Time-domain Counterpart Research Articles

Dynamic Harmonic Domain Modeling of Transients in Three-Phase Transmission Lines

This paper presents a traveling wave based transmission line model which includes harmonics in transient state. The line model is interfaced with a nonlinear load and both are simulated through the dynamic harmonic domain technique. This technique permits the user to follow step-by-step the harmonics of the propagating waveforms during transient conditions. An illustrative example involving a transmission line network with nonlinear loads is presented and the proposed model is compared with its time domain counterpart.

Cooray–Rubinstein Formula for the Evaluation of Lightning Radial Electric Fields: Derivation and Implementation in the Time Domain

Ground conductivity plays an important role both in the evaluation of the electromagnetic (EM) fields due to a lightning event and in the calculation of the line parameters, which are, in turn, fundamental in the analysis of the lightning-induced voltages on overhead lines. The exact formulation of the EM fields over a lossy ground involves the numerical evaluation of the Sommerfeld integrals, which are slowly converging and can only be computed in the frequency domain. For this reason, a great effort has been devoted in the derivation of approximate formulas that can provide accurate results with low computational costs. The most popular one is the Cooray-Rubinstein formula, which has been proposed in the frequency domain. Here, its time-domain counterpart is mathematically derived, and an efficient algorithm for its implementation is presented together with some comparisons with the exact approach.

On the Relationship Between the Time-Domain and Frequency-Domain TLM Methods

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The time- and frequency-domain transmission line matrix (TLM) methods have been developed and shown to be effective and powerful in solving electromagnetic problems. However, their direct relationship has not been clearly described so far. In this letter, we show that if a time-domain TLM method is developed, its corresponding frequency-domain counterpart can also be obtained through the discrete time Fourier transform; in a similar manner, if a frequency-domain TLM method is developed, its time-domain counterpart can also be obtained through the inverse discrete time Fourier transform. The choice of using the frequency- or time-domain depends very much on the types of the problems to be solved and the familiarity of a user with the methods. </para>

Iterative Frequency Domain Joint-over-Antenna Detection in Multiuser MIMO

Multiuser multiple-input-multiple-output (MIMO) wireless systems have great potential in improving information rate, diversity and resistance to against interference. The primary objective of this paper is to derive for broadband signaling a new iterative frequency domain (FD) multiuser MIMO signal detection technique for joint-over-antenna (JA) detection. The proposed detector is based on soft-cancellation and minimum mean square error (MMSE) filtering, followed by maximum a posteriori probability (MAP) detector to detect several of each users transmit antennas. The purpose of jointly detecting several transmit antennas is to preserve the degrees of freedom (DoF) for MMSE. Computational complexities with FD and its time domain (TD) counterpart are evaluated in this paper, and it is shown that FD requires significantly lower complexity than TD. Numerical results show that JA significantly outperforms the receiver that detects transmit antenna signals antenna-by- antenna (AA). The proposed iterative FD JA technique achieves larger performance gains compared to AA when the total number of transmit antennas is larger than the number of receiver antennas, as well as in the presence of spatial correlation.

Frequency- and time-domain methods for the numerical modeling of full-bridge aeroelasticity

A numerical framework for full-bridge aeroelasticity is presented, based on unsteady cross-sectional load models and on the finite-element modeling of the structure. A frequency-domain approach based on aeroelastic derivatives and nonlinear complex eigenvalue analysis is compared to its equivalent time-domain counterpart based on indicial functions and direct integration of the equations of motion. A version of the time-domain load model consistent with the quasi-steady limit behavior is developed and a procedure for the numerical identification of the indicial functions from measured aeroelastic derivatives is presented. The aeroelastic stability analysis is chosen as benchmark. A numerical example is offered where the equivalency of the two approaches is proved for a full-bridge model. Advantages and disadvantages of the two techniques are discussed.

