Fourier Transforms of Finite Energy Signals

Pierre Brémaud ()
Additional contact information
Pierre Brémaud: École Polytechnique Fédérale de Lausanne

Chapter C3 in Mathematical Principles of Signal Processing, 2002, pp 155-160 from Springer

Abstract: Abstract A stable signal as simple as the rectangular pulse has a Fourier transform that is not integrable, and therefore one cannot use the Fourier inversion theorem for stable signals as it is. However, there is a version of this inversion formula that applies to all finite-energy functions (for instance, the rectangular pulse). The analysis becomes slightly more involved, and we will have to use the framework of Hilbert spaces. This is largely compensated by the formal beauty of the results, due to the fact that a square-integrable function and its FT play symmetrical roles.

Keywords: Autocorrelation Function; Compact Support; Inversion Formula; Rectangular Pulse; Stable Signal (search for similar items in EconPapers)
Date: 2002
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4757-3669-4_10

Ordering information: This item can be ordered from
http://www.springer.com/9781475736694

DOI: 10.1007/978-1-4757-3669-4_10

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().