• The Journal of Korean Institute of Communications and Information Sciences
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• v.39A no.12
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• pp.739-745
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• 2014

It has been shown in compressive sensing that every s-sparse $x{\in}R^N$ can be recovered from the measurement vector y=Ax or the noisy vector y=Ax+e via ${\ell}_1$-minimization as soon as the 3s-restricted isometry constant of the sensing matrix A is smaller than 1/2 or smaller than $1/\sqrt{3}$ by applying the Iterative Hard Thresholding (IHT) algorithm. However, recovery can be guaranteed by practical algorithms for some certain assumptions of acquisition schemes. One of the key assumption is that the sensing matrix must satisfy the Restricted Isometry Property (RIP), which is often violated in the setting of many practical applications. In this paper, we studied a generalization of RIP, called Restricted Biorthogonality Property (RBOP) for anisotropic cases, and the new recovery algorithms called oblique pursuits. Then, we provide an analysis on the success of sparse recovery in terms of restricted biorthogonality constant for the IHT algorithms.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.427-456
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• 1997

This paper concerns constructing wavelet bases on the unit interval, where a new boundary treatment is provided to overcome certain drawbacks of eariler constructions. Wavelet expansions on the unit interval usually suffer from artificial boundary effects and poor convergence at the boundaries. Many researchers have suggested a solution to the drawbacks. From a practical point of view, their solutions also have a common disadvantage. This paper provides a new solution using biorthogonality near the boundaries, that avoids the disadvantage while preserving their advantages.

• Journal of the Korean Mathematical Society
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• v.51 no.5
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• pp.941-953
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• 2014

In this paper, a 2-circular matrix theory is developed, and a concept of spectral radius for biorthogonal wavelet is introduced. We propose a novel design method by minimizing the spectral radius and obtain a wavelet which has better performance than the famous 9-7 wavelet in terms of image compression coding.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.618-621
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• 1995

In this paper, in order to obtain a disturbance decouplable as well as effective and disturbance suppressible controller, a simultaneous assignment methodology of the left and right eigenstructure is proposed. The biorthogonality property between the left and right model matrices of a system as well as the relations between the achievable right model matrix and states selsction matrices are used to develop the methodology. the proposed concurrent eigenstructure assignment methodologh guarantees that the desired eigenvalues are achieved exactly and the desired left and right eigenvectors are assigned to the best possible(achievable) sets of eigenvectors in the least square sense, respectively.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.162-167
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• 1994

An effective and disturbance suppressible controller can be obtained by assigning the left eigenstructure (eigenvalues/left eigenvectors) of a system. However, the disturbance decouplability is governed by the right eigenstructure(eigenvalues/right eigenvectors) of the system. In this paper, in order to obtain a disturbance decouplable as well as effective and disturbance suppressible controller, the concurrent assignment scheme of the left and right eigenstructure is proposed. The biorthogonality property between the left and right modal matrices of a system well as the relations between the achievable right modal matrix and states selection matrices are used to develop the scheme. The proposed concurrent eigenstructure assignment scheme guarantees that the desired eigenvalues are achieved exactly and the desired left and right eigenvectors are assigned to the best possible(achievable) sets of eigenvectors in the least square sense, respectively. A numerical example is presented to illustrate the usefulness of the proposed scheme.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.463-473
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• 2009

A family of quasi-interpolatory wavelet system was introduced in [10], extending and unifing the biorthogonal Coiffman wavelet system. The corresponding refinable functions and wavelets have vanishing moment of a certain order (say, L), which is a key property for data representation and approximation. One of main advantages of this wavelet systems is that we can get optimal smoothness in the sense of smoothing factors in the scaling filters. In this paper, we first discuss the biorthogonality condition of the quisi-interpolatory wavelet system. Then, we study the properties of the scaling and wavelet filters, related to the polynomial reproduction and the vanishing moment respectively, which in fact determines the approximation orders of biorthogonal projections. In addition, we discuss the approximation orders of the wavelet projections.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.230-235
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• 1996

Eigenstructure (eigenvalues/eigenvectors) assignment has been shown to be a useful tool for flight control system design. In the sense of the eigenstructure assignment, the effectiveness and disturbance suppressibility of a controller depend mainly on the left eigenstructure (eigenvalues/left eigenvectors) of a system. On the other hand, the disturbance decouplability is governed by the right eigenstructure (eigenvalues/right eigenvectors) of the system. In this paper, in order to obtain a disturbance decouplable as well as effective and disturbance suppressible controller, a concurrent assignment methodology of the left and right eigenstructures is proposed. The biorthogonality condition between the left and right modal matrices of a system as well as the relations between the achievable right modal matrix and state selection matrices are used to develop the methodology. The proposed concurrent eigenstructure assignment methodology guarantees that the desired eigenvalues are achieved exactly and the desired left and right eigenvectors are assigned to the best possible(achievable) sets of eigenvectors in the least square sense, respectively. The proposed design methodology is applied to designing a lateral flight control system for an L-1011 aircraft with disturbances.

• Journal of Institute of Control, Robotics and Systems
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• v.1 no.1
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• pp.4-12
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• 1995

In the sense of eigenstructure (eigenvalues/eignenvectors) assignment, the effectiveness and disturbance suppressibility of a controller depend mainly on the left eigenstructure (eignevalues/left eigenvectors) of a system. On the other hand, the disturbance decouplability is governed by the right eigenstructure (eignevalues/right eigenvectors) of the system. In this paper, in order to obtain a disturbance decouplable as well as effetive and disturbance suppressible controller, a concurrent assignment methodology of the left and right eigenstructure is proposed. The biorthogonality condition between the left and right modal matrix and state selection matrices are used to develop the methodology. The proposed concurrent eigenstructure assignment methodology guarantees that the desired eigenvalues are achieved exactly and the desired left and right eigenvectors are assigned to the best possible (achievable) sets of eigenvectors in the least square sense, respectively. A numerical example is presented to illustrate the validity and usefulness of the proposed methodology.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.10
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• pp.915-922
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• 2010

This paper presents an efficient method for determining the forced response of a spinning flexible disk-spindle system supported by fluid dynamic bearings(FDBs) in a computer hard disk drive(HDD). The spinning flexible disk-spindle system is represented by the asymmetric finite element equations of motion originating from the asymmetric dynamic coefficients of the FDBs and the gyroscopic moment of a spinning disk-spindle system. The proposed method utilizes only the right eigenvectors of the eigenvalue problem to transform the large asymmetric finite element equations of motion into a small number of coupled equations, guaranteeing the accuracy of their numerical integration. The results are then back-substituted into the equations of motion to determine the forced response. The effectiveness of the proposed method was verified by comparing it with the responses from the classical methods of mode superposition with the general eigenvalue problems, and mode superposition with modal approximation. The proposed method was shown to be effective in determining the forced response represented by the asymmetric finite element equations of motion of a spinning flexible disk-spindle system supported by FDBs.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.36S no.10
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• pp.10-20
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• 1999

In this paper, we propose and analyze a multiuser receiver using a decorrelating filter and Viterbi decoders for trellis coded DS/CDMA systems with biorthgonal signal constellation in asynchronous channels. The biorthogonality is implemented by user signature waveforms and the decorrelating filter. The performance of the proposed system is investigated with emphasis on the asymptotic cases. It is shown that the proposed system can provide us with some coding gain and near-far resistance. We also analyze the performance of the proposed system with base-station antenna array.