Construction and properties of multiwavelet packets with arbitrary scale and the related algorithms of decomposition and reconstruction

A more flexible method of constructing multiwavelet packets with the scale a ≥ 2 from the same set of multiwavelets is discussed in this paper. The properties of these packets are studied. The formulae for performing iterations and decomposition are given. L2(R) can be further decomposed by these multiwavelet packets and good bases of L2(R) are given. Finally, we provide the algorithms for the decomposition and reconstruction using these multiwavelet packets.