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In magnetron sputtering systems, an arc and arcing may happen at the cathode of a magnetron when operating in a reactive environment. To avoid their occurrence, pulse operating modes are used. For this, rectangular unipolar or bipolar pulses can be used or in the form of a sine wave with frequencies from 10 kHz to 1 MHz. The purpose of this work is to study the electronic component of a magnetron discharge when it is excited by a pulse in the form of a damped sine wave, the so-called impact excitation. A comparison of its characteristics with similar characteristics of a magnetron discharge which is excited by unipolar rectangular pulses of the same duration, also. A physically topological model of a magnetron sputtering system has been created to compare the characteristics of an electron cloud when a discharge is excited by rectangular pulses and pulses in the form of a damped sine wave. A pulse of this shape is obtained by applying a current pulse to the oscillating circuit. A feature of this discharge is the ultrahigh voltage of the first pulses. This is caused by resonant phenomena in the power circuit. The work presents a 2D design of a simulated magnetron sputtering system, a structural diagram of a physical-topological model, and input parameters. The physical models for calculating magnetic and electric fields, the distribution in space and time of electron density and their energy are also given. As a result of the calculations, the distribution of the magnetic and electric fields in the magnetron sputtering system, the distribution of electron density in space and time, the distribution of electron energy in space and time of electrons during rectangular and impact excitation of the discharge were obtained. An analysis of the results confirmed the feature previously indicated by other authors. This is the formation of an increased electron density at the fronts of discharge excitation pulses. This can be explained by the acquisition by the electrons at the front of the momentum of energy which corresponds to the ionization cross section of Ar atoms. The electron energy leaves the optimal energy range for ionization of Ar atoms with a further increase of the voltage. Therefore, the ionization efficiency of the operating gas atoms decreases. It was also found that upon impact excitation of a magnetron discharge: 1) The electron energy above the surface of the target is several times higher than when the discharge was excited by a rectangular pulse. Therefore, the sputtering of the target surface is more intense; 2) The erosion zone of the target increases and therefore the utilization rate of the target material increases 3) Ions bombard and sputter the deposited film in the positive period of the sine wave, if it is under the ground potential.

In this paper, the output waveform of EMP coupled to 10 MHz monopole antenna analyzed by simulation, and the susceptibility of LNA(Low Noise Amplifier) was evaluated. The waveform of EMP coupled to the monopole antenna is a 10 MHz damped sinusoidal waveform, and the peak voltage is about 22 kV. The susceptibility of LNAs was evaluated using the 10 MHz damped sine wave generator. DFR(Destruction Failure Rate) was measured to investigate the susceptibility of LNA. The susceptibility level of LNA was assessed by voltage of damped sine wave. The voltage of destruction threshold is 71 V and 107.5 V respectively. The coupling voltage is higher than the destruction threshold of LNAs. Therefore, the communication system can be damaged by EMP. It is necessary to apply the protection device to the communication system. Based on these results, susceptibility of LNA can be applied to a basic data for applying the protection device to the communication system against EMP.

In this study, a three-phase motor inverter with sinusoidal output voltages based on the application of gallium nitride transistors and advanced control is analysed. In comparison to standard silicon-insulated gate bipolar transistors much higher feasible switching frequencies of 100 kHz and above are possible and reduce the output sine filter component size such that the filter can be directly included into the inverter. This considerably improves the electromagnetic interference (EMI) behaviour of the drive system as well as the acoustic noise, eases the inverter-to-motor wiring and protects the motor isolation against high d u /d t rates. The study describes the dimensioning and design of the used two-stage LC filter including motor current control based on proportional-integral-type phase current controllers. The LC filter damping is performed actively by capacitor current feedback. Using this active damping scheme avoids additional losses of conventional sine filters and guarantees high system efficiency up to 98%. Finally, experimental results of a laboratory prototype verify the proper behaviour of the proposed concept.

A generator of repetitive voltage pulses in the form of a damped sine wave with a period of ~6 ns, an amplitude of the first voltage half-wave of up to ~400 kV, and a pulse repetition frequency of up to 60 Hz is described. The generator is powered from a storage battery (7 A h, 36 V) and has several voltage build-up stages.

