Foundations and Trends® in Signal Processing > Vol 2 > Issue 1

An Introduction to Frames

Jelena Kovačević, Center for Bioimage Informatics, Carnegie Mellon University, USA, j.kovacevic@ieee.org Amina Chebira, Center for Bioimage Informatics, Carnegie Mellon University, USA, achebira@ieee.org
 
Suggested Citation
Jelena Kovačević and Amina Chebira (2008), "An Introduction to Frames", Foundations and Trends® in Signal Processing: Vol. 2: No. 1, pp 1-94. http://dx.doi.org/10.1561/2000000006

Published: 15 Oct 2008
© 2008 J. Kovačević and A. Chebira
 
Subjects
Digital and multirate signal processing
 

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In this article:
1 Introduction
2 Review of Bases
3 Frame Definitions and Properties
4 Finite-Dimensional Frames
5 Infinite-Dimensional Frames via Filter Banks
6 All in the Family
7 Applications
Conclusions
A Nomenclature and Notation
Acknowledgments
References

Abstract

This survey gives an introduction to redundant signal representations called frames. These representations have recently emerged as yet another powerful tool in the signal processing toolbox and have become popular through use in numerous applications. Our aim is to familiarize a general audience with the area, while at the same time giving a snapshot of the current state-of-the-art.

DOI:10.1561/2000000006
ISBN: 978-1-60198-068-7
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ISBN: 978-1-60198-069-4
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Table of contents:
1: Introduction
2: Review of Bases
3: Frame Definitions and Properties
4: Finite-Dimensional Frames
5: Infinite-Dimensional Frames via Filter Banks
6: All in the Family
7: Applications
Conclusions
A. Nomenclature and Notation
Acknowledgements
References

An Introduction to Frames

An Introduction to Frames is an introduction to redundant signal representations called frames. These representations have recently emerged as yet another powerful tool in the signal processing toolbox, spurred by a host of recent applications requiring some level of redundancy. It asks the question: Why and where should one use frames? And answers emphatically: Anywhere where redundancy is a must. It then goes on to discuss a host of applications that richly illustrate that answer. An Introduction to Frames is geared primarily toward engineering students and those without extensive mathematical training. It is also intended to help researchers and practitioners decide whether frames are the right tool for their application

 
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