IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v3y2015i2p299-318d49055.html
   My bibliography  Save this article

On the Duality of Discrete and Periodic Functions

Author

Listed:
  • Jens V. Fischer

    (Studies conducted at the Institute of Mathematics, Ludwig Maximilians University Munich, 80333 Munich, Germany)

Abstract

Although versions of Poisson’s Summation Formula (PSF) have already been studied extensively, there seems to be no theorem that relates discretization to periodization and periodization to discretization in a simple manner. In this study, we show that two complementary formulas, both closely related to the classical Poisson Summation Formula, are needed to form a reciprocal Discretization-Periodization Theorem on generalized functions. We define discretization and periodization on generalized functions and show that the Fourier transform of periodic functions are discrete functions and, vice versa, the Fourier transform of discrete functions are periodic functions.

Suggested Citation

  • Jens V. Fischer, 2015. "On the Duality of Discrete and Periodic Functions," Mathematics, MDPI, vol. 3(2), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:3:y:2015:i:2:p:299-318:d:49055
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/3/2/299/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/3/2/299/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:3:y:2015:i:2:p:299-318:d:49055. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.