| 具有紧支采样函数的子波空间采样定理 |
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| 引用本文： | 余越,柯有安.具有紧支采样函数的子波空间采样定理[J].信号处理,1997(1). |
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| 作者姓名： | 余越 柯有安 |
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| 作者单位： | 北京理工大学电子工程系 |
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| 摘 要： | 从复制核Hilbert空间的观点出发，本文详细地讨论了子波空间采样定理，提出了子波空间推广的主尺度函数概念，证明了它是构造紧支子波空间采样函数的充要条件，从而得到具有紧支采样函数的子波空间采样定理。本文还详细地研究了推广的主正交尺度函数的性质，证明了紧支的推广主正交尺度函数所对应的子波函数仅有一阶消失矩，采样函数的紧支性和所对应的子波函数的光滑性是不可兼得的。
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| 关 键 词： | 复制核Hilbert空间 采样函数 采样定理 尺度函数 子波 子波空间 |
Sampling Theorem with Compactly Supported Sampling Function for Wavelet Subspaces |
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| Yu Yue,Ke Youan.Sampling Theorem with Compactly Supported Sampling Function for Wavelet Subspaces[J].Signal Processing,1997(1). |
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| Authors: | Yu Yue Ke Youan |
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| Affiliation: | Yu Yue;Ke Youan |
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| Abstract: | Based on reproducing kernel Hilbert space theory , the sampling theorem for wavelet subspace is studied in this paper. We present the concept of generalized cardinal scaling function (GCSF) and show that GCSF is sufficcient and necessary conditions which form compactly supported sampling function with compactly supported scaling function. In the end, we study the properties of orthogonal GCSF and show that the wavelet function with orghogonal GCSF have only have one vanishing moment, so we couldn't get compactly supported Sampling function with smooth wavelet function. |
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| Keywords: | Reproducing kernels Hilbert space Sampling function Sampling theorem Scaling function Wavelet Wavelet space |
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