Damped Sinusoids Research Articles

REAL-VALUED DAMPED SINUSOID PARAMETER ESTIMATION USING A THREE-POINT INTERPOLATED DISCRETE FOURIER TRANSFORM ALGORITHM

This paper proposes new real-valued damped sinusoid frequency and damping factor estimators. They exploit a three-point Interpolated discrete Fourier transform (IpDFT) algorithm based on the Rife-Vincent class I (RVCI) windows and complex-valued DFT samples. The accuracies of the proposed estimators are compared with those provided by other state-of-the-art interpolated Fourier algorithms using computer simulations when pure, noisy, and noisy and harmonically distorted damped sinusoids are analyzed.

Frequency and damping factor estimation of damped sinusoid by using DFT and DTFT

An algorithm for estimating the frequency and damping factor of damped complex sinusoidal signal is presented. After the rough estimation of frequency by discrete Fourier transform (DFT), the fine estimation of frequency and damping factor is achieved by utilizing the DFT bin with the maximum magnitude and two arbitrarily spaced discrete time Fourier transform (DTFT) spectral lines located on the same side of the maximum DFT spectrum bin. Then the theoretical mean square error (MSE) in additive white noise is analyzed. Simulation results show that the proposed algorithm tracks the Cramer-Rao lower bound (CRLB), and the parameters estimation accuracy is higher than the competing algorithms in most situations. The computational requirements are almost the same as several existing methods.

Features of distribution of electric field strength and current density in the reactor during treatment of liquid media with high-voltage pulse discharges

Purpose. Development and use of a mathematical model of the stages of formation of high-voltage pulse discharges in gas bubbles in the discharge gap «rod-plane» to identify the features of the electric field intensity distribution in the reactor and determine the current density in the load during disinfection and purification of liquid media by high-voltage pulse discharges and find the most rational treatment. Methodology. To achieve this goal, we used computer modeling using the finite element method as a method of numerical analysis. An experimental reactor model was created that takes into account the dynamics of discharges in gas bubbles in water. The equations describing the system include the generalized Ampere equation, the Poisson equation and the electric displacement equation, taking into account the corresponding initial and boundary conditions, as well as the properties of materials. The dependence of the potential of a high-voltage electrode on time has the form of a damped sinusoid, and the specific electrical conductivity in a gas bubble is a function of time. Processes occurring at the front of the voltage pulse from 0 to 20 ns are considered. Results. It is shown that with an increase in conductivity and high-voltage potential to amplitude values in a gas bubble, the electric field strength in the water layer in the reactor reaches 70 kV/cm, and it is in the water layer that there is a strong electric field. The calculations show that already by 19th ns the density of conduction currents in water prevails over that of displacement currents. At the same time, additional inclusions in the water significantly affect the distribution of electric field strength and current density, creating a significant difference in their values at the boundaries of the interface between the bubble, conductive element and water. Originality. A simulation of the dynamics of transient discharge processes in a gas bubble and a layer of water with impurities was carried out, including an analysis of the distribution of the electric field strength and current density in a system with rod-plane electrodes in the phase transition section of a gas bubble-water. This approach allows us to reveal the features of processes in reactors and to investigate the influence of phase transitions on the distribution of electrophysical quantities. Practical value. Computer simulations confirm the prospect of using nanosecond discharges generated in gas bubbles within a volume of water for widespread industrial use and are of great interest for further experimental and theoretical research. References 25, figures 9.

Frequency and damping factor estimation of real-valued damped sinusoids by means of an improved two-point Interpolated DFT algorithm

The contribution of this paper is two-fold. Firstly, the well-known two-point Interpolated Discrete Fourier Transform (IpDFT) algorithm based on a Maximum Sidelobe Decay (MSD) window is generalized to the estimation of the frequency and the damping factor of a real-valued damped sinusoids. Analytical expressions for the detrimental contributions on the obtained estimators due to the image frequency component and wideband noise are then derived and their accuracies are verified through computer simulations. Secondly, leveraging on the derived expression, an improved version of the IpDFT algorithm is proposed which ensure more accurate estimates by compensating the contribution of the image frequency component. The performance of the improved IpDFT algorithm is compared with those provided by various state-of-the-art algorithms through meaningful computer simulations.

