• Structural Engineering and Mechanics
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• v.45 no.1
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• pp.95-110
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• 2013

In the recent decade, practical of wavelet technique is being utilized in various domain of science. Particularly, engineers are interested to the wavelet solution method in the time series analysis. Fundamentally, seismic responses of structures against time history loading such as an earthquake, illustrates optimum capability of systems. In this paper, a procedure using particularly discrete Haar wavelet basis functions is introduced, to solve dynamic equation of motion. In the proposed approach, a straightforward formulation in a fluent manner is derived from the approximation of the displacements. For this purpose, Haar operational matrix is derived and applied in the dynamic analysis. It's free-scaled matrix converts differential equation of motion to the algebraic equations. It is shown that accuracy of dynamic responses relies on, access of load in the first step, before piecewise analysis added to the technique of equation solver in the last step for large scale of wavelet. To demonstrate the effectiveness of this scheme, improved formulations are extended to the linear and nonlinear structural dynamic analysis. The validity and effectiveness of the developed method is verified with three examples. The results were compared with those from the numerical methods such as Duhamel integration, Runge-Kutta and Wilson-${\theta}$ method.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.10
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• pp.977-982
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• 2008

In this paper Haar functions are developed to approximate the solutions of continuous time linear system. Properties of Haar functions are first presented, and an explicit expression for the inverse of the Haar operational matrix is presented. Using the inverse of the Haar operational matrix the full order Stein equation should be solved in terms of the solutions of pure algebraic matrix equations, which reduces the computation time remarkably. Finally a numerical example is illustrated to demonstrate the validity of the proposed algorithm.

• The Korean Journal of Applied Statistics
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• v.31 no.6
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• pp.707-719
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• 2018

Various time series representation methods have been proposed for efficient time series clustering and classification. Lin et al. (DMKD, 15, 107-144, 2007) proposed a symbolic aggregate approximation (SAX) method based on symbolic representations after approximating the original time series using piecewise local mean. The performance of SAX therefore depends heavily on how well the piecewise local averages approximate original time series features. SAX equally divides the entire series into an arbitrary number of segments; however, it is not sufficient to capture key features from complex, large-scale time series data. Therefore, this paper considers data-adaptive local constant approximation of the time series using the unbalanced Haar wavelet transformation. The proposed method is shown to outperforms SAX in many real-world data applications.

• Journal of the Korea Society for Simulation
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• v.16 no.4
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• pp.13-22
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• 2007

Fault detection of cycle-based signals is typically performed using statistical approaches. Univariate SPC using few representative statistics and multivariate analysis methods such as PCA and PLS are the most popular methods for analyzing cycle-based signals. However, such approaches are limited when dealing with information-rich cycle-based signals. In this paper, process fault defection method based on wavelet analysis is proposed. Using Haar wavelet, coefficients that well reflect the process condition are selected. Next, Hotelling's $T^2$ chart using selected coefficients is constructed for assessment of process condition. To enhance the overall efficiency of fault detection, the following two steps are suggested, i.e. denoising method based on wavelet transform and coefficient selection methods using variance difference. For performance evaluation, various types of abnormal process conditions are simulated and the proposed algorithm is compared with other methodologies.

• Journal of the Korean Magnetic Resonance Society
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• v.6 no.1
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• pp.12-19
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• 2002

A shift-averaged Haar wavelet transform was introduced as a new and excellent tool to distinguish real peaks from the noise contaminated NMR signals. It is based on Haar wavelet transform and translation-invariant denoising process. Donoho＇s universal threshold was newly introduced to the shift-averaged Haar wavelet transform for the purpose of automated noise suppression, and was quantitatively compared with the conventional uniform threshold method in terms or threshold and signal to noise ratio (SNR). New algorithm was combined with a routine to suppress a large solvent peak by singular value decomposition (SVD). Combined algorithm was applied to the real spectrum that containing large solvent peak.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.12
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• pp.1270-1277
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• 2008

A Haar wavelet based numerical method for solving singularly perturbed linear time invariant system is presented in this paper. The reduced pure slow and pure fast subsystems are obtained by decoupling the singularly perturbed system and differential matrix equations are converted into algebraic Sylvester matrix equations via Haar wavelet technique. The operational matrix of integration and its inverse matrix are utilized to reduce the computational time to the solution of algebraic matrix equations. Finally a numerical example is given to demonstrate the validity and applicability of the proposed method.

• Proceedings of the Korea Information Processing Society Conference
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• 2009.11a
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• pp.249-250
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• 2009

음향 신호 이미지 처리, human vision 등의 분야에서 널리 쓰이는 wavelet transform의 가장 간단한 형태인 one-dimension haar wavelet transform을 CUDA로 구현하고 hardware 특성을 살린 optimizing을 함으로써 Data-parallelism의 성능과 CUDA memory architecture의 상관 관계를 살펴본다.

• Korean Journal of Remote Sensing
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• v.24 no.1
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• pp.57-64
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• 2008

In the previous study, the Haar wavelet was used as the sole basis function for the 3D discrete wavelet transform because the number of bands is too small to decompose a remotely sensed image in band direction with other basis functions. However, it is possible to use other basis functions for wavelet decomposition in horizontal and vertical directions because wavelet decomposition is independently performed in each direction. This study aims to classify a high spatial resolution image with the six types of basis function including the Haar function and to compare those results. The other wavelets are more helpful to classify high resolution imagery than the Haar wavelet. In overall accuracy, the Coif4 wavelet has the best result. The improvement of classification accuracy is different depending on the type of class and the type of wavelet. Using the basis functions with long length could be effective for improving accuracy in classification, especially for the classes of small area. This study is expected to be used as fundamental information for selecting optimal basis function according to the data properties in the 3D DWT based image classification.

• Journal of Korea Multimedia Society
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• v.14 no.8
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• pp.992-999
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• 2011

This paper proposed a human body posture recognition program based on haar-like feature and hand activity detection. Its distinguishing features are the combination of face detection and motion detection. Firstly, the program uses the haar-like feature face detection to receive the location of human face. The haar-like feature is provided with the advantages of speed. It means the less amount of calculation the haar-like feature can exclude a large number of interference, and it can discriminate human face more accurately, and achieve the face position. Then the program uses the frame subtraction to achieve the position of human body motion. This method is provided with good performance of the motion detection. Afterwards, the program recognises the human body motion by calculating the relationship of the face position with the position of human body motion contour. By the test, we know that the recognition rate of this algorithm is more than 92%. The results show that, this algorithm can achieve the result quickly, and guarantee the exactitude of the result.

• Proceedings of the Korea Institute of Convergence Signal Processing
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• 2003.06a
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• pp.34-37
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• 2003

본 논문에서는 가역변환 (reversible transform)에 기반을 둔 가역 워터마킹 기법에 관해 기술한다. 워터마크를 삽입한 후 원본 데이터에 영구적으로 남아있는 기존의 워터마킹 기법과는 달리 가역 워터마킹 기법의 경우, 컨텐츠의 인증이 이루어진 후 삽입되었던 워터마크 신호를 컨텐츠로부터 제거함으로써, 원 영상을 화소단위로 무손실 복원할 수 있는 특징이 있다. 본 논문에서는 가역 변환인 Haar 웨이블릿 변환(Haar Wavelet Transform) 이용하여 원 영상을 변환한 후 웨이블릿 계수를 이용하여 워터마크를 삽입 및 추출한다. 이러한 가역워터마킹 기법은 판사 목적의 영상 혹은 의료영상과 같은 민감한 영상신호처리가 요구되는 분야로 응용될 수 있을 것이다.