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The purpose of this paper is to analyze the mechanism and filter efficacy of accumulation generation operator (AGO)/inverse accumulation generation operator (IAGO) in the frequency domain.

The AGO/IAGO in time domain will be transferred to the frequency domain by the Fourier transform. Based on the consistency of the mathematical expressions of the AGO/IAGO in the gray system and the digital filter in digital signal processing, the equivalent filter model of the AGO/IAGO is established. The unique methods in digital signal processing systems “spectrum analysis” of AGO/IAGO are carried out in the frequency domain.

Through the theoretical study and practical example, benefit of spectrum analysis is explained, and the mechanism and filter efficacy of AGO/IAGO are quantitatively analyzed. The study indicated that the AGO is particularly suitable to act on the system's behavior time series in which the long period parts is the main factor. The acted sequence has good effect of noise immunity.

The AGO/IAGO has a wonderful effect on the processing of some statistical data, e.g. most of the statistical data related to economic growth, crop production, climate and atmospheric changes are mainly affected by long period factors (i.e. low-frequency data), and most of the disturbances are short-period factors (high-frequency data). After processing by the 1-AGO, its high frequency content is suppressed, and its low frequency content is amplified. In terms of information theory, this two-way effect improves the signal-to-noise ratio greatly and reduces the proportion of noise/interference in the new sequence. Based on 1-AGO acting, the information mining and extrapolation prediction will have a good effect.

The authors find that 1-AGO has a wonderful effect on the processing of data sequence. When the 1-AGO acts on a data sequence X, its low-pass filtering effect will benefit the information fluctuations removing and high-frequency noise/interference reduction, so the data shows a clear exponential change trends. However, it is not suitable for excessive use because its equivalent filter has poles at the non-periodic content. But, because of pol effect at zero frequency, the 1-AGO will greatly amplify the low-frequency information parts and suppress the high-frequency parts in the information at the same time.

We present an approach for blind separation of acoustic sources produced from multiple speakers mixed in realistic room environments. We first transform recorded signals into the time‐frequency domain to make mixing become instantaneous. We then separate the sources in each frequency bin based on an independent component analysis (ICA) algorithm. For the present paper, we choose the complex version of fixedpoint iteration (CFPI), i.e. the complex version of FastICA, as the algorithm. From the separated signals in the time‐frequency domain, we reconstruct output‐separated signals in the time domain. To solve the so‐called permutation problem due to the indeterminacy of permutation in the standard ICA, we propose a method that applies a special property of the CFPI cost function. Generally, the cost function has several optimal points that correspond to the different permutations of the outputs. These optimal points are isolated by some non‐optimal regions of the cost function. In different but neighboring bins, optimal points with the same permutation are at almost the same position in the space of separation parameters. Based on this property, if an initial separation matrix for a learning process in a frequency bin is chosen equal to the final separation matrix of the learning process in the neighboring frequency bin, the learning process automatically leads us to separated signals with the same permutation as that of the neighbor frequency bin. In each bin, but except the starting one, by chosen the initial separation matrix in such a way, the permutation problem in the time domain reconstruction can be avoided. We present the results of some simulations and experiments on both artificially synthesized speech data and real‐world speech data, which show the effectiveness of our approach.

The convergence of the transfinite‐element (TFE) method for high frequency methods is analyzed in this paper. Two different potential formulations will be compared in the frequency and time domain.

The A*‐and A,v‐formulation for time domain and frequency domain transfinite elements are described. The convergence properties of the methods are investigated and demonstrated on a simple test problem.

It is shown that the convergence of the frequency domain method depends also on the discretization of areas where the field values do not change very much. A numerical example shows that for the calculation of the whole frequency range, the time domain approach is much more faster than the frequency domain method.

Further, work should also cover additional formulations like, e.g. the T,Φ‐formulation.

Pros and cons of different formulations and methods for solving high frequency problems for printed circuit boards or microwave structures are investigated.

The originality of the paper is the comparison, the discussion and the explanations of the convergence of the TFE method for wave propagation.

