Wavelet Filtering Algorithm of Wavelet Sampling

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.