One-Dimensional Wavelet Systems

Howard L. Resnikoff () and Raymond O. Wells ()
Additional contact information
Howard L. Resnikoff: Future WAVE Inc.
Raymond O. Wells: Rice University, Department of Mathematics

Chapter 5 in Wavelet Analysis, 1998, pp 86-139 from Springer

Abstract: Abstract In this chapter, we introduce the basic scaling and wavelet functions of wavelet analysis, using the algebraic tools developed in the previous chapter. The principal result is that for any wavelet matrix A ∈ WM (m, g ; C), there is a scaling function ϕ(x) and m — 1 wavelet functions ψ1(x), …, ψm−1(x) which satisfy specific scaling relations defined in terms of the wavelet matrix A. These functions are all compactly supported and square-integrable, and their rescalings and translations, called the wavelet system determined by A, provide a basis for L 2 (R). Generically, the wavelet system will be an orthonormal basis, but in all cases, even when orthogonality is not present, these functions will allow reconstruction of a given f ∈ L2 (R) from the scalar products of f with the elements of the wavelet system, just as if it had been an orthonormal basis (this is the tight frame property of wavelets, discussed in Section 5.3.1).

Keywords: Scaling Function; Wavelet Function; Multiresolution Analysis; Tight Frame; Biorthogonal Wavelet (search for similar items in EconPapers)
Date: 1998
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0593-7_5

Ordering information: This item can be ordered from
http://www.springer.com/9781461205937

DOI: 10.1007/978-1-4612-0593-7_5

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().