• Journal of the Korean earth science society
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• v.35 no.5
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• pp.333-341
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• 2014

A new set of basis functions was constructed using the Rossby-Haurwitz waves, which are the eigenfunctions of nondivergent barotropic vorticity equations on the sphere. The basis functions were designed to be non-separable, that is, not factored into functions of either the longitude or the latitude. Due to this property, the nodal lines of the functions are aligned neither along with the meridian nor the parallel. The basis functions can be categorized into groups of which members have the same degree or the total wavenumber-like index on the sphere. The orthonormality of the basis functions were found to be close to the machine roundoffs, giving the error of $O(10^{-15})$ or $O(10^{-16})$ for double-precision computation (64 bit arithmetic). It was demonstrated through time-stepping procedure that the basis functions were also the eigenfunctions of the non-divergent barotropic vorticity equations. The projection of the basis functions was carried out onto the low-resolution geopotential field of Gaussian bell, and compared with the theory. The same projections were performed for the observed atmospheric-geopotential height field of 500 hPa surface to demonstrate decomposition into the fields that contain disturbance of certain range of horizontal scales. The usefulness of the new basis functions was thus addressed for application to the eigenmode analysis of the atmospheric motions on the global domain.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.26.1-26
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• 2001

In this paper, we will expand and generalize the orthogonal functions as basis functions for dynamical system representations. The orthogonal functions can be considered as generalizations of, for example, the pulse functions, Laguerre functions, and Kautz functions, and give rise to an alternative series expansion of rational transfer functions. It is shown row we can exploit these generalized basis functions to increase the speed of convergence in a series expansion. The set of Kautz functions is discussed in detail and, using the power-series equivalence, the truncation error is obtained. And so we will present the influence of noises to use Kautz function on the identification accuracy.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.1430-1436
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• 2007

A principal components analysis (PCA) of the median head-related impulse responses (HRIRs) in the CIPIC HRTF database reveals that the individual HRIRs can be adequately reconstructed by a linear combination of 12 orthonormal basis functions. These basis functions can be used generally to model arbitrary HRIRs, which are not included in the process to obtain the basis functions. To clarify whether these basis functions can be used to model other set of arbitrary HRIRs, an numerical error analysis for modeling and a series of subjective listening tests were carried out using the measured and modeled HRIRs. The results showed that the set of individual HRIRs, which were measured in our lab using different measurement conditions, techniques, and source positions, can be well modeled with reasonable accuracy. Furthermore, all subjects reported not only the accurate vertical perception but also the front-back discrimination with the modeled HRIRs based on 12 basis functions. However, as less basis functions were used for HRIR modeling, the modeling accuracy and localization performance deteriorated.

• Korean Journal of Mathematics
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• v.22 no.2
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• pp.289-305
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• 2014

In this paper we propose a new approach to the variable selection problem for a primary resolution and wavelet basis functions in wavelet regression. Most wavelet shrinkage methods focus on thresholding the wavelet coefficients, given a primary resolution which is usually determined by the sample size. However, both a primary resolution and the basis functions are affected by the shape of an unknown function rather than the sample size. Unlike existing methods, our method does not depend on the sample size and also takes into account the shape of the unknown function.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.435-443
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• 2007

An important approach towards solving the scattered data problem is by using radial basis functions. However, for a large class of smooth basis functions such as Gaussians, the existing theories guarantee the interpolant to approximate well only for a very small class of very smooth approximate which is the so-called 'native' space. The approximands f need to be extremely smooth. Hence, the purpose of this paper is to study approximation by a scattered shifts of a radial basis functions. We provide error estimates on larger spaces, especially on the homogeneous Sobolev spaces.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.05a
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• pp.120-126
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• 2007

A principal components analysis of the entire median HRIRs in the CIPIC HRTF database reveals that the individual HRIRs can be adequately reconstructed by a linear combination of several orthonormal basis functions. The basis functions cover the inter-individual and inter-elevation variations in median HRIRs. There are elevation-dependent tendencies in the weights of basis functions, and the basis functions can be ordered according to the magnitude of standard deviation of the weights at each elevation. We propose a HRIR customization method via tuning of the weights of 3 dominant basis functions corresponding to the 3 largest standard deviations at each elevation. Subjective listening test results show that both front-back reversal and vertical perception can be improved with the customized HRIRs.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.4
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• pp.448-457
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• 2008

A principal components analysis (PCA) of the median-plane head-related impulse responses (HRIRs) in the CIPIC HRTF database reveals that the individual HRIRs in the median plane can be adequately reconstructed by a linear combination of 12 orthonormal basis functions. These basis functions can be used to model arbitrary median-plane HRIRs, which are not included in the process to obtain the basis functions. Memory size can be reduced up to 5-fold depending on the number of HRIRs to be modeled. To clarify whether these basis functions can be used to model other set of arbitrary median plane HRIRs, a numerical error analysis for modeling and a series of subjective listening tests were carried out using the measured and modeled HRIRs. The results showed that the set of individual HRIRs in the median plane, which were measured in our lab using different measurement conditions, techniques, and source positions, can be modeled with reasonable accuracy. All subjects, involved in the subjective listening test, reported not only the accurate vertical perception but also the front-back discrimination with the modeled HRIRs based on 12 basis functions.

• Journal of the Korean Chemical Society
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• v.57 no.2
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• pp.172-175
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• 2013

We compare the relative usefulness of common basis functions and numerical integration methods in representing complex resonance state encountered in the molecular scattering problem of aluminum dimer electronic predissociation. Specifically, the basis set size and computing CPU times are monitored in order to find the minimum requirement for ensuring the modest accuracy of calculated resonance energies (0.1 $cm^{-1}$) for more than 100 resonance states. The combination of the so-called one-dimensional box eigenfunctions and energy-dependent boundary functions are found to be most efficient if integration is done using the basis set quadrature rules.

• ETRI Journal
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• v.35 no.3
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• pp.397-405
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• 2013

In this paper, two sets of spectrally efficient ultra-wideband (UWB) pulses using zinc and frequency-domain Walsh basis functions are proposed. These signals comply with the Federal Communications Commission (FCC) regulations for UWB indoor communications within the stipulated bandwidth of 3.1 GHz to 10.6 GHz. They also demonstrate high energy spectral efficiency by conforming more closely to the FCC mask than other UWB signals described in the literature. The performance of these pulses under various modulation techniques is discussed in this paper, and the proposed pulses are compared with Gaussian monocycles in terms of spectral efficiency, autocorrelation, crosscorrelation, and bit error rate performance.

• 한국전산유체공학회:학술대회논문집
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• 2009.11a
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• pp.49-55
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• 2009

This paper evaluates performances of a recently developed divergence-free finite element method based on Hermite interpolated stream functions. Velocity bases are derived from Hermite interpolated stream functions to form divergence-free basis functions. These velocity basis functions constitute a solenoidal function space, and the simple gradient of the Hermite functions constitute an irrotational function space. The incompressible Navier-Stokes equation is orthogonally decomposed into a solenoidal and an irrotational parts, and the decoupled Navier-Stokes equations are projected onto their corresponding spaces to form proper variational formulations. To access accuracy and convergence of the present algorithm, three test problems are selected. They are lid-driven cavity flow, flow over a backward-facing step and buoyancy-driven flow within a square enclosure. Hermite interpolation functions from cubic to quintic are chosen to run the test problems. Numerical results are shown. In all cases it has shown that the present method has performed well in accuracies and convergences. Moreover, the present method does not require an upwinding or a stabilized term.