Variance of Signals and Their Finite Fourier Transforms

D. V. Chudnovsky (), G. V. Chudnovsky () and T. Morgan ()
Additional contact information
D. V. Chudnovsky: Polytechnic Institute of NYU, IMAS
G. V. Chudnovsky: Polytechnic Institute of NYU, IMAS
T. Morgan: Polytechnic Institute of NYU, IMAS

A chapter in Additive Number Theory, 2010, pp 53-76 from Springer

Abstract: Summary The study of properties of the finite Fourier matrix can be traced back to I. Schur and his use of the Gauss reciprocity law to determine the spectral properties of the finite Fourier matrix. Unlike the continuous Fourier transform, there is no widely accepted eigenvector basis. We present different approaches to eigenvector construction for the finite Fourier matrix, and a new set of extremality principles for the finite Fourier transform. One of the consequences of this construction is a new discrete uncertainty principle, analogous to a classical Heisenberg–Weyl formulation.

Keywords: Eigenvectors; Fourier matrix; Fractional fourier transform (search for similar items in EconPapers)
Date: 2010
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:978-0-387-68361-4_4

Ordering information: This item can be ordered from
http://www.springer.com/9780387683614

DOI: 10.1007/978-0-387-68361-4_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 ().