Vector-Valued Nonuniform Wavelet Packets. (25th January 2018) - Mittal, Meenakshi; Manchanda, P.
ABSTRACT: 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 ϕ of the form ϕ ( x −λ)λ∈ Λ where Λ = 0, r ∕ N +2 ℤ, N ≥1 is an integer and r is an odd integer with 1≤ r ≤2 N −1 such that r and N are relatively prime and ℤ is the set of all integers and the corresponding dilation factor is 2 N . 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.