Vector-Valued Nonuniform Wavelet Packets
Meenakshi Mittal, Pammy Manchanda · Numerical Functional Analysis and Optimization · 2017
We have introduced vector-valued nonuniform multiresolution analysis(VNUMRA) in [12 Meenakshi, P. Manchanda, and A. H. Siddiqi (2014). Wavelets associated with vector-valued nonuniform multiresolution analysis. Appl. Anal. 93(1):84–104.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]] where the associated subspace V0 of L2(ℝ,ℂs) has, an orthonormal basis, a collection of translates of a vector valued function ϕ of the form {ϕ(x−λ)}λ∈Λ where Λ = {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 L2(ℝ,ℂs) is constructed from these wavelet packets and the orthonormal decomposition relation is also given.