In this paper, for a given d x d we investigate the compactly supported expansive matrix M with ｜ det M｜ = 2, M-wavelets for L^2（R^d）. Starting with N a pair of compactly supported refinable functions and satis...In this paper, for a given d x d we investigate the compactly supported expansive matrix M with ｜ det M｜ = 2, M-wavelets for L^2（R^d）. Starting with N a pair of compactly supported refinable functions and satisfying a mild condition, we obtain an explicit construction of a compactly supported wavelet p such that {2J/2b（Mj -k）：j E Z, k c gg} forms a Riesz basis for L2（Ra）. The （anti-）symmetry of such ~b is studied, and some examples are also provided.展开更多
In this paper, the notion of p-wavelet packets on the positive half-line P＋ is introduced. A new method for constructing non-orthogonal wavelet packets related to Walsh functions is developed by splitting the wavelet...In this paper, the notion of p-wavelet packets on the positive half-line P＋ is introduced. A new method for constructing non-orthogonal wavelet packets related to Walsh functions is developed by splitting the wavelet subspaces directly instead of using the lowpass and high-pass filters associated with the multiresolution analysis as used in the classical theory of wavelet packets. Further, the method overcomes the difficulty of constructing non-orthogonal wavelet packets of the dilation factor p 〉 2.展开更多
文摘In this paper, for a given d x d we investigate the compactly supported expansive matrix M with ｜ det M｜ = 2, M-wavelets for L^2（R^d）. Starting with N a pair of compactly supported refinable functions and satisfying a mild condition, we obtain an explicit construction of a compactly supported wavelet p such that {2J/2b（Mj -k）：j E Z, k c gg} forms a Riesz basis for L2（Ra）. The （anti-）symmetry of such ~b is studied, and some examples are also provided.
文摘In this paper, the notion of p-wavelet packets on the positive half-line P＋ is introduced. A new method for constructing non-orthogonal wavelet packets related to Walsh functions is developed by splitting the wavelet subspaces directly instead of using the lowpass and high-pass filters associated with the multiresolution analysis as used in the classical theory of wavelet packets. Further, the method overcomes the difficulty of constructing non-orthogonal wavelet packets of the dilation factor p 〉 2.