A novel frequency domain approach, which combines the pseudo excitation method modified by the authors and multi-domain Fourier transform (PEM-FT), is proposed for analyzing nonstationary random vibration in this paper.

For a structure subjected to a nonstationary random excitation, the closed-form solution of evolutionary power spectral density of the response is derived in frequency domain.

The deterministic process and random process in an evolutionary spectrum are separated effectively using this method during the analysis of nonstationary random vibration of a linear damped system, only modulation function of the system needs to be estimated, which brings about a large saving in computational time.

The method is general and highly flexible as it can deal with various damping types and nonstationary random excitations with different modulation functions.

A number of works have been published in the scientific literature proposing the solution of heat diffusion problems by first transforming the relevant partial differential equation to the frequency domain. The purpose of this paper is to present a mesh-free strategy to assess transient heat propagation in the frequency domain, also allowing incorporating initial non-zero conditions.

The strategy followed here is based in Kansa's method, using the MQ RBF as a basis function. The resulting method is truly mesh-free, and does not require any domain or boundary integrals to be evaluated. The definition of good values for the free parameter of the MQ RBF is also addressed.

The strategy was found to be accurate in the calculation of both frequency and time-domain responses. The time evolution of the temperature considering an initial non-uniform distribution of temperatures compared well with a standard time-marching algorithm, based on an implicit Crank-Nicholson implementation. It was possible to calculate frequency-dependent values for the free parameter of the radial basis function.

As far as the authors are aware, previous implementations of the frequency domain heat transfer approach required domain integrals to be evaluated in order to implement non-zero initial conditions. This is totally avoided with the present formulation. Additionally, the method is truly mesh-free, accurate and does not require any element or background mesh to be defined.

The purpose of this paper is to construct a frequency-domain framework to study the asymmetric spillover effects of international economic policy uncertainty on China’s stock market industry indexes.

This paper follows the time domain spillover model, asymmetric spillover model and frequency domain spillover model, which not only studies the degree of spillover in time domain but also studies the persistence of spillover effect in frequency domain.

It is found that China’s economic policy uncertainty plays a dominant role in the spillover effect on the stock market, while the global and US economic policy uncertainty is relatively weak. By decomposing realized volatility into quantified asymmetric risks of “good” volatility and “bad” volatility, it is concluded that economic policy uncertainty has a greater impact on stock downside risk than upside risk. For different time periods, the sensitivity of long-term and short-term spillover economic policy impact is different. Among them, asymmetric high-frequency spillover in the stock market is more easily observed, which provides certain reference significance for the stability of the financial market.

The originality aims at extending the traditional research paradigm of “time domain” to the research perspective of “frequency domain.” This study uses the more advanced models to analyze various factors from the static and dynamic levels, with a view to obtain reliable and robust research conclusions.

The spectral boundary element method for solving two‐dimensional transient heat conduction problems is developed. This method is combined with the fast Fourier transform (FFT) to convert the solution between the time and frequency domains. The fundamental solutions in the frequency domain, required for the present method, are discussed. The resulting line integrations in the frequency domain are discretized using constant boundary elements and used in a Fortran boundary element program. Three examples are used to illustrate the accuracy and effectiveness of the method in both the frequency and time domains. First, the frequency domain solution procedure is verified using the steady‐state example of a semi‐infinite half space with a heat flux applied to a patch of the surface. This spectral boundary element method is then applied to the problem of a circular hole in an infinite solid subjected to a time‐varying heat flux, and solutions in both the frequency and time domains are presented. Finally, the method is used to solve the circular hole problem with a convection boundary condition. The accurary of these results leads to the conclusion that the spectral boundary element method in conjunction with the FFT is a viable option for transient problems. In addition, this spectral approach naturally produces frequence domain information which is itself of interest.

The purpose of this paper is to identify the flexible aircraft model accurately from the frequency responses.

The frequency domain output error method is used to estimate the aerodynamic (rigid body and elastic body) derivatives, and mode shape parameters in the process of identification of flexible aircraft model. The accurate identification of lightly damped low frequency rigid-body response modes requires a careful selection of the frequency sweep length and the fast Fourier transform (FFT) window size, as the FFT window length cannot be longer than any individual sweep records. To address this issue, an effort is made to derive the FFT window length for the application of frequency domain estimation approach.

The investigations are initially made to select a suitable FFT window size for the accurate identification of the lightly damped low frequency rigid-body response modes of the flexible aircraft. Subsequently, frequency domain estimation approach is applied to simulated data of flexible aircraft. Besides the stability and control derivatives, the structural modes of the flexible aircraft are also estimated as part of state space model identification, and it is shown that all the model parameter estimates are accurate. Identification of such flexible aircraft aerodynamic (rigid body and elastic body) derivatives and structural mode shape parameters will lead to mathematical models of flexible aircraft that are accurate over a wide frequency range. The identified models are validated using the time response of frequency sweep data.

Aircraft system identification is an integral part of aerospace system design and life cycle process. This becomes a complex process when the aircraft has significant effects of flexibility on the flight dynamics, especially as the frequencies of the elastic modes become lower and approach those of the rigid body modes. Thus, an integrated mathematical model of flexible aircraft is required to develop, and it should be valid for a wide frequency range and relevant for the design of flight control system.

This paper focuses on the application of frequency domain approach to identify the valid model of flexible aircraft by estimating the aerodynamic (rigid body and elastic body) derivatives and structural mode shape parameters of flexible aircraft. The unknown frequencies of structural modes are also able to identify accurately in frequency domain. This gives more value addition to analyze the flight data of flexible aircraft, as it is challenging problem in parameter estimation of flexible aircraft.

The purpose of this paper is to analyze the spectral characteristics of moving average operator and to propose a novel time-frequency hybrid sequence operator.

Firstly, the complex data is converted into frequency domain data by Fourier transform. An appropriate frequency domain operator is constructed to eliminate the impact of disturbance. Then, the inverse Fourier transform transforms the frequency domain data in which the disturbance is removed, into time domain data. Finally, an appropriate moving average operator of N items is selected based on spectral characteristics to eliminate the influence of periodic factors and noise.

Through the spectrum analysis of the real-time data sensed and recorded by microwave sensors, the spectral characteristics and the ranges of information, noise and shock disturbance factors in the data can be clarified.

The real-time data analysis results for a drug component monitoring show that the hybrid sequence operator has a good effect on suppressing disturbances, periodic factors and noise implied in the data.

Firstly, the spectral analysis of moving average operator and the novel time-frequency hybrid sequence operator were presented in this paper. For complex data, the ideal effect is difficult to achieve by applying the frequency domain operator or time domain operator alone. The more satisfactory results can be obtained by time-frequency hybrid sequence operator.

The purpose of this paper is to develop an easy-to-implement and accurate fast boundary element method (BEM) for solving large-scale elastodynamic problems in frequency and time domains.

A newly developed kernel-independent fast multipole method (KIFMM) is applied to accelerating the evaluation of displacements, strains and stresses in frequency domain elastodynamic BEM analysis, in which the far-field interactions are evaluated efficiently utilizing equivalent densities and check potentials. Although there are six boundary integrals with unique kernel functions, by using the elastic theory, the authors managed to accelerate these six boundary integrals by KIFMM with the same kind of equivalent densities and check potentials. The boundary integral equations are discretized by Nyström method with curved quadratic elements. The method is further used to conduct the time-domain analysis by using the frequency-domain approach.

Numerical results show that by the fast BEM, high accuracy can be achieved and the computational complexity is brought down to linear. The performance of the present method is further demonstrated by large-scale simulations with more than two millions of unknowns in the frequency domain and one million of unknowns in the time domain. Besides, the method is applied to the topological derivatives for solving elastodynamic inverse problems.

An efficient KIFMM is implemented in the acceleration of the elastodynamic BEM. Combining with the Nyström discretization based on quadratic elements and the frequency-domain approach, an accurate and highly efficient fast BEM is achieved for large-scale elastodynamic frequency domain analysis and time-domain analysis.