A Physical Interpretation of Tight Frames

Peter G. Casazza, Matthew Fickus, Jelena Kovacevic, Manuel T. Leon, Janet C. Tremain

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We characterize the existence of finite tight frames whose frame elements are of predetermined length. In particular, we derive a “fundamental inequality” which completely characterizes those sequences which arise as the lengths of a tight frame’s elements. Furthermore, using concepts from classical physics, we show that this characterization has an intuitive physical interpretation.

Original languageEnglish (US)
Title of host publicationApplied and Numerical Harmonic Analysis
PublisherSpringer International Publishing
Pages51-76
Number of pages26
Edition9780817637781
DOIs
StatePublished - Jan 1 2006

Publication series

NameApplied and Numerical Harmonic Analysis
Number9780817637781
ISSN (Print)2296-5009
ISSN (Electronic)2296-5017

Fingerprint

Tight Frame
Physics
Intuitive
Interpretation
Concepts

Keywords

  • Dual Frame
  • Frame Operator
  • Orthogonal Complement
  • Potential Energy Function
  • Tight Frame

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Casazza, P. G., Fickus, M., Kovacevic, J., Leon, M. T., & Tremain, J. C. (2006). A Physical Interpretation of Tight Frames. In Applied and Numerical Harmonic Analysis (9780817637781 ed., pp. 51-76). (Applied and Numerical Harmonic Analysis; No. 9780817637781). Springer International Publishing. https://doi.org/10.1007/0-8176-4504-7_4

A Physical Interpretation of Tight Frames. / Casazza, Peter G.; Fickus, Matthew; Kovacevic, Jelena; Leon, Manuel T.; Tremain, Janet C.

Applied and Numerical Harmonic Analysis. 9780817637781. ed. Springer International Publishing, 2006. p. 51-76 (Applied and Numerical Harmonic Analysis; No. 9780817637781).

Research output: Chapter in Book/Report/Conference proceedingChapter

Casazza, PG, Fickus, M, Kovacevic, J, Leon, MT & Tremain, JC 2006, A Physical Interpretation of Tight Frames. in Applied and Numerical Harmonic Analysis. 9780817637781 edn, Applied and Numerical Harmonic Analysis, no. 9780817637781, Springer International Publishing, pp. 51-76. https://doi.org/10.1007/0-8176-4504-7_4
Casazza PG, Fickus M, Kovacevic J, Leon MT, Tremain JC. A Physical Interpretation of Tight Frames. In Applied and Numerical Harmonic Analysis. 9780817637781 ed. Springer International Publishing. 2006. p. 51-76. (Applied and Numerical Harmonic Analysis; 9780817637781). https://doi.org/10.1007/0-8176-4504-7_4
Casazza, Peter G. ; Fickus, Matthew ; Kovacevic, Jelena ; Leon, Manuel T. ; Tremain, Janet C. / A Physical Interpretation of Tight Frames. Applied and Numerical Harmonic Analysis. 9780817637781. ed. Springer International Publishing, 2006. pp. 51-76 (Applied and Numerical Harmonic Analysis; 9780817637781).
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