The Fourier Transform

Tim Olson ()
Additional contact information
Tim Olson: University of Florida, Department of Mathematics

Chapter Chapter 4 in Applied Fourier Analysis, 2017, pp 121-148 from Springer

Abstract: Abstract The transition from Fourier Series which were introduced in Chapter 2 , to the Fourier Transform is similar to the transition from the dot product to the inner product. When dealing with functions, the question became “How many samples of the function are sufficient to approximate, accurately, the dot product that would be used to compare vectors?”. The answer is that the safe way to make sure you have enough samples is to not sample, but rather use the integral, or inner product, instead of the dot product. That way convergence issues are not an issue, and everything was certain, while preserving the geometry of the dot product.

Keywords: Continuous Fourier Transform; Gibbs Ringing; Constant Coefficient Linear Differential Equations; Fourier Series Estimator; Uniform Dilatation (search for similar items in EconPapers)
Date: 2017
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:978-1-4939-7393-4_4

Ordering information: This item can be ordered from
http://www.springer.com/9781493973934

DOI: 10.1007/978-1-4939-7393-4_4

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 ().