals appear at low frequencies, approximately 0.5–1.5. Although our numerical experiments are limited to only two specific cases, our HHT analyses of time–frequency, marginal spectra, and energy and quasi-periodicity of each IMF provide a novel approach to exploring the profound and phenomena-rich Lorenz system.

DFT Spectrum-Sparsity-based Quasi-Periodic Signal Identification and Application

This study addresses identification of the quasi-periodic sequence based on the discrete Fourier transform spectrum-sparsity. A quasi-periodic signal displays similarities to a periodic signal but ...

Estimation of the instantaneous signal parameters using a modified Prony’s method

A method for approximation of an arbitrary continuous function in the neighborhood of a given point by complex exponential functions (exponentials) is described. The method is similar to the Taylor series to the effect that approximation is performed by the derivatives at the given point. Determination of parameters of the exponentials is made on the basis of a modified Prony’s method. It is shown that the method makes it possible to simulate the local behavior of periodic and quasiperiodic processes more effectively than a Taylor series. An algorithm for estimating the instantaneous parameters of the single-component quasiperiodic continuous signals is obtained. The relation to a known energy separation algorithm (ESA) is shown. A separate algorithm for discrete signals by using finite differences is obtained. The applicability of the algorithm for practical analysis of discrete signals with consideration of the influence of additive noise on the accuracy of the parameter estimates is investigated. Experimental comparison of the algorithm with the known methods of estimating instantaneous parameters on the basis of the Prony’s method and ESA is performed.

English

Quasi-periodic signals can be contaminated with random distortions (“artifacts”) not manifested periodically and homogenously,without affecting all signal cycles.These distortions cannot be characterized statistically or modelled with a known probability function. In this paper, a stochastic analysis method to detect the presence of such distortions is proposed. The aim of the method is identifying the affected cycles, which exhibit a different morphology compared to the unaffected cycles.The identification of the affected cycles (or non-homogeneous cycles) allows to estimate parameters and extract the useful information needed for a correct characterization of the signal.The method compares nearly periodic signal cycles through the mean square error and the estimated variance of the inherent noise affecting the signal. Expressions are derived to estimate this error and compared with experimental results.

Classification of periodic, chaotic and random sequences using approximate entropy and Lempel–Ziv complexity measures

‘Complexity’ has several definitions in diverse fields. These measures are indicators of some aspects of the nature of the signal. Such measures are used to analyse and classify signals and as a signal diagnostics tool to distinguish between periodic, quasiperiodic, chaotic and random signals. Lempel–Ziv (LZ) complexity and approximate entropy (ApEn) are such popular complexity measures that are widely used for characterizing biological signals also. In this paper, we compare the utility of ApEn, LZ complexities and Shannon’s entropy in characterizing data from a nonlinear chaotic map (logistic map). In this work, we show that LZ and ApEn complexity measures can characterize the data complexities correctly for data sequences as short as 20 in length while Shannon’s entropy fails for length less than 50. In the case of noisy sequences with 10% uniform noise, Shannon’s entropy works only for lengths greater than 200 while LZ and ApEn are successful with sequences of lengths greater than 30 and 20, respectively.

A study of the middle time-scale periodic behavior of light curve of BL Lac object OJ287

In this paper, we collect the 37 years' data observed for BL Lac object OJ287 in the optical band, and construct its light curve from 1972 to 2009. Using the method of Lomb-Scargle Fourier transform, we analyze the middle time-scale periodic behavior and discover the primary periodic compositions of 52.0±1.1 day and 255±23 day. Then, we simulate the quasi-periodic signal of period doubling bifurcations and compare it with the observation data at different time-interval in their phase diagram and correlation dimension. Result indicates that OJ287 has multi-period scale features. At different time-intervals, there are different harmonic period components in the quasi-periodic light curve. Variation of harmonic period component is related with the disturbance of accretion flow which is from the secondary black hole to the primary black hole, and the periodicity variability may bifurcate the harmonic period component when the primary accretion flow is influenced by a strong disturbance.

Two-Dimensional Warping for One-Dimensional Signals—Conceptual Framework and Application to ECG Processing

We propose a novel method for evaluating the similarity between two 1d patterns. Our method, referred to as two-dimensional signal warping (2DSW), extends the basic ideas of known warping techniques such as dynamic time warping and correlation optimized warping. By employing two-dimensional piecewise stretching 2DSW is able to take into account inhomogeneous variations of shapes. We apply 2DSW to ECG recordings to extract beat-to-beat variability in QT intervals (QTV) that is indicative of ventricular repolarization lability and typically characterised by a low signal-to-noise ratio. Simulation studies show high robustness of our approach in presence of typical ECG artefacts. Comparison of short-term ECG recorded in normal subjects versus patients with myocardial infarction (MI) shows significantly increased QTV in patients (normal subject 2.36 ms ± 1.05 ms vs. MI patients 5.94 ms ± 5.23 ms (mean ± std), ). Evaluation of a standard QT database shows that 2DSW allows highly accurate tracking of QRS-onset and T-end. In conclusion, the two-dimensional warping approach introduced here is able to detect subtle changes in noisy quasi-periodic biomedical signals such as ECG and may have diagnostic potential for measuring repolarization lability in MI patients. In more general terms, the proposed method provides a novel means for morphological characterization of 1d signals.

Gear Fault Diagnosis Based on Continuous Wavelet Spectrum Slice

Analysis the common gear fault signal, using continuous wavelet transform well time-frequency characteristics and failure mechanism gear features, combined with quasi-periodic signal rotary mechanical characteristics of the continuous wavelet transform fault signal. This method can reduce the noise source and other incentives interference, remove the specific needs of the signal to improve signal stripping effect, the use of a certain type of gear failures this step, to get a clear diagnosis results show that this method has proven a strong application space.