Skip to main content
SpringerLink
Log in

Applications of the discrete-time Fourier transform to data analysis

  • Regular Paper
  • Published:
International Journal of Data Science and Analytics Aims and scope Submit manuscript

Abstract

We define a discrete analogue of the characteristic function for discrete random variable and develop numerical procedures for computing the discrete characteristic function for several well-known discrete random variables. We rigorously define what is meant by the Fourier transform of a probability mass function and also show how to reverse the process to recover the probability mass function of a discrete random variable, given a procedure for computing the characteristic function. Unlike previous work on the subject, our approach is novel in that we are not computing closed-form solutions of a continuous random variable but are focused on applying the methods to real-world data sets.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Lukacs, E.: Characteristic Functions. Griffin, London (1970)

    MATH  Google Scholar 

  2. Pinsky, M.: Introduction to Fourier Analysis and Wavelets. Brooks/Cole. ISBN 978-0-534-37660-4 (2002)

Download references

Funding

Not applicable.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Calgary, Calgary, AB, Canada

    Dayne Sorvisto

Authors
  1. Dayne Sorvisto
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

This manuscript and all contents in its entirety were created by the author Dayne Sorvisto.

Corresponding author

Correspondence to Dayne Sorvisto.

Ethics declarations

Conflict of interest

I hereby confirm there are no conflicts of interest associated with this manuscript.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix A: Library for simulating characteristic function

Appendix A: Library for simulating characteristic function

figure c

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sorvisto, D. Applications of the discrete-time Fourier transform to data analysis. Int J Data Sci Anal 16, 435–440 (2023). https://doi.org/10.1007/s41060-023-00409-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41060-023-00409-5

Keywords

Search

Navigation