A Frequency-domain Based Test for Non-correlation between Stationary Time Series

A one-sided asymptotically normal test for non-correlation between two stationary time series is proposed based on the spectral coherence function. The test statistic is a properly standardized version of the integrated spectral coherency and has similar asymptotic properties as a previously introduced time domain based test for non-correlation. Unlike its time domain counterpart, the proposed test does not require prewhitening of the time series and, thus, is a truly nonparametric test for non-correlation. In a simulation study, we evaluate the small sample performance of the proposed test in comparison with the time domain test and address the problem of bandwidth selection. Furthermore, we present a modification of the test statistic that allows to test for non-correlation over frequency bands. This version shows higher power of detecting interrelationships restricted to the frequency band of interest.

Frequency-domain implementation of the transmitted-reference ultra-wideband receiver

This paper presents a mixed-signal frequency-domain implementation of the autocorrelation receiver used in the detection of ultra-wideband communication signals that are modulated with transmitted-reference signaling. The digital receiver architecture is based on samples provided by an analog-to-digital converter (ADC) in the frequency domain. Among the advantages of the new receiver are the relaxation of the conversion speed achieved by the inherent parallel architecture of the frequency-domain ADC and the flexibility and simplicity of an all-digital receiver architecture that follows the mixed-signal ADC radio front-end. The paper provides the symbol detection formulas and the corresponding system implementation and makes comparisons with the conventional time-domain implementations. Additionally, a time synchronization technique for the new receiver structure is proposed, which makes the receiver insensitive to any time offset at the pulse level. Furthermore, as a particular case of great practical interest, we consider a single bit for the ADC implementation, and we show with experimental results that the resultant frequency-domain mono-bit digital receiver provides a performance gain that increases with the number of frequency samples, when compared with its time-domain counterpart.

Timed arrays in a nutshell

Timed arrays are the time-domain counterpart of phased arrays, where each array element is excited by wideband instead of narrowband signals. By referring to idealized, but meaningful canonical configurations, the array parameters in the transmit and receive mode are defined in a simple way, by following a purely time-domain intuitive analysis. Obtained results extend steady-state concepts of beamwidth, directivity, gain, effective receiving area, Fresnel and Fraunhofer regions to the case of transient excitation. Application is made to both real and synthetic arrays. The final main conclusion is that the role of the carrier wavelength associated with narrowband excitation is taken by the spatial width of the (carrierless) pulse. This result appears to be rather robust, because it turns out to be independent from the different norms used in the definition of the antenna parameters: it sheds light on the physics of the transient radiation and may be very useful for initiating a more technical analysis of the array performance.

Long range nonlinear propagation in an ocean acoustic waveguide

The Nonlinear Progressive Wave Equation (NPE) [McDonald and Kuperman, J. Acoust. Soc. Am. 81, 1406–1417 (1987)] is an approximation of the Euler equations for nonlinear compressional waves in an inviscid fluid and, actually, is the nonlinear time domain counterpart of the frequency domain linear parabolic wave equation (PE) for small angle propagation. Simulations using a npe code were used to study both harmonic (high frequency) and parametric (low frequency) generation. This code was coupled with a linear adiabatic normal mode program which allows range-dependent cases treatment to study propagation in shallow or deep water with longer range propagation paths. Included in the modeling are both shock dissipation and linear attenuation in the sediment layer. The results of these studies are presented.

Long‐term memory in stock market returns: international evidence

AbstractA lot of recent work has addressed the issue of the presence of long memory components in stock prices because of the controversial implications of such a finding for market efficiency and for martingale models of asset prices used in financial economics and technical trading rules used for forecasting. This paper examines the presence of long memory in the stock returns of seven countries, namely Japan, Korea, New Zealand, Malaysia, Singapore, the USA and Australia. The classical and modified rescaled range tests, the semiparametric test proposed by Geweke and Porter‐Hudak, the frequency domain score test proposed by Robinson and its time‐domain counterpart derived by Silvapulle, are applied to these returns in order to detect the long memory property. Evidence suggests that the Korean, Malaysian, Singapore and New Zealand stock returns are long‐term dependent, indicating that these two markets are not efficient. The results of this study should be useful to regulators, practitioners and derivative market participants, whose success precariously depends on the ability to forecast stock price movements. Copyright © 2001 John Wiley &amp; Sons, Ltd.

