A Design of M-Channels Lifting Wavelet Filter in Signal Processing

The key idea of the lifting scheme is constructed wavelet filters by several predict operators and update operators. We know that the poly-phase matrix can be factored into finite matrixes, and these matrixes can be regarded as the predict operators and update operators. According to the theory of M-channels wavelet transform, the construction of the M-channels wavelet filters based on the lifting scheme are given in this paper. It's different to the traditional method. Any filters based on the lifting scheme are automatically satisfied with the exact reconstruction condition, the constructing predict filters are satisfied with degree dual vanishing moments and the constructing update filters are satisfied with degree basal vanishing moments, and some examples are given.