Share This Article:

Time Domain Signal Analysis Using Wavelet Packet Decomposition Approach

Abstract Full-Text HTML Download Download as PDF (Size:889KB) PP. 321-329
DOI: 10.4236/ijcns.2010.33041    9,023 Downloads   16,687 Views   Citations


This paper explains a study conducted based on wavelet packet transform techniques. In this paper the key idea underlying the construction of wavelet packet analysis (WPA) with various wavelet basis sets is elaborated. Since wavelet packet decomposition can provide more precise frequency resolution than wavelet decomposition the implementation of one dimensional wavelet packet transform and their usefulness in time signal analysis and synthesis is illustrated. A mother or basis wavelet is first chosen for five wavelet filter families such as Haar, Daubechies (Db4), Coiflet, Symlet and dmey. The signal is then decomposed to a set of scaled and translated versions of the mother wavelet also known as time and frequency parameters. Analysis and synthesis of the time signal is performed around 8 seconds to 25 seconds. This was conducted to determine the effect of the choice of mother wavelet on the time signals. Results are also prepared for the comparison of the signal at each decomposition level. The physical changes that are occurred during each decomposition level can be observed from the results. The results show that wavelet filter with WPA are useful for analysis and synthesis purpose. In terms of signal quality and the time required for the analysis and synthesis, the Haar wavelet has been seen to be the best mother wavelet. This is taken from the analysis of the signal to noise ratio (SNR) value which is around 300 dB to 315 dB for the four decomposition levels.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

M. Gokhale and D. Khanduja, "Time Domain Signal Analysis Using Wavelet Packet Decomposition Approach," International Journal of Communications, Network and System Sciences, Vol. 3 No. 3, 2010, pp. 321-329. doi: 10.4236/ijcns.2010.33041.


[1] S. Mallat, “A wavelet tour of signal processing,” Second Edition, Academic Press, 1998.
[2] D. Donoho, “De-noising by soft-thresholding,” IEEE Transactions on Information Theory, Vol. 41, pp. 613– 627, May 1995.
[3] I. Daubechies, “Ten lectures on wavelets,” SIAM, New York, 1992.
[4] J. W. Seok and K. S. Bae, “Speech enhancement with reduction of noise