Generalized multi-point interpolated DTFT frequency and damping factor estimators of real-valued damped sinusoids

In this paper a generalized multi-point interpolated Discrete-Time Fourier Transform (DTFT) is proposed for frequency and damping factor estimation of real-valued damped sinusoids. The acquired data are weighted by a Maximum Sidelobe Decay (MSD) window and the interpolation function is defined as the ratio between two linear combinations of DTFT samples located one bin apart, which is generalized exploiting a tuning parameter. Analytical expressions for the estimated parameter errors due to the interference of the fundamental image component are derived. Leveraging on these expressions an improved version of the algorithm is also proposed and optimized by selecting a suitable value for the tuning parameter. The developed theory is applied to both a three-point and a four-point interpolated Discrete Fourier Transform (IpDFT) estimators published in the literature and the achieved accuracy improvements are verified through simulations.

Poles and residues of lossy and dispersive electromagnetic metamaterials

This paper proposes a system-based pole-residue approach to describe loss and dispersion in double-positive (DPS), epsilon-negative (ENG), and epsilon-near-zero (ENZ) isotropic metamaterials. The matrix pencil (MP) method extracts the poles and residues from the damped sinusoids of the singular expansion (SEM) of the impulse responses of the transmitted and reflected waves. The complex values of poles and residues serve as a basis for a computational tool to discriminate between lossless, lossy, and dispersive materials. The extracted poles and residues can also be used to classify the material under test as a DPS, an ENG, or an ENZ metamaterial. The proposed method delivers reliable results even with noisy transmission and reflection data.

Change in the growth parameters of soft wheat Triticum aestivum (L.) after pretreatment of seeds with a pulsed magnetic field

The article presents the results of experimental studies on increasing the growth rates of three varieties of soft wheat Triticum aestivum (L.) after pretreatment of seeds with a pulsed magnetic field (PMF). The pulse effect shape is a damped sinusoid, the effect intensity is induction B = (0.53÷5.21) T, the effect duration is microseconds, the number of pulses n = 3 with an interval between them Δτ= 3 s. Previously, the magnetic field effect with such parameters in crop production has not been studied. The greatest stimulating effect of the magnetic field is observed on wheat sprouts of the Tulaykovskaya Nadezhda variety: a statistically significant increase in the length of the sprouts by 3.4-3.6 times compared with the control. An assumption has been made about the mechanism of such a PMF effect on growth indicators: stimulation of oxidative stress in plants, increase in the concentration of mineral elements in the cell due to changes in membrane permeability. The ways of further research are determined.

Theoretical Analysis of Bandwidth Requirements for Damped Sinusoid Measurement

Theoretical Analysis of Bandwidth Requirements for Damped Sinusoid Measurement

Algorithmical determination of the equilibrium/stead position of a dynamic system by the finite-step method

The problem of algorithmic estimation of the equilibrium/stationary state of the dynamic system based on the minimum number of measurements of the output quantity at equidistant time points is considered. For this, a finite-step method was used, which consists in the formation, according to certain rules, of the sums and differences of the values of the output quantity, which are located symmetrically on the time axis relative to a certain moment that can be determined a priori. As a result, overdetermined systems of linear equations are formed with respect to the introduced fictitious unknowns, and based on the necessary condition for the existence of a solution to these systems, formulas are found to determine the equilibrium/stationary position of the dynamic system. Algorithms for determining the equilibrium /stationary state for the following mathematical models of the output value are given: in the form of a constant component and a damped exponent, in the form of a constant component and a damped sinusoid, in the form of a constant component and two undamped sinusoids, in the form of a constant component and a damped sinusoid. It is shown that in the absence of measurement errors of the output value, the error in estimating the equilibrium/stationary state of the transient process depends only on the error in solving the system of linear equations. Ways of using the redundant number of measurements are discussed.
 Keywords: equilibrium position, stationary state, dynamic system, mathematical model, finite-step method, numerical algorithm.

