Vector-Valued Nonuniform Wavelet Packets. (25th January 2018)

• Record Type: Journal Article
• Authors: Mittal, Meenakshi; Manchanda, P.
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 2(2018)
• Page Start: 179
• Page End: 200
• Publication Date: 2018-01-25
• Subjects: Nonuniform multiresolution analysis -- vector-valued wavelets -- wavelets -- wavelet packets; 42A38 -- 42A55 -- 42C15 -- 42C40 -- 43A70; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1355814
• Languages: English
• ISSNs: 0163-0563

Abstract

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.