This paper presents sufficient conditions which guarantee that the equilibrium of the damped harmonic oscillator x + h ( t ) x ′ + ω 2 x = 0 \begin{equation*} x + h(t)\!\:x’ + \omega ^2x = 0 \end{equation*} is uniformly asymptotically stable, where h : [ 0 , ∞ ) → [ 0 , ∞ ) h\!: [0,\infty ) \to [0,\infty ) is locally integrable. These conditions work to suppress the rapid growth of the frictional force expressed by the integral amount of the damping coefficient h h . The obtained sufficient conditions are compared with known conditions for uniform asymptotic stability. Two diagrams are included to facilitate understanding of the conditions. By giving a concrete example, remaining problems are pointed out.

The capillary-based pulsed plasma thruster (PPT) has high-energy transfer efficiency, which provides potential to improve traditional PPT performance. In this paper, the discharge characteristics of a capillary-based PPT have been investigated. First, the typical process of voltage and current waveform is recognized. It is featured with a fast voltage drop (~25 ns) and a consequent damped sine wave oscillation discharge. Then based on the circuit analysis, the equivalent plasma resistance has been calculated. The current waveform is well fit with a linearly increasing resistance model. The influence of charging voltage has also been studied. The deposited energy increases while the transfer efficiency decreases with the increasing applied voltage. The cavity dimension has effects on the equivalent circuit parameters. The results show that longer cavity and smaller diameter lead to more deposited energy and higher transfer efficiency. The influence of voltage and capillary dimension on the mass shot characteristic has been discussed. Finally, the estimated impulse bit has been calculated and the impulse bit characteristics have been discussed. These results can contribute to the further optimization of PPT.

This paper presents a novel observer-based method for estimating the parameters of an exponentially damped sinusoid, including the frequency, amplitude, phase and the damping factor. A second-order sliding-mode-based adaptation law is designed for estimating the frequency and the damping factor, while amplitude and phase are obtainable from the said parameters by straightforward algebra. The stability and robustness analysis in presence of an additive disturbance proves the existence of a tuning parameter set for which the estimator’s dynamics are asymptotic stable and the estimation error asymptotically converges to a residual set whose size depends on the amplitude of the disturbance. Numerical and comparative examples show the effectiveness of the proposed estimation approach.

Evading fixed point theorems we prove the interior approximate controllability of the following semilinear strongly damped wave equation with impulses and delay in the space Z1/2 = D((−Δ)1/2)×L2(Ω),where r > 0 is the delay, Γ = (0, τ)×Ω, ∂Γ = (0, τ) × ∂Ω, Γr = [−r, 0] × Ω, (ϕ,ψ) ∈ C([−r, 0]; Z1/2), k = 1, 2, . . . , p, Ω is a bounded domain in ℝℕ(ℕ ≥ 1), ω is an open nonempty subset of , 1 ω denotes the characteristic function of the set ω, the distributed control u ∈ L2(0, τ; U), with U = L2(Ω),η,γ, are positive numbers and f , Ik ∈ C([0, τ] × ℝ × ℝ; ℝ), k = 1, 2, 3, . . . , p. Under some conditions we prove the following statement: For all open nonempty subsets Ω of the system is approximately controllable on [0,τ]. Moreover, we exhibit a sequence of controls steering the nonlinear system from an initial state (ϕ (0), ψ(0)) to an ε-neighborhood of the final state z1 at time τ > 0.

The purpose of the study is to summarize the application rule of multi-frequency sine wave compound magneto-optical modulation in measuring roll angle. Firstly, we establish the model of compound modulation signal composed of fundamental and multi-frequency sine wave signals, and then the modulated signal is analyzed with Bessel function. Secondly, we analyze the characteristic of AC signal extracted from the modulated signal, and discuss the feasibility of establishing angle measurement model with extremum in AC signal. Finally, we draw the conclusion that study on the fundamental sine wave signal superimposed on itself compound modulation in roll angle measurement is enough, the others is unnecessary. The study result has an important guiding significance on the application of multi-frequency sine wave compound magneto-optical modulation in measuring roll angle.

We study the Cauchy problem for nonlinear damped wave equations with a critical defocusing power nonlinearity | u | 2 n u , where n denotes the space dimension. For n = 1 , 2 , 3 , global in time existence of small solutions was shown in [4] . In this paper, we generalize the results to any spatial dimension via the method of decomposition of the equation into the high and low frequency components under the assumption that the initial data are small and decay rapidly at infinity. Furthermore we present a sharp time decay estimate of solutions with a logarithmic correction.