Nonlinear Ringdown at the Black Hole Horizon.

The gravitational waves emitted by a perturbed black hole ringing down are well described by damped sinusoids, whose frequencies are those of quasinormal modes. Typically, first-order black hole perturbation theory is used to calculate these frequencies. Recently, it was shown that second-order effects are necessary in binary black hole merger simulations to model the gravitational-wave signal observed by a distant observer. Here, we show that the horizon of a newly formed black hole after the head-on collision of two black holes also shows evidence of nonlinear modes. Specifically, we identify one quadratic mode for the l=2 shear data, and two quadratic ones for the l=4, 6 data in simulations with varying mass ratio and boost parameter. The quadratic mode amplitudes display a quadratic relationship with the amplitudes of the linear modes that generate them.

Search for postmerger gravitational waves from binary neutron star mergers using a matched-filtering statistic

In this paper, we present a new method to search for a short, a few tens of millis long, postmerger gravitational-wave (GW) signal following the merger of two neutron stars. Such a signal could follow the event GW170817 observed by Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo detectors. Our method is based on a matched filtering statistic and an approximate template of the postmerger signal in the form of a damped sinusoid. We test and validate our method using postmerger numerical simulations from the CoRe database. We find no evidence of the short postmerger signal in the LIGO data following the GW170817 event and we obtain upper limits. For short postmerger signals investigated, our best upper limit on the root sum square of the GW strain emitted from 1.15 kHz to 4 kHz is at 50% detection efficiency. The distance corresponding to this best upper limit is 4.64 Mpc.

Modal Filter Based on a Microstrip Line With Two Side Conductors Grounded at Both Ends

This article presents a modal filter (MF) based on a microstrip line with two side conductors grounded at both ends. New analytical expressions for calculating the time response in such a structure are given. For their validation, an MF prototype was made and the transmission coefficient was measured in the frequency range from 0 to 12 GHz. In addition, the full-wave electrodynamic simulation and the analysis based on the transmission line theory were carried out. The MF frequency responses were converted into time domain responses in the Advanced Design System. At the MF output, the responses to an ultra-wideband pulse, a high-frequency damped sinusoid, and a sinusoid with Gaussian modulation were analyzed. The results for the analytical model are in good agreement with the results of measurements and simulations by the two approaches. It was experimentally proven that the structure under study provides the protection of electrical circuits from different types of interference by separating them in time and decreasing their effect on the components. Finally, signal integrity was evaluated for two data rates. It was found that the MF under investigation may be used in signal circuits up to 1 Gb/s.

A Parameter Estimation Algorithm for Damped Real-value Sinusoid in Noise

Abstract To improve the parameter estimation performance of damped real-value sinusoid in noise, a novel algorithm with high accuracy and computational efficiency is proposed that combines the characteristics of good anti-interference, small computation of frequency-domain methods, and high parameter estimation accuracy of time-domain methods. First, the Discrete Fourier Transform (DFT) algorithm and the two-point spectrum interpolation algorithm of the frequency-domain methods are used to improve the noise immunity. Then, the linear prediction property and the enhancement filter of the time-domain methods are used to improve the parameter estimation accuracy. In addition, the parameter estimation performance of the proposed algorithm is verified by computational complexity analysis and test experiments, and the practical application effectiveness of the proposed algorithm is demonstrated on the Coriolis Mass Flowmeter (CMF) experimental platform. The experimental results show that the proposed algorithm effectively improves the real-time performance and the parameter estimation accuracy is better than that of the existing excellent algorithms.

