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Four Particular Cases of the Fourier Transform

In previous studies we used Laurent Schwartz’ theory of distributions to rigorously introduce discretizations and periodizations on tempered distributions. These results are now used in this study to derive a validity statement for four interlinking formulas. They are variants of Poisson&#8217...

Ausführliche Beschreibung

Gespeichert in:
1. Verfasser: Jens V. Fischer
Format: Artigo
Sprache:Inglês
Veröffentlicht: MDPI AG 2018-12-01
Schriftenreihe:Mathematics
Schlagworte:
Fourier transform
Fourier series
Discrete-Time Fourier Transform (DTFT)
Discrete Fourier Transform (DFT)
generalized functions
tempered distributions
Schwartz functions
Poisson Summation Formula
discretization
periodization
Online-Zugang:https://www.mdpi.com/2227-7390/6/12/335
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