In the present study, viscously damped free and forced vibrations of a rectangular membrane are investigated using a closed form exact method. The method is exact and yields closed form expressions for the vibratory displacements. This is in contrast with the well known eigenfunction superposition method which requires expressing the distributed forcing functions and the displacement response functions as infinite sums of free vibration eigenfunctions. Instead of undamped natural frequencies which are typically computed and applied in the free and forced vibrations, damped natural frequencies are done. The damped natural frequency equation and the critical viscous damping equation are exactly derived. In the damped free vibration, effects of viscous damping on natural frequencies and mode shapes are studied. Some contour plots of damped mode shapes are given. Accurate displacement amplitude vs. forcing frequency curves showing the forced response due to distributed loading are displayed.

We study the diffusion phenomena for damped wave equations. We prove that the solution of an abstract damped wave equation becomes closer to the solution of a heat type equation as time tends to infinity under some assumption to the resolvent. As an application of our approach, we also study the asymptotic behavior of the damped wave equation in Euclidean space under the geometric control condition.

The Spacecraft (S/C) numerical sine test-predictions are usually performed through Finite Element Method (FEM) Frequency Response Analysis (FRA), that is the hypothesis of steady-state responses to harmonic excitation to the S/C base is made. In the test practice, the responses are transient and may be significantly different from those predicted through FRA. One of the most significant causes of discrepancy between prediction and test consists in the beating phenomena. After a brief overview of the topic, the typical causes of beating are described in the first part of the paper. Subsequently, focus is made on the sine sweep rate effect, which often leads to have beatings after the resonance of weakly damped modes. In this work, the approach illustrated in the literature for calculating the sine sweep rate effect in the case of Single-Degree-Of-Freedom (SDOF) oscillators is extended to Multi-Degrees-Of-Freedom (MDOF) systems, with the aim of increasing the accuracy of the numerical sine test-predictions. Assumptions and limitations of the proposed methodology are detailed along the paper. Several assessments with test results are discussed and commented.

An electronic analog circuit of the edge-emitting semiconductor laser is proposed. It is powered with a sine wave, triangular wave and square wave. The numerical results are compared to the experimental one and an agreement is found. By using one parameter controlling the normalized reverse bias of the injection current, the Bifurcation diagram obtained when the electronic system is powered with the triangular wave shows that the system exhibits a period-doubling to chaos and this bifurcation diagram appears to be a shift compare to the one obtained with the sinusoidal wave.

In this paper we consider two types of the generalized damped oscillator. One is governed by a single frictional force which has a position dependent frictional coecient and is proportional to the N-th power of the velocity. Another is a quadratically damped harmonic oscillator. For two models, we construct two independent constants of motion.

We study the large time behavior of small solutions to the Cauchy problem for a nonlinear damped wave equation. We proved that the solution is approximated by the Gauss kernel with suitable choice of the coefficients and powers of $t$ for $N+1$ th order for all $N \in \mathbb{N}$. Our analysis is based on the approximation theorem of the linear solution by the solution of the heat equation [37]. In particular, as pointed out by Galley-Raugel [4], we explicitly observe that from third order expansion, the asymptotic behavior of the solutions of a nonlinear damped wave equation is different from that of a nonlinear heat equation.

International audience; We prove local and global energy decay for the asymptotically periodic damped wave equation on the Euclidean space. Since the behavior of high frequencies is already mostly understood, this paper is mainly about the contribution of low frequencies. We show in particular that the damped wave behaves like a solution of a heat equation which depends on the H-limit of the metric and the mean value of the absorption index.

Recognition of wireless and non-battery measurement systems makes passive surface acoustic wave (SAW) sensors valuable. The interrogation unit coordinates the SAW sensor system and provides the sensor's energy by transmitting pulse signals. The SAW sensor also transmits its response to the interrogation unit after being charged. The response signal of the SAW sensor is a noisy damped sine wave that should be received by the interrogation unit antenna. The received signal resonates at the SAW intrinsic frequency which changes with sensing characteristics. So the interrogation unit has the responsibility of detecting this damped sine wave frequency accurately and finding the exact value of the sensing parameter. Fast Fourier transform (FFT), zero crossing, and peak detection methods are used in most papers. However, after studying these methods, it is concluded that all of them have fundamental disadvantages namely inaccuracy and low speed. So by using estimation formulae, a new frequency detection method is designed based on FFT and used to compensate the drawbacks. Finally, the proposed method can help researchers to reduce the sampling frequency of the analog-to-digital converter (ADC) used in the interrogation unit. Also, the proposed method detects the initial phase and the amplitude of the response signal.