Fast interpolated DTFT estimators of frequency and damping factor of real-valued damped sinusoids

This paper deals with the estimation of real-valued damped sinusoid frequency and damping factor. To that aim an Interpolated Discrete Time Fourier Transform (IpDTFT) algorithm is proposed which extends to real-valued signal an algorithm proposed in the literature for complex-valued damped sinusoids. The proposed algorithm provides fast estimates of the unknown parameters of either undistorted or distorted real-valued noisy damped sinusoids with accuracy generally better than the one ensured by state-of-the-art estimators, especially when few sinusoid cycles are analysed. Accuracy improvement is obtained by both weighting the acquired signal using a Maximum Sidelobe Decay (MSD) window and compensating the contribution of the spectral image component on the estimated parameters. Analytical expressions for the estimator variances due to wideband noise are also derived.

An iterative three-point interpolation algorithm for one/multiple damped real-valued sinusoids

Aiming at improving the accuracy of parameter estimation, this paper proposes an iterative algorithm for one/multiple damped real-valued sinusoids. Firstly, an initial three-point interpolation estimator is established for one damped real-valued sinusoid by completely removing the negative-frequency interference. Secondly, to reduce the effect of the theoretical frequency on the estimation accuracy, a fine estimator is further presented. Finally, based on the fine estimator, parameters including the frequency, the damping factor, the amplitude, the phase can be further iteratively estimated from multiple damped real-valued sinusoids. In the numerical analysis, the root of mean square error (RMSE) returned by the proposed algorithm is compared with RMSEs returned by other state-of-the-art algorithms, as well as the square root of the Cramér-Rao lower bound (CRLB). Results show that the RMSE returned by the proposed algorithm is much closer to the square root of the CRLB, which implies that the proposed algorithm can effectively achieve high-accuracy parameter estimation from one/multiple damped real-valued sinusoids.

Robust sparse reconstruction of attenuated acoustic field with unknown range of source.

In this paper, we present a gridless algorithm to recover an attenuated acoustic field without knowing the range information of the source. This algorithm provides the joint estimation of horizontal wavenumbers, mode amplitudes, and acoustic attenuation. The key idea is to approximate the acoustic field in range as a finite sum of damped sinusoids, for which the sinusoidal parameters convey the ocean information of interest (e.g., wavenumber, attenuation, etc.). Using an efficient finite rate of innovation algorithm, an accurate recovery of the attenuated acoustic field can be achieved, even if the measurement noise is correlated and the range of the source is unknown. Moreover, the proposed method is able to perform joint recovery of multiple sensor data, which leads to a more robust field reconstruction. The data used here are acquired from a vertical line array at different depths measuring a moving source at several ranges. We demonstrate the performance of the proposed algorithm both in synthetic simulations and real shallow water evaluation cell experiment 1996 data.

Detection Circuits for System-Level Signal and Power Noises Due to High-Power Electromagnetic Pulses

Four types of circuits for detecting system-level noises due to high-power electromagnetic (HPEM) pulses have been proposed and implemented in compact modules. The detection circuit provides digital information about the level or polarity of noises generated at specific power or signal nets. The sensed data are directly saved in the hardware, which is free from malfunctions of the applied system. For characterization and evaluation of the proposed circuits, transmission line pulse (TLP) and damped sinusoidal (DS) sources were constructed. The operation threshold curves of each detection circuit were theoretically derived and validated by measurements using the TLP source. The proposed detection circuits were then applied to the radiated HPEM experiments with the DS source. From the operation data of the detectors, the system-level noises generated by the radiated HPEM waves were quantitatively analyzed based on the operation threshold curve of each detector. The proposed detection circuits can play a role of a noninvasive diagnosis method for evaluating the effects of HPEM pulses inside a target application system.

