WAVELET ANALYSIS ON THE CANTOR DYADIC GROUP

WAVELET ANALYSIS ON THE CANTOR DYADIC GROUP
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Cantor二元群的小波分析

DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
Giles Auchmuty
Giles Auchmuty
中科院分区：
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文献类型：
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作者：
W. C. Lang;Giles Auchmuty

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紧支撑正交小波是建立在Cantor并元群（并元或a-级数局部域）上的。给出了三角多项式尺度滤波器的穆尔分辨分析的充要条件。定义了Lipschitz正则性条件，并对正则小波展开（p > 1）给出了一个无条件P-收敛结果.给出了尺度滤波器为2n项三角多项式的小波，详细讨论了具有8项滤波器的正则小波。这些小波与真实的直线上的某些沃尔什级数相一致。给出了小波的Mallat树算法。
Compactly supported orthogonal wavelets are built on the Can- tor dyadic group (the dyadic or a-series local field). Necessary and sufficient conditions are given on a trigonometric polynomial scaling filter for a mul- tiresolution analysis to result. A Lipschitz regularity condition is defined and an unconditional P-convergence result is given for regular wavelet ex- pansions (p > 1). Wavelets are given whose scaling filter is a trigonometric polynomial with 2n many terms; regular wavelets with filters with 8 terms are detailed. These wavelets are identified with certain Walsh series on the real line. A Mallat tree algorithm is given for the wavelets.