This article describes how a triangular wave is converted into a sine wave by using a piecewise linear transfer characteristic. A detailed analysis is given of the basic circuit, and its actual imp...

Instead of the $L^p$ estimates, we study the modulation space estimates for the solution to the damped wave equation. Decay properties for both the linear and semilinear equations are obtained. The estimates in modulation space differ in many aspects from those in $L^p$ space.

Techniques to generate damped waves in linear shallow water equations are developed. Delta-shaped source functions are derived for four different cases with the source function and damping coefficient either in the continuity or momentum equation. Source terms are also found by relating the source function method to the source term addition method. For the transport of the source term in damped waves, we define complex valued source-term velocity which is different from the real valued energy velocity. We verify the present wave generation techniques with the source-term velocity by simulating damped waves on a horizontal bottom both in the one- and two-dimensional domains, and also damped waves shoaling and refracting on a plane slope in the two-dimensional domain.

In this paper, we consider the damped harmonic oscillator with a time-dependent damping constant and a time-dependent angular frequency, which is actually the generalized Caldirola-Kanai Hamiltonian. For some choices of the time-dependent damping constant and the time-dependent angular frequency, we investigate the exact solutions. We also obtain the corresponding conserved quantities and finally discuss the quantum damped harmonic oscillator with a time-dependent damping constant and a time-dependent angular frequency.

This paper introduces an exact analytical solution predicting variations in excess pore-air and pore-water pressures and settlement considering the two-dimensional (2D) plane strain consolidation of an unsaturated soil stratum subjected to different time-dependent loadings. Based on the proposed solution, the distributions of excess pore pressures along vertical and horizontal directions can be determined. The general solution is first expressed in a series of eigenfunctions of homogeneous partial differential equations (PDEs) and is then substituted into the governing flow equations. Using term-by-term differentiation and the orthogonality of the sine function, the governing equations become ordinary differential equations (ODEs). Once the complex domain is obtained by applying the Laplace transformation technique, the closed-form analytical solutions describing the dissipation of excess pore-air and pore-water pressures can be obtained by taking a Laplace inverse. In this study, four external loadings, including ramping, asymptotic, sinusoid and damped sine wave, are simulated and incorporated into the proposed solutions. For the data analysis, the 2D consolidation behavior is investigated against variations in the permeability ratio ( k a / k w ) . Additionally, parametric studies regarding loading functions are presented in this paper.

© 2016 American Society of Civil Engineers. This paper presents an analytical solution to predict the axisymmetric consolidation in unsaturated soil deposits subjected to different time-dependent loadings. The mathematical procedure uses the separation of variables and Laplace transformation methods to obtain the final solution. A set of polar governing equations of flow are obtained and presented under the partial differential equations (PDEs), and then the variable separation technique is used to alter the PDEs to ordinary differential equations (ODEs) consisting of distinctive variables. Fourier Bessel and sine series are used to present functions of radial and vertical flows, respectively, and the Laplace transformation is used to obtain a function of time. Four primary time-dependent loading functions, including ramping, asymptotic, sinusoid, and damped sine wave, are mathematically simulated and incorporated into the proposed solutions. This study investigates changes in excess pore-air and pore-water pressures as well as consolidation settlement against the air-to-water permeability ratio and various loading parameters. Moreover, changes in suction and net stress induced by ramped and asymptotic loadings are also presented in the worked examples.

