• Journal of Electrical Engineering and Technology
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• v.7 no.2
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• pp.163-170
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• 2012

This paper presents a DFT (Discrete Fourier Transform) based estimation algorithm for the parameters of a low-frequency oscillating signal. The proposed method estimates the parameters, i.e., the frequency, the damping factor, the mode amplitude, and the phase, by fitting a discrete Fourier spectrum with an exponentially damped cosine function. Parameter estimation algorithms that consider the spectrum leakage of the discrete Fourier spectrum are introduced. The multi-domain mode test functions are tested in order to verify the accuracy and efficiency of the proposed method. The results show that the proposed algorithms are highly applicable to the practical computation of low-frequency parameter estimations based on DFTs.

• Journal of Electrical Engineering and Technology
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• v.12 no.1
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• pp.378-384
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• 2017

In this paper, an efficient short-time Fourier analysis method for the quasi-periodic signals is proposed via an optimal fixed-lag finite impulse response (FIR) smoother approach using a receding horizon scheme. In order to deal with time-varying Fourier coefficients (FCs) of quasi-periodic signals, a state space model including FCs as state variables is augmented with the variants of FCs. Through an optimal fixed-lag FIR smoother, FCs and their increments are estimated simultaneously and combined to produce final estimates. A lag size of the optimal fixed-lag FIR smoother is chosen to minimize the estimation error. Since the proposed estimation scheme carries out the correction process with the estimated variants of FCs, it is highly probable that the smaller estimation error is achieved compared with existing approaches not making use of such a process. It is shown through numerical simulation that the proposed scheme has better tracking ability for estimating time-varying FCs compared with existing ones.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.6
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• pp.1078-1086
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• 2009

This paper presents a Fourier based algorithm for estimating the parameters of the low frequency oscillating modes. The proposed methods estimates various parameters(frequency, damping factor, mode magnitude, phase) by fitting Fourier spectrum and phase with a damped exponential cosine function. Dominant frequency is selected by taking frequency corresponding to the peak spectrum, and damping factor is estimated using the left/right spectra of Fourier spectrum. In addition, mode magnitude is calculated by the normalized peak spectrum, and phase is estimated from spectrum phase. Also, we introduce an accuracy index in order to determine the accuracy of the estimated parameters, and the index is calculated using the deviations of the peak spectrum and the left/right spectra. The parameter estimation methods proposed in this paper include very simple arithmetical processes, so the algorithms are simple and the calculation speed is very fast. The proposed methods are applied to test functions with two dominant modes. The results show that the proposed methods are highly applicable to low frequency parameter estimation.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.55 no.7
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• pp.265-272
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• 2006

This paper describes a method of parameter estimation of time series data using discrete Fourier transform(DFT). DFT have been mainly used to precisely and rapidly obtain the frequency of a signal. In a dynamic system, a real part of a mode used to learn damping characteristics is a more important factor than the frequency of the mode. The parameter estimation method of this paper can directly estimate modes and parameters, indicating the characteristics of a dynamic system, on the basis of the Fourier transform of the time series data. Real part of a mode estimates by subtracting a frequency of the Fourier spectrum corresponding to 0.707 of a magnitude of the peak spectrum from a peak frequency, or subtracting a frequency of the power spectrum corresponding to 0.5 of the peak power spectrum from a peak frequency, or comparing the Fourier(power) spectrum ratio. Also, the residue and phase of time signal calculate by simple equation with the real part of the mode and the power spectrum that have been calculated. Accordingly, the proposed algorithm is advantageous in that it can estimate parameters of the system through a single DFT without repeatedly calculating a DFT, thus shortening the time required to estimate the parameters.

• Communications for Statistical Applications and Methods
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• v.4 no.3
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• pp.833-845
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• 1997

Fourier expansion is considered for the deconvolution problem of estimating a probability density function when the sample observations are contaminated with random noise. In the log-Fourier method of density estimation for data without noise, the logarithm of the unknown density function is approximated by a trigonometric function, the unknown parameters of which are estimated by maximum likelihood. The log-Fourier density estimation method, which has been considered theoretically by Koo and Chung (1997), is studied for the finite-sample case with noise. Numerical examples using simulated data are given to show the performance of the log-Fourier deconvolution.

• Proceedings of the KIEE Conference
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• 2004.11c
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• pp.165-168
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• 2004

This paper propose a target tracker using phase correlation. The tracker consist of a pre-processing module, a translation estimation module based on phase correlation, a fine motion estimation module applied when confidence rate could not fulfill a threshold value and a reference image update module. The fine motion estimation module measure the shift, rotation and scale of input image compared to reference using Fourier-Mellin transform. Proposed tracker was tested its accuracy and robustness using some real indoor and outdoor image sequences.

• Proceedings of the Korean Statistical Society Conference
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• 2002.11a
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• pp.109-114
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• 2002

In this paper we propose a change-point estimator with left and right regressions using the sample Fourier coefficients on the orthonormal bases. The asymptotic properties of the proposed change-point estimator are established. The limiting distribution and the consistency of the estimator are derived.

• Journal of IKEEE
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• v.18 no.4
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• pp.463-470
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• 2014

In stratified flows of two immiscible liquids, due to the vibration in a pipe, the shape of the interface is not always periodic and it causes the different end points of the interfacial boundary. In this case the performance is not good. To solve this, in this paper, the hybrid-type Fourier series is proposed, which consists of both the polynomial and the trigonometric terms. Under the stationary interfacial boundary during acquiring a full set of voltage data, the performance of the proposed method is evaluated through the numerical experiments. The results show that the proposed method performs better than the conventional Fourier series in estimating the interfacial boundary.

• Communications for Statistical Applications and Methods
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• v.29 no.1
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• pp.127-150
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• 2022

We discuss multiple change-point estimation as edge detection in piecewise smooth functions with finitely many jump discontinuities. In this paper we propose change-point estimators using concentration kernels with Fourier coefficients. The change-points can be located via the signal based on Fourier transformation system. This method yields location and amplitude of the change-points with refinement via concentration kernels. We prove that, in an appropriate asymptotic framework, this method provides consistent estimators of change-points with an almost optimal rate. In a simulation study the proposed change-point estimators are compared and discussed. Applications of the proposed methods are provided with Nile flow data and daily won-dollar exchange rate data.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.9
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• pp.1485-1490
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• 2008

This paper proposes a new Fourier transform-based phasor estimation method to eliminate the adverse influence of the exponentially decaying dc offsets when Discrete Fourier Transform (DFT) is used to calculate the phasor of the fundamental frequency component in a relaying signal. By subtracting the result of odd-sample-set DFT from the result of even-sample-set DFT, the information of dc offsets can be obtained. Two dc offsets in a relaying signal are treated as one dc offset which is piecewise approximated in one cycle data window. The effect of the dc offsets can be eliminated by the approximated dc offset. The performance of the proposed algorithm is evaluated by using computer-simulated signals and EMTP-generated signals. The algorithm is also tested on a hardware board with TMS320C32 microprocessor. The evaluation results indicate that the proposed algorithm has the stable and accurate eliminating performance even if the input signal contains two decaying dc components having different time constants.