Preprint
Article

There Is Only One Fourier Transform

Altmetrics

Downloads

2585

Views

1478

Comments

0

A peer-reviewed article of this preprint also exists.

This version is not peer-reviewed

Submitted:

24 December 2017

Posted:

25 December 2017

Read the latest preprint version here

Alerts
Abstract
Four Fourier transforms are usually defined, the Integral Fourier transform, the Discrete-Time Fourier transform (DTFT), the Discrete Fourier transform (DFT) and the Integral Fourier transform for periodic functions. However, starting from their definitions, we show that all four Fourier transforms can be reduced to actually only one Fourier transform, the Fourier transform in the distributional sense.
Keywords: 
Subject: Computer Science and Mathematics  -   Analysis
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
Prerpints.org logo

Preprints.org is a free preprint server supported by MDPI in Basel, Switzerland.

Subscribe

© 2024 MDPI (Basel, Switzerland) unless otherwise stated