一类紧支撑正交多小波的显式构造 |
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引用本文: | 张建基,雷巧莉,关惠惠,张静. 一类紧支撑正交多小波的显式构造[J]. 甘肃科学学报, 2016, 0(3): 20-25. DOI: 10.16468/j.cnki.issn1004-0366.2016.03.005 |
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作者姓名: | 张建基 雷巧莉 关惠惠 张静 |
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作者单位: | 1. 新疆师范大学 数学科学学院,新疆 乌鲁木齐,830054;2. 西安铁路职业技术学院,陕西 西安,710014 |
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摘 要: | 以所构造的正定矩阵为基础,给出了2尺度紧支撑正交多小波的构造方法,证明了当2尺度r重紧支撑正交多尺度函数的系数矩阵Pi是r×r阶可逆矩阵,存在正交矩阵A,使PiPTi与diag(λi,1,λi,2,…,λi,r)合同。算例的结果说明,当AT(2I-PiPTi)-1 PiPiTA是对角的正定矩阵时,可构造出2重紧支撑正交多小波函数。
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关 键 词: | 紧支撑正交多小波 对称正定矩阵 对角矩阵 |
Explicit Construction of First Class Compact Supported Orthogonal Multi Wavelets |
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Abstract: | Based on the constructed positive definite matrix,construction method of compact supported or-thogonal multi wavelets with dilation factor 3 are presented to prove that coefficient matrix of compact supported orthogonal multi-scaling functions with dilation factor 2 is an invertible matrix with order,and orthogonal matrix exists in making same with.The result of example indicates that 2 compact supported or-thogonal multi-wavelet function can be constructed when is diagonal positive definite matrix. |
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Keywords: | Compact supported orthogonal multi wavelets Symmetric positive definite matrix Diagonal matrix |
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