A View on the Fourier Integrals and Related Delta Function

Yoshihiko AKAIWA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E87-A   No.12   pp.3420-3423
Publication Date: 2004/12/01
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: General Fundamentals and Boundaries
Keyword: 
Fourier analysis,  signal analysis,  Fourier transform,  

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Summary: 
The Fourier integrals are treated as a rigorous extension of the Fourier series expansion. The reward for this is that so called, in the Fourier integrals, singular functions that are not absolutely integrable, e.g., trigonometric functions can be discussed within a field of ordinary function giving a foundation for the delta function as distribution.