Spectral methods for multiaxial random fatigue analysis of metallic structures

This paper presents computationally efficient frequency domain methods for estimating the high-cycle fatigue life of metallic structures subjected to a random multiaxial loading. The equivalent von Mises stress method proposed earlier by the senior author is first reviewed. It is then shown that the multiaxial rainflow method, initially formulated in the time domain, can be implemented in the frequency domain in a formally similar way. The consistency of the results are checked by comparison with a time domain method based on the critical plane. It is observed that frequency domain methods produce enormous computer savings and correlate fairly well with the time domain method in terms of localizing the critical areas in the structure. A frequency domain implementation of Crossland's failure criterion is also proposed; it is found in very good agreement and much faster than its time domain counterpart.

Time-Domain Green Function Corresponding to a Time-Harmonic Point Source in Complex Space

ABSTRACT The time-domain counterpart of the scalar field arising from a time-harmonic point source in the complex space is derived. The solution corresponds to the complex-space source Green function, which has grown very important in various electromagnetic problems, because it can be applied to approximate the narrow radiation of the Gaussian beam type. The time-domain counterpart presented in the present paper is seen to be real and causal. The solution is demonstrated to an asymptotic case of the Sommerfeld half-space problem in time domain.

Impulse response functions for elastic structures with rigid-body degrees of freedom

A procedure based on the theory of generalized functions is developed which allows the calculation of impulse response functions for discrete and continuous elastic systems with structural damping and rigid-body degrees of freedom. For any degree of freedom the procedure divides the Fourier transform of the impulse response function into two parts. The first part contains the singularity due to the rigid-body degree of freedom. Its time-domain counterpart is obtained in closed form. The second part exhibits no singularities, and its time-domain counterpart is obtained by numerical integration using a Fast Fourier Transform routine. The procedure is applied to two systems for which closed form solutions are also obtained: a system consisting of two point masses connected by an elastic spring which slide without friction on a horizontal plane, and a non-dispersive mechanical slider with elastic deformations due to shear strain. The agreement between the results yielded by the proposed procedure and the closed form solutions is shown to be excellent. The procedure is then used to calculate the impulse response function for the tip displacement of a dispersive medium consisting of a flexible robot manipulator with the mechanical properties of a Timoshenko beam.

PCs for AP

The MlNlNEC System: Microcomputer Analysis of Wire Antennas, J. W. Rockway, J. C. Logan, D. W. S. Tam, & S. T. Li, Artech House, Boston, 1988, ISBN 0-89006-264-1. If there are any of you reading this column who use PCs for antenna modeling but haven't yet heard of MININEC, you're probably in a small minority. MlNlNEC began in the early 1980s initially as an experiment to demonstrate that "real" modeling using a moment-method code on a PC was actually feasible. As a matter of fact, the feature article from which this column originated, published in the August 1983 AP-S Newsletter, briefly described two wire models then running on Apple II+ micros, the original MININEC, afrequency-domain code, and TWTD as a time-domain counterpart.

Linear and nonlinear acoustics in the time domain: Long-range pulse propagation

During recent years the nonlinear progressive wave equation (NPE) model has been developed as a nonlinear time domain counterpart of the linear frequency domain parabolic equation (PE) model [B. E. McDonald and W. A. Kuperman, J. Acoust. Soc. Am. 81, 1406–1417 (1987)]. It was motivated by investigation of nonlinear wave evolution, so that time domain formulation was natural. With nonlinearity absent, the NPE gives an efficient algorithm for linear broadband propagation in the time domain. (No Fourier transforms between frequency and time domains are involved.) Recent simulation results from the NPE model (given in a color movie) illustrate linear and nonlinear pulse propagation through a deep ocean convergence zone. Differences in physics between broadband linear and nonlinear propagation will be pointed out and discussed. Linear results reveal transients whose time scale as a function of range is “remembered” from the source. In corresponding nonlinear results, steepening and shock formation cause the source's time scale to be gradually “forgotten.” For the parameters of the example given, nonlinear spreading behind the shock increases the transients' time scale by roughly a factor of 3 in the farfield.

