Vector-Valued Nonuniform Wavelet Packets

We have introduced vector-valued nonuniform multiresolution analysis(VNUMRA) in [12] where the associated subspace V-0 of L-2(R, C-s) has, an orthonormal basis, a collection of translates of a vector valued function phi of the form {phi(x - lambda)}(lambda is an element of Lambda) where Lambda = {0, r/N} + 2Z, N >= 1 is an integer and r is an odd integer with 1 <= r <= 2N - 1 such that r and N are relatively prime and Z is the set of all integers and the corresponding dilation factor is 2N. The notion of vector-valued nonuniform wavelet packets is introduced in this paper and their various properties are investigated. The orthonormal basis of L-2(R, C-s) is constructed from these wavelet packets and the orthonormal decomposition relation is also given.