On the splitting trick and wavelets packets with arbitrary dilation matrix of L2(Rs)

Wavelet packets possess excellent characteristics in differentiations of space and spectrum. In this paper, The splitting trick coined by Daubechies is used to construct wavelet packets with an arbitrary dilation matrix A. Different from the classical wavelet packets, instructed by Coifman et al., our method is that we split the wavelet subspaces directly instead of using the low-pass and the high-pass filters associated with the multiresolution analysis. Furthermore, the method overcomes the difficulty of constructing non-orthogonal wavelet packets of the dilation matrix not equal to 2I. Finally, we show how to construct various Riesz basis from the wavelet packets.