Wavelets, approximation, and comperssion

Document Type : Translation Paper

Authors

1 Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran

2 Department of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran

3 Faculty of Mathematical Sciences and Computer, Kharazmi University, 50 Taleghani avenue, Tehran 1561836314, Iran

Abstract

Over the last decade or so, wavelets have had a growing impact on signal processing theory and practice, both because of their unifying role and their successes in applications. Filter banks, which lie at the heart of wavelet-based algorithms, have become standard signal processing operators, used routinely in applications ranging from compression to modems. The contributions of wavelets have often been in the subtle interplay between discrete-time and continuous-time signal processing. The purpose of this article is to look at recent wavelet advances from a signal processing perspective. In particular, approximation results are reviewed, and the implication on compression algorithms is discussed. New constructions and open problems are also addressed. Finding a good basis to solve a
problem dates at least back to Fourier and his investigation of the heat equation. The series proposed by Fourier has several distinguishing features: The series is able to represent any finite energy function on an interval. The basis functions are eigenfunctions of linear shift invariant systems or, in other words, Fourier series diagonalize linear, shift invariant operators.

Keywords

Main Subjects

References

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Mathematics and Society
Volume 9, Issue 3 - Serial Number 3
September 2024
Pages 35-79

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History

  • Receive Date: 31 May 2023
  • Revise Date: 12 March 2024
  • Accept Date: 12 March 2024
  • Publish Date: 21 November 2024

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