IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4612-0593-7_5.html

One-Dimensional Wavelet Systems

In: Wavelet Analysis

Author

Listed:
  • Howard L. Resnikoff

    (Future WAVE Inc.)

  • Raymond O. Wells Jr.

    (Rice University, Department of Mathematics)

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).

Suggested Citation

  • Howard L. Resnikoff & Raymond O. Wells Jr., 1998. "One-Dimensional Wavelet Systems," Springer Books, in: Wavelet Analysis, chapter 5, pages 86-139, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0593-7_5
    DOI: 10.1007/978-1-4612-0593-7_5
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-1-4612-0593-7_5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.