October 1997
Intermediate to advanced
342 pages
8h 22m
English
Content preview from Wavelets: Theory and Applications
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Appendix
The Fourier Transform
The Fourier transform appears as a fundamental tool in this book, so its main results and properties have been summarized here. Detailed studies of Fourier analysis can be found in the books of Rudin [Rud79] and Yosida [Yos64].
In the following let f be a fast-decaying function in 
or a function in
. The Fourier transform of f is given by
where 
. The scalar product in 
is denoted by 〈 f, g 〉L 2 = 
. We have Parseval’s relation
Thus the Fourier transform can be extended to and even to the space of
tempered distributions 
. By Parseval's relation, the Fourier transform ...
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