• The Journal of the Acoustical Society of Korea
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• v.20 no.4E
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• pp.39-44
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• 2001

We investigate the numerical instability of linear prediction for discrete harmonic spectra of audio signals. It is identified that the eigenvalue spread is very large when discrete harmonic spectra are confined only in a lower part of the entire signal bandwidth. A simple method that redefines the sampling frequency and associate harmonic frequencies is proposed to improve the numerical stability. Simulation results using real audio signals indicate its superior stabilizing ability and improved accuracy in the discrete spectral estimation for both LP and DAP.

• Kyungpook Mathematical Journal
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• v.47 no.4
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• pp.529-548
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• 2007

The purpose of this article is to find a relation between the finite difference method and the boundary element method, and propose a new approach deriving a discrete approximation formula as like that of the finite difference method for harmonic functions. We develop a discrete approximation formula on a uniform grid based on the boundary integral formulations. We consider three different boundary integral formulations and derive one discrete approximation formula on the uniform grid for the harmonic function. We show that the proposed discrete approximation formula has the same computational molecules with that of the finite difference formula for the Laplace operator ${\nabla}^2$.

• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1033-1046
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• 1999

This paper is devoted to the point wise error estimate up to boundary for the standard finite element solution of Poisson equation with Dirichlet boundary condition. Our new approach used the discrete maximum principle for the discrete harmonic solution. once the mesh in our domain satisfies the $\beta$-condition defined by us, the discrete harmonic solution with dirichlet boundary condition has the discrete maximum principle and the pointwise error should be bounded by L-errors newly obtained.

• Journal of the Korean Mathematical Society
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• v.61 no.2
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• pp.377-393
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• 2024

In this paper, we study the positive solutions to a discrete harmonic function for a random walk satisfying finite range and ellipticity conditions, killed at the boundary of an unbounded cylinder in ℤ^d. We first prove the existence and uniqueness of positive solutions, and then establish that all the positive solutions are generated by two special solutions, which are exponential growth at one end and exponential decay at the other. Our method is based on maximum principle and a Harnack type inequality.

• The Journal of Engineering Research
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• v.5 no.1
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• pp.37-44
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• 2004

n this paper, an efficient LP method for discrete harmonic spectra is proposed and discussed. A new efficient LP method is a combination of recursive and frequency selective LP. While the recursive LP provides better spectral matching in spectral hill, frequency selective LP eliminates numerical instability and improves spectral matching when the harmonics are confined in the low frequency region. The proposed LP method is applied to the HILN coder. Simulation results using a verification model(VM) software for real audio signals show a definite trend of significant improvement.

• Journal of Power Electronics
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• v.18 no.6
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• pp.1659-1669
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• 2018

An improved circulating current suppression control method is proposed in this paper. In the proposed controller, an outer loop of the average capacitor voltage control model is used to balance the sub-module capacitor voltage. Meanwhile, an individual voltage balance controller and an arm voltage balance controller are also used. The DC and harmonic components of the circulating current are separated using a low pass filter. Therefore, a multiple quasi-proportional-resonant (multi-quasi-PR) controller is introduced in the inner loop to eliminate the circulating harmonic current, which mainly contains second-order harmonic but also contains other high-order harmonics. In addition, the parameters of the multi-quasi-PR controller are designed in the discrete domain and an analysis of the stability characteristic is given in this paper. In addition, a simulation model of a three-phase MMC system is built in order to confirm the correctness and superiority of the proposed controller. Finally, experiment results are presented and compared. These results illustrate that the improved control method has good performance in suppressing circulating harmonic current and in balancing the capacitor voltage.

• Nuclear Engineering and Technology
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• v.52 no.6
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• pp.1137-1147
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• 2020

The discrete ordinates method (S_N) is one of the major shielding calculation method, which is suitable for solving deep-penetration transport problems. Our objective is to explore the available quadrature sets and to improve the accuracy in shielding problems involving strong anisotropy. The linear discontinuous finite-element (LDFE) quadrature sets based on the icosahedron (in short, ICLDFE quadrature sets) are developed by defining projected points on the surfaces of the icosahedron. Weights are then introduced in the integration of the discontinuous finite-element basis functions in the relevant angular regions. The multivariate secant method is used to optimize the discrete directions and their corresponding weights. The numerical integration of polynomials in the direction cosines and the Kobayashi benchmark are used to analyze and verify the properties of these new quadrature sets. Results show that the ICLDFE quadrature sets can exactly integrate the zero-order and first-order of the spherical harmonic functions over one-twentieth of the spherical surface. As for the Kobayashi benchmark problem, the maximum relative error between the fifth-order ICLDFE quadrature sets and references is only -0.55%. The ICLDFE quadrature sets provide better integration precision of the spherical harmonic functions in local discrete angle domains and higher accuracy for simple shielding problems.

• Journal of Electrical Engineering and Technology
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• v.12 no.2
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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.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.7
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• pp.551-558
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• 2000

In this paper a systematic approach to automatic classificationi of power system harmonic disturbances is proposed where the proposed approach consists of the following three steps:(i) detecting and localizing each harmonic disturbance by applying discrete wavelet transform(DWT) (ii) extracting an efficient feature vector from each detected disturbance waveform by utilizing FFT and principal component analysis (PCA) along with Fisher's criterion and (iii) classifying the corresponding type of each harmonic disturbance by recognizing the pattern of each feature vector. To demonstrate the performance and applicability of the proposed classification procedure some simulation results obtained by analyzing 8-class power system harmonic disturbances being generated with Matlab power system blockset are also provided.

• Journal of Electrical Engineering and Technology
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• v.10 no.5
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• pp.2018-2030
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• 2015

A two stage ac drive configuration consisting of a single-phase line commutated rectifier and a three-phase voltage source inverter (VSI) is very common in low and medium power applications. The deterministic pulse width modulation (PWM) methods like sinusoidal PWM (SPWM) could not be considered as an ideal choice for modern drives since they result mechanical vibration and acoustic noise, and limit the application scope. This is due to the incapability of the deterministic PWM strategies in sprawling the harmonic power. The random PWM (RPWM) approaches could solve this issue by creating continuous harmonic profile instead of discrete clusters of dominant harmonics. Insufficient filtering at dc link results in the amplitude distortion of the input dc voltage to the VSI and has the most significant impact on the spectral errors (difference between theoretical and practical spectra). It is obvious that the sprawling effect of RPWM undoubtedly influenced by input fluctuation and the discrete harmonic clusters may reappear. The influence of dc link fluctuation on harmonics and their spreading effect in the VSI remains invalidated. A case study is done with four different filter capacitor values in this paper and results are compared with the constant dc input operation. This paper also proposes an ingenious RPWM, a ripple dosed sinusoidal reference-random carrier PWM (RDSRRCPWM), which has the innate capacity of suppressing the effect of input fluctuation in the output than the other modern PWM methods. MATLAB based simulation study reveals the fundamental component, total harmonic distortion (THD) and harmonic spread factor (HSF) for various modulation indices. The non-ideal dc link is managed well with the developed RDSRRCPWM applied to the VSI and tested in a proto type VSI using the field programmable gate array (FPGA).