Similarity solution for low Mach number spherical shocks

A nonlinear progressive wave equation (NPE) describes the evolution of a low Mach number shock wave. The NPE is the nonlinear time domain counterpart of the frequency domain linear parabolic wave equation (PE) for small angle propagation. The NPE in spherical symmetry admits a similarity solution that specifies both the shape of the pulse and the shock strength as a function of range. For finite amplitude spherical waves whether self-similar or not, the theory predicts constancy of an impulse integral corresponding to that of linear theory. For the self-similar waves, theory and available data are in qualitative agreement in the following areas: (1) The shock strength decreases with range as an approximate power law; (2) the temporal behavior of the solution at fixed range is a shock discontinuity followed by a roughly exponential decay; and (3) the effective relaxation time behind the shock is in reasonable agreement with data for slightly more than the first decade in range.

Time domain formulation for pulse propagation including nonlinear behavior at a caustic

This paper derives a simple three-dimensional time domain formulation for small angle propagation of finite amplitude acoustic pulses and weak shocks in a medium that can be range dependent. The formulation is closely related to a full wave model, and does not contain the artificial singularities of ray-based models at caustics. The simplicity of the formulation suggests that it may be of value for broadband linear as well as nonlinear propagation. Two derivations are given: one heuristic and the other a formal series expansion from the fluid equations. The result is a first-order nonlinear progressive wave equation (NPE) cast in a wave-following frame of reference.The NPE is shown to be the nonlinear time domain counterpart of the frequency domain parabolic wave equation (PE). The NPE gives a natural separation of terms governing refraction, spreading, and nonlinear steepening. Numerical calculations (not involving Fourier synthesis) are presented using the NPE to simulate the following cases: (a) broadband linear pulse propagation in a waveguide; (b) the development of an initially smooth nonlinear pulse into an N wave; and (c) the behavior of a weak shock at a caustic. Cases (a) and (b) are compared with analytic solutions.

Time-domain solution of the parabolic equation including nonlinearity

This paper develops a two-dimensional (range and depth) formulation for small-angle propagation of nonlinear acoustic pulses and weak shocks in a refracting medium which can be range dependent. The formulation readily extends to three dimensions. The nonlinearity is most efficiently treated in the time domain, so the signal is not Fourier decomposed into component frequencies. Beginning with a second-order wave equation which includes the lowest-order nonlinearity, an approximate first-order nonlinear progressive wave equation (NPE) is derived. The NPE is the nonlinear time-domain counterpart of the linear frequency-domain parabolic equation (PE). The derivation is accomplished by transforming the wave equation to a pulse-following frame and perturbing about a unidirectional plane-wave signal. The NPE manifests a natural separation of terms governing refraction, diffraction, spreading and nonlinear steepening. Numerical methods are outlined for the solution of the time-domain problem. Calculations using the formulation developed here successfully follow the development of initially smooth pulses into N waves and the reflection of weak shocks from a caustic.

The Schur algorithm and its applications

The Schur algorithm and its time-domain counterpart, the fast Cholseky recursions, are some efficient signal processing algorithms which are well adapted to the study of inverse scattering problems. These algorithms use a layer stripping approach to reconstruct a lossless scattering medium described by symmetric two-component wave equations which model the interaction of right and left propagating waves. In this paper, the Schur and fast Chokesky recursions are presented and are used to study several inverse problems such as the reconstruction of nonuniform lossless transmission lines, the inverse problem for a layered acoustic medium, and the linear least-squares estimation of stationary stochastic processes. The inverse scattering problem for asymmetric two-component wave equations corresponding to lossy media is also examined and solved by using two coupled sets of Schur recursions. This procedure is then applied to the inverse problem for lossy transmission lines.

Edge diffraction of transient nondispersive wave—theory and experiment

Edge diffraction of transient nondispersive waves in two dimensions is considered. The characteristic single‐edge diffraction pattern for time‐harmonic waves is described by the Fresnel function. The time domain counterpart of the Fresnel function is derived. We argue that the time domain wavefield representation is more insightful than its frequency domain counterpart. It shows, for example, that the diffracted pulse which originates at the shadow casting edge is of opposite polarity in the illuminated and shadow regions. Theoretical and experimental results are compared. [Work supported by ONR.]