Gas-filled glass plasma electrodes coupled with high-frequency high-voltage generators are used in medicine and dentistry for more than a century. In recent literature, therapeutic effects of such procedure have been explained through topical bio-oxidative effects of ozone generated by the dielectric barrier discharge. The aim of this study was to evaluate characteristics of electric field and optical emission spectrum generated in the treatment field by the glow discharge of the plasma electrode. Emission spectrum in red and near- infrared wavelength range (540–886 nm) and pulsed electric field (impulse frequency 1053 Hz, exponentially damped sine wave in the range of 33 kHz, duty cycle 20%) were recorded. Estimated electric field strength at 1-mm distance was in the range from 5.8 to 13.7 kV/m and between 1E6 and 1E8 V/m in the close proximity of electrode's surface (below 0.01 mm). Recorded factors are integral constituents in the treatment field and their properties can be correlated to the known biological and therapeutic effects of photostimulation and electrostimulation. These factors present important bioactive components which could be responsible for therapeutic effects, reported in number of clinical studies, especially those which could not be explained through topical bio-oxidative effects of ozone.

This paper is aimed at eliminating the influence of the problem of the harmonic response analysis of non-classically damped systems with lower-higher-modal truncation. Based on the Neumann expansion theorem and the frequency shifting technique, the relationships satisfied by eigensolutions and system matrices are established and an explicit expression on the lower-higher-modal truncation error of harmonic responses can be expressed as a sum of available modes and system matrices. A correction method, which only involves the available modes and system matrices, is then presented to calculate the harmonic responses. The method maintains original-space without having to involve the state-space equation of motion such that it is efficient in computational effort and storage capacity. The method is convergent if and only if all the modes whose resonant frequencies lie within the range of excitation frequencies are available. Finally, a two-stage floating raft isolation system and a sandwich plate are used to to validate the effectiveness of the presented method.

Sinusoidal signal generator is common electronic equipment. In this paper, the writer designed a kind of integrated CMOS sine signal generator, which generator uses wien bridge oscillation circuit.This generator circuit mainly constitutes by amplifier, leveled and low-pass filter circuit, which uses Cadence software to simulate and analysis its amplification circuit, in order to get a sine wave which has high performance accuracy and stability. Through simulating this generator, we can get a kind of sine wave which includes the frequency as the 1.109 kHz, the center potential as 2.5V, the amplitude as 2.58V, distortion is less than 2%, and this sine wave is more practical for the lower voltage supply system.

The theory of planar dynamical systems is applied in this paper to carry out a qualitative analysis to the planar dynamical system corresponding to the bounded traveling wave solution of the Zakharov–Kuznetsov–Burgers equation, and obtain the existence and uniqueness of the bounded traveling wave solutions. According to the discussions on the relationships between the shapes of bounded traveling wave solutions and the dissipation coefficient d, a critical value d 0 is found for arbitrary traveling wave speed v and integral constant g. This equation has a unique monotone kink profile solitary wave solution as the dissipation coefficient d satisfies | d ¯ | > d 0 ; while it has a unique damped oscillatory solution as | d ¯ | d 0 . This paper also presents the exact bell profile solitary wave solution as d = 0 . Furthermore, we appropriately design the structure of the damped oscillatory solution in light of the evolution relationships of the solution orbit in the global phase portraits to which the damped oscillatory solution corresponds and obtain its approximate solution by means of the undetermined coefficients method. Finally, based on the integral equation that reflects the relationships between the approximate damped oscillatory solution and its exact solution, the error estimate is given for the approximate damped oscillatory solution. The error is infinitesimal decreasing in exponential form.

Sine wave signal is a kind of typical electronic technology signal waveform, and frequency, amplitude and phase are three elements of the sine wave respectively. In order to measure the elements more accurately, scientific research methods is adopt in the design. Based on high precision of peak detection circuit combined with MSP430 MCU, the circuit for measuring frequency and amplitude of sine wave signal is implemented, and the results could be shown in the display circuit at the same time. The circuit can work within the 1kHz - 20kHz and 240mV - 5V sine wave signal, and has display circuit, which can display accurate measurement results, to achieve human-computer interaction.

A glance at Bessel functions shows they behave similar to the damped sinusoidal function. In this paper two physical examples (pendulum and spring-mass system with linearly increasing length and mass respectively) have been used as evidence for this observation. It is shown in this paper how Bessel functions can be approximated by the damped sinusoidal function. The numerical method that is introduced works very well in adiabatic condition (slow change) or in small time (independent variable) intervals. The results are also compared with the Lagrange polynomial.

The time dependence of probability and Shannon entropy of a modified damped harmonic oscillator is studied by using single and double Gaussian wave functions through the Feynman path method. We establish that the damped coefficient as well as the system frequency and the distance separating two consecutive waves of the initial double Gaussian function influences the coherence of the system and can be used to control its decoherence.

