One-Dimensional Approximate Decomposition Waves via the cubic moving least square method

• Main Authors: Yu-Hao Chao, 趙昱豪
• Other Authors: Y.N. Jeng
• Format: Others
• Language: zh-TW
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/75345603461148461998

碩士 === 國立成功大學 === 航空太空工程學系碩博士班 === 91 === This thesis employs the cubic moving least squares method to smear the high frequency error of the result of the Jeng high/low passed filter via the modified Hilbert transforms. When the frequency difference is large enough, numerical tests show that this improvement can provide a satisfactory wave decomposition. The reason of employing the cubic moving least squares method is that it has a better curvature resolution capability than the fast Gaussian smoothing method.On the other hand, if the frequency difference is not significantly large, the smearing is not effective. This paper also studies a procedure of linearized wave decomposition via the least squares method. The high non-linearity introduced by the production between the amplitude and cosine function is linearized and is equipped with the cubic spline interpolation. Since the degrees of freedom of the linearized product between the amplitude and cosine function can not be properly settled, the penalty of the high frequency error is always presented. After employing the cubic moving least squares method to smear the high frequency error, two least squares method basing on the amplitude modification and phase modification are applied, respectively. Finally, the cubic moving least squares method is again employed to provide the decoupled wave. Because of the first study, a uniform nodal spacing strategy is employed. A numerical test gives a satisfactory result which reflects the potential of the proposed wave decomposition procedure.