Flexibility and facilitation of frames compared to bases in signal processing

Document Type : Research Paper

Authors

Malayer University

Abstract

Bases are fundamental tools in applied mathematics, and from the past to the present, from polynomial bases to wavelet bases, they have always played an indispensable role in expanding the frontiers of knowledge. However, the conditions that a basis must satisfy are highly restrictive. In fact, the elements of a basis must be linearly independent and ideally orthogonal to each other. Such a requirement makes accessing bases with suitable flexibility difficult or even impossible. Frames, on the other hand, are a suitable option for accessing bases with fewer restrictive characteristics and more flexibility. In order to better understand the advantages of using frames in various practical fields, we will briefly review the role of frames in reducing the effects of random disturbances in signal processing.

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References

[1] O. Christensen, FRAMES AND BASES: An introductory Course, Birkhauser publication, 2008.
[2] V. K. Goyal, J. Kovacevic and A. J. Kelner, Quantised frame expansions with erasures., Appl. Comp. Harm. Anal., 10 (2000) 203–233.
[3] O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser publication, 2016.
[4] O. Christensen, Approximation Theory: From Taylor polynomials to wavelets, Birkhauser publication, 2006.

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History

  • Receive Date: 06 August 2015
  • Revise Date: 14 March 2017
  • Accept Date: 21 April 2018
  • Publish Date: 23 August 2018

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