This paper aims at analyzing the shapes of the bounded traveling wave solutions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and conditions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefficients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approximate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate solutions. It can be seen that the error is infinitesimal decreasing in the exponential form.

In this paper we use a modified test function method to derive nonexistence results for the semilinear wave equation with time-dependent speed and damping. The obtained critical exponent is the same exponent of some recent results on global existence of small data solutions.

A novel technique is proposed to generate robust, low distortion sine waves. In this method, outputs of a phase shift oscillator (PSO) are weighted and summed to obtain multiple outputs with very low distortion and precise phase relationship. The method allows a programmable number of harmonic distortion components to be cancelled over a wide frequency range. This work derives the condition for the weights on the outputs of the PSO to be a real quantity, and demonstrates how this can be used to generate low distortion sine waves. With the proposed method, in an N-stage PSO, harmonics up to N-2th can be canceled. Simulation results using commercial operational amplifier spice models are presented to demonstrate low distortion sine wave generation over 2 kHz-180 kHz frequency range. The method has been experimentally verified using extremely low-cost, discrete components to produce 100 dB total harmonic distortion (THD) sine wave.

We obtain some space-time estimates for the fundamental solution u ( t , x ) to the damped fractional wave equation. Our space frame is the modulation space. As an application, we obtain the global solution to the nonlinear Cauchy problem, with small initial data.

We consider a variable-coefficient wave equation with nonlinear damped acoustic boundary conditions. Well-posedness in the Hadamard sense for strong and weak solutions is proved by using the theory of nonlinear semigroups.

In this paper, we derive a class of analytical solution of the damped Helmholtz–Duffing oscillator that is based on a recently developed exact solution for the undamped case. Our solution procedure indicates that this solution holds for specific system parametric choice values.

WOS:000390602900047 Using Riccati type transformations, the authors establish some new oscillation criteria for the fractional differential equation (D-0+(1+alpha) y) (t) + p(t) (D-0+(alpha) y) (t) + q(t) f(G(t)) = 0, t > 0, where D-0+(alpha) is the Riemann-Liouville fractional derivative of order alpha of y, G(t) = integral(t)(0) (t - s)(-alpha) y(s)ds, and alpha is an element of(0, 1). Examples are provided to illustrate the relevance of the results.

In this paper, we apply the theory of planar dynamical systems to make a qualitative analysis to the traveling wave solutions of nonlinear Kakutani-Kawahara equation $u_t+uu_x+bu_{x x x}-a(u_t+uu_x)_x=0$ ($b>0, a\ge0$) and obtain the existent conditions of the bounded traveling wave solutions. In dispersion-dominant case, we find that the unique bounded traveling wave solution of this equation has not only oscillatory property but also damped property. Furthermore, according to the evolution of orbits in the global phase portraits, we present an approximate damped oscillatory solution for this equation by the undetermined coefficients method. Finally, by the idea of homogenization principles, we obtain an integral equation which reflects the relation between this approximate damped oscillatory solution and its exact solution, thereby having the error estimate. The error is an infinitesimal decreasing in exponential form. From the results in this paper, it can be seen that the damped oscillatory solution of Kakutani-Kawahara equation in dispersion-dominant case still remains some properties of solitary wave solution for KdV equation.

We show how both zero- and low-frequency information can be obtained by applying an exponentially decaying damping function to a seismic signal containing no low-frequency information. The discrete Fourier transformation of a damped signal is identical to a circular convolution of the signal and the damping function in the frequency‐domain. Therefore, the zero- and low-frequency components of a damped signal are a weighted summation of the frequency components of the original signal. We also prove the existence of these components using a Fourier series. As the Fourier transforms of damped sine and cosine signals have both zero- and low-frequency components, a causal wavefield that can be represented by the summation of sines and cosines also has these components. These zero- and low-frequency components are not equivalent to the original low-frequency information. Instead, they can be thought as a blurring of the original signal. The Laplace-domain inversion utilizes this information to build a large-scale velocity model. We demonstrate this through numerical examples using the Marmousi velocity model. The examples show that a Laplace-domain inversion result is similar to that of a frequency-domain inversion using very low-frequency information.