Sustainable Slope Stability Analysis: A Critical Study on Methods

When studying the stability of a slope, the first issue that needs to be clarified is the slip surface, which determines the minimum safety factor. The slopes investigated here are homogenous with three distinct gradients (1:1.5; 1:1; 2:1), two defined heights (H-3 m; H-8 m), and four different soil characteristics (S1—clayey silt, S2—sandy clayey silt, S3—sandy silty clay, S4—clay). The purpose of this paper is to develop a new methodology capable of estimating the safety factor and the shape and centre of the critical slip surface, delivering an improved estimate of slope probability of failure, which can represent a significant component in a more precise risk assessment. This paper compares distinct methods used in the slope stability analysis, examining their hypotheses and effects on the estimated safety factor and the centre and shape of the critical slip surface. The study compares the limit equilibrium results with those determined by the shear strength reduction method using an approach based on the upper-bound limit analysis to compare the predictions extracted from these methods with those from the finite element method (FEM) analysis. The finite element method discretizes the soil mass into finite elements. Hence, it establishes a kinematically admissible velocity field searching for the failure mechanism of the slope. Results for FEM show the influence of the slope geometry and the mesh size and density on the safety factor. In the study, plots of the regression curves of five different critical slip surface shapes, including a circular slip surface (benchmark), show that the shape of the failure surface depends on the shape and material of the slope. Furthermore, they show that the critical slip surface layout can approach a logarithmic spiral, damped sinusoid, parabola, etc.; the slip surface is not always circular. The analysis reveals that none of the approaches can consider all uncertainties concerning the factor of safety and the interpretations of critical slip surfaces.

Combined Damped Sinusoidal Oscillation Solutions to the (3 + 1)-D Variable-Coefficient Generalized NLW Equation in Liquid with Gas Bubbles

This paper investigates the combined damped sinusoidal oscillation solutions to the 3 + 1 -D variable-coefficient (VC) generalized nonlinear wave equation. The bilinear form is considered in terms of Hirota derivatives. Accordingly, we utilize a binary Bell polynomial transformation for reducing the Cole-Hopf algorithm to get the exact solutions of the VC generalized NLW equation. The damped sinusoidal oscillations for two cases of the nonlinear wave ordinary differential equation will be studied. Using suitable mathematical assumptions, the novel kinds of solitary, periodic, and singular soliton solutions are derived and established in view of the trigonometric and rational functions of the governing equation. To achieve this, the illustrative example of the VC generalized nonlinear wave equation is provided to demonstrate the feasibility and reliability of the procedure used in this study. The trajectory solutions of the traveling waves are shown explicitly and graphically. The effect of the free parameters on the behavior of acquired figures of a few obtained solutions for two nonlinear rational exact cases was also discussed. By comparing the proposed method with the other existing methods, the results show that the execution of this method is concise, simple, and straightforward.

A comprehensive Bayesian reanalysis of the SARAS2 data from the epoch of reionization

ABSTRACT We present a Bayesian re-analysis of the sky-averaged 21-cm experimental data from SARAS2 using nested sampling implemented with polychord, spectrally smooth foreground modelling implemented with maxsmooth, detailed systematic modelling and rapid signal emulation with globalemu. Our analysis differs from previous analysis of the SARAS2 data through the use of a full Bayesian framework and separate modelling of the foreground and non-smooth systematics. We use the most up-to-date signal models, including Lyman-α and CMB heating parametrized by astrophysical parameters such as star formation efficiency, X-ray heating efficiency, minimal virial circular velocity of star forming galaxies, CMB optical depth, and the low energy cutoff of the X-ray spectral energy distribution. We consider models with an excess radio background above the CMB produced via radio emission from early galaxies and parametrized by a radio production efficiency. A non-smooth systematic is identified and modelled as both a frequency damped sinusoid introduced by the electronics and separately from the sky. The latter is modulated by the total efficiency of the antenna and marginally favoured by the data. We consider three different models for the noise in the data. The SARAS2 constraints on individual astrophysical parameters are extremely weak, however, we identify classes of disfavoured signals. We weakly disfavour standard astrophysical models with high Lyman-α fluxes and weak heating and more confidently disfavour exotic models with high Lyman-α fluxes, low X-ray efficiencies, and high radio production efficiencies in early galaxies.