中文摘要：

针对经典小波采样理论不能如同香农定理应用采样值对连续信号进行滤波,该文在小波采样存在条件下,提出一种基于采样值的小波滤波算法。该算法突破经典小波采样理论仅研究单个Hilbert空间信号重构的局限性,从多分辨分析逼近出发,基于采样值构建信号逼近准则函数,进而计算信号在小波空间的正交投影,实现小波滤波。仿真试验证明该算法能够有效地基于采样值,对连续信号进行小波滤波。

英文摘要：

A new algorithm of wavelet sampling is proposed since the typical wavelet sampling lacks the capacity to filter the continuous signal by the samples as Shannon sampling does.From the viewpoint of Multiresolution approximation,a new cost function based on the samples is introduced to estimate the approximation of signal in this algorithm,so that the signal is decomposed into the orthogonal components,which has break through the limit of typical wavelet sampling that only considers the construction of signal in one Hilbert space.