• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1157-1169
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• 2010

This paper presents the analytical solution of the fractional Fokker-Planck equation by Adomian decomposition method. By using initial conditions, the explicit solution of the equation has been presented in the closed form and then the numerical solution has been represented graphically. Two different approaches have been presented in order to show the application of the present technique. The present method performs extremely well in terms of efficiency and simplicity.

• International Journal of Naval Architecture and Ocean Engineering
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• 제11권2호
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• pp.939-951
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• 2019

A novel empirical mode decomposition strategy based on Fourier transform and band-pass filter techniques, contributing to efficient instantaneous vibration analyses, is developed in this study. Two key improvements are proposed. The first is associated with the adoption of a band-pass filter technique for intrinsic mode function sifting. The primary characteristic of decomposed components is that their bandwidths do not overlap in the frequency domain. The second improvement concerns an attempt to design narrowband constraints as the essential requirements for intrinsic mode function to make it physically meaningful. Because all decomposed components are generated with respect to their intrinsic narrow bandwidth and strict sifting from high to low frequencies successively, they are orthogonal to each other and are thus suitable for an instantaneous frequency analysis. The direct Hilbert spectrum is employed to illustrate the instantaneous time-frequency-energy distribution. Commendable agreement between the illustrations of the proposed direct Hilbert spectrum and the traditional Fourier spectrum was observed. This method provides robust identifications of vibration modes embedded in vibration processes, deemed to be an efficient means to obtain valuable instantaneous information.

• Journal of Power Electronics
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• 제13권5호
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• pp.884-895
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• 2013

In this paper, the Fourier-based PLL (Phase-locked Loop) is introduced with a new structure, capable of selective harmonic detection in single and three-phase systems. The application of the FB-PLL to harmonic detection is discussed and a new model applicable to three-phase systems is introduced. An analysis of the convergence of the FB-PLL based on a linear model is presented. Simulation and experimental results are included for performance analysis and to support the theoretical development. The decomposition of an input signal in its harmonic components using the Fourier theory is based on previous knowledge of the signal fundamental frequency, which cannot be easily implemented with input signals with varying frequencies or subjected to phase-angle jumps. In this scenario, the main contribution of this paper is the association of a phase-locked loop system, with a harmonic decomposition and reconstruction method, based on the well-established Fourier theory, to allow for the tracking of the fundamental component and desired harmonics from distorted input signals with a varying frequency, amplitude and phase-angle. The application of the proposed technique in three-phase systems is supported by results obtained under unbalanced and voltage sag conditions.

• 음성과학
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• 제8권4호
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• pp.45-58
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• 2001

Modulated components of a speech signal are frequently used for speech coding, speech recognition, and speech synthesis. Time-frequency representation (TFR) reveals some information about instantaneous frequency, instantaneous bandwidth and boundary of each component of the considering speech signal. In many cases, the extraction of AM-FM components corresponding to instantaneous frequencies is difficult since the Fourier spectra of the components with time-varying instantaneous frequency are overlapped each other in Fourier frequency domain. In this paper, an efficient method decomposing speech signal into AM-FM components is proposed. A variable bandwidth filter is developed for the decomposition of speech signals with time-varying instantaneous frequencies. The variable bandwidth filter can extract AM-FM components of a speech signal whose TFRs are not overlapped in timefrequency domain. Also, amplitude and instantaneous frequency of the decomposed components are estimated by using Hilbert transform.

• Journal of Electrical Engineering and Technology
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• 제12권2호
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• pp.559-568
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• 2017

Harmonic/inter-harmonic detection and analysis is an important issue in power system signal processing. This paper proposes a fast algorithm based on matching pursuit (MP) sparse signal decomposition, which can be employed to extract the harmonic or inter-harmonic components of a distorted electric voltage/current signal. In the MP iterations, the method extracts harmonic/inter-harmonic components in order according to the spectrum peak. The Fast Fourier Transform (FFT) and nonlinear optimization techniques are used in the decomposition to realize fast and accurate estimation of the parameters. First, the frequency estimation value corresponding to the maxim spectrum peak in the present residual is obtained, and the phase corresponding to this frequency is searched in discrete sinusoids dictionary. Then the frequency and phase estimations are taken as initial values of the unknown parameters for Nelder-Mead to acquire the optimized parameters. Finally, the duration time of the disturbance is determined by comparing the inner products, and the amplitude is achieved according to the matching expression of the harmonic or inter-harmonic. Simulations and actual signal tests are performed to illustrate the effectiveness and feasibility of the proposed method.

• Structural Engineering and Mechanics
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• 제75권4호
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• pp.425-434
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• 2020

Practical non-synoptic fluctuating wind often exhibits nonstationary features and should be modeled as nonstationary random processes. Generally, the coherence function of the fluctuating wind field has time-varying characteristics. Some studies have shown that there is a big difference between the fluctuating wind field of the coherent function model with and without time variability. Therefore, it is of significance to simulate nonstationary fluctuating wind field with time-varying coherent function. However, current studies on the numerical simulation of nonstationary fluctuating wind field with time-varying coherence are very limited, and the proposed approaches are usually based on the traditional spectral representation method with low simulation efficiency. Especially, for the simulation of multi-variable wind field of large span structures such as transmission tower-line, not only the simulation is inefficient but also the matrix decomposition may have singularity problem. In this paper, it is proposed to conduct the numerical simulation of nonstationary fluctuating wind field in one-spatial dimension with time-varying coherence based on the wavenumber-frequency spectrum. The simulated multivariable nonstationary wind field with time-varying coherence is transformed into one-dimensional nonstationary random waves in the simulated spatial domain, and the simulation by wavenumber frequency spectrum is derived. So, the proposed simulation method can avoid the complicated Cholesky decomposition. Then, the proper orthogonal decomposition is employed to decompose the time-space dependent evolutionary power spectral density and the Fourier transform of time-varying coherent function, simultaneously, so that the two-dimensional Fast Fourier transform can be applied to further improve the simulation efficiency. Finally, the proposed method is applied to simulate the longitudinal nonstationary fluctuating wind velocity field along the transmission line to illustrate its performances.

• IEIE Transactions on Smart Processing and Computing
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• 제4권2호
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• pp.103-109
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• 2015

In this paper, a novel method for the classification of term and preterm birth is proposed based on time-frequency analysis of electrohysterogram (EHG) using multivariate empirical mode decomposition (MEMD). EHG is a promising study for preterm birth prediction, because it is low-cost and accurate compared to other preterm birth prediction methods, such as tocodynamometry (TOCO). Previous studies on preterm birth prediction applied prefilterings based on Fourier analysis of an EHG, followed by feature extraction and classification, even though Fourier analysis is suboptimal to biomedical signals, such as EHG, because of its nonlinearity and nonstationarity. Therefore, the proposed method applies prefiltering based on MEMD instead of Fourier-based prefilters before extracting the sample entropy feature and classifying the term and preterm birth groups. For the evaluation, the Physionet term-preterm EHG database was used where the proposed method and Fourier prefiltering-based method were adopted for comparative study. The result showed that the area under curve (AUC) of the receiver operating characteristic (ROC) was increased by 0.0351 when MEMD was used instead of the Fourier-based prefilter.

• 한국음향학회지
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• 제34권6호
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• pp.493-498
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• 2015

물로 채워진 음향 펄스 튜브 내에는 가진 조건들에 따라 복잡한 형태의 음향 신호들이 형성될 수 있다. 이는 펄스 튜브를 이용해 저주파수 대역에서 평면파 반사계수를 측정하는 것을 어렵게 한다. 본 연구에서는 COMSOL Multiphysics를 이용하여 튜브 벽이 가진되는 경우 펄스 튜브 내에 평면파 뿐 아니라 비평면파 모우드의 복잡한 음장이 발생됨을 보였다. 모우드 분리 방법인 이차원 푸리에 필터링으로 입사 또는 반사하는 평면파 모우드만을 각각 분리할 수 있었다. 이에 시간 게이팅을 적용하므로 음향 시편의 평면파 반사계수를 보다 정확하게 결정할 수 있게 하였다.

• 한국전자파학회:학술대회논문집
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• 한국전자파학회 2000년도 종합학술발표회 논문집 Vol.10 No.1
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• pp.29-33
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• 2000

Stripmap SAR 시스템에서 레이더는 Slant range-domain에서 고정된 Strip상에 Data acquisition period 동안 계속해서 같은 Broadside 방사 패턴을 유지하며, Range domain에서 고정돈 Strip내의 지형의 지도를 제공하는 SAR 영상 시스템이다. Stripmap SAR를 위한 고전적인 영상 복원을 Synthetic aperture (slow-time) domain에서 Deramping 또는 Chirp deconvolution을 이용하는 Fresnel approximaptio에 의존하였다. 또 다른 Stripmap SAR 영상화의 접근방법으로 SAR wavefront reconstruction이론과 레이더 방사형태에 대한 spherical wave Fourier decomposition을 통하여 slow-time domain에서의 SAR 신호의 분석에 기본을 두고 있다. 본 논문에서는 컴퓨터 모의 실험을 통해 생성된 Stripmap SAR 데이터를 이용하여 Fresnel approximation 기법과 Wavefront Reconstruction 기법을 비교 분석한다.

• Geomechanics and Engineering
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• 제7권2호
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• pp.149-164
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• 2014

One of the most advanced classes of techniques for ground response analysis is based on the use of Transfer Functions. They represent the ratio of Fourier spectrum of amplitude motion at the free surface to the corresponding spectrum of the bedrock motion and they are applied in frequency domain usually by FFT method. However, Fourier spectrum only shows the dominant frequency in each time step and is unable to represent all frequency contents in every time step and this drawback leads to inaccurate results. In this research, this process is optimized by decomposing the input motion into different frequency sub-bands using Wavelet Multi-level Decomposition. Each component is then processed with transfer Function relating to the corresponding component frequency. Taking inverse FFT from all components, the ground motion can be recovered by summing up the results. The nonlinear behavior is approximated using an iterative procedure with nonlinear soil properties. The results of this procedure show better accuracy with respect to field observations than does the Conventional method. The proposed method can also be applied to other engineering disciplines with similar procedure.