Wavelets' applications in signal processing

Document Type : Translation Paper

Authors

1 Applied Mathematics, Faculty of Mathematics, Shahrekord University, Iran

2 Electrical Engineering, Faculty of Technology, Shahrekord University, Iran

Abstract

Wavelets are powerful tools for decomposition, analysis, and processing of digital signals. The wavelet transform represents the time-domain of a signal in terms of wavelet coefficients, converting it into a frequency-time representation. Wavelet coefficients can be utilized as part of a frequency-dependent method to achieve various signal processing effects. Additionally, the inverse wavelet transform converts the obtained wavelet coefficients back into the time-domain representation to obtain a modified signal. In this article, after a brief overview of the Fourier method and wavelet transform, the Haar wavelet and Daubechies wavelet are described. Following that, several signal processing techniques using wavelets, including noise reduction, wavelet denoising, data compression, musical effects, and a Java-based wavelet processor, will be examined.

Keywords

References

[1] D. Lokenath, Wavelet Transforms Their Applications, Birkhauser, 2001 pp. 12.
[2] T. Anthony, Computational Signal Processing with Wavelets, Birkhauser, 1998 60–61 and 173-174.
[3] M. Stephane, A Wavelet Tour of Signal Processing, 2nd ed, Academic Press , pp. 5 and 257, 1999.
[4] R. Curtis, The Computer Music Tutorial, MIT Press, pp. 446 and 581–589 and 1087, 1996.
[5] N. Yves, Wavelets Made Easy, Birkhauser, 3-60, 1999.
[6] A. Jensen, Ripples in Mathematics: The Discrete Wavelet Transform, Springer, pp. 102 and 155-158, 2001.

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History

  • Receive Date: 18 July 2019
  • Revise Date: 02 October 2019
  • Accept Date: 11 October 2019
  • Publish Date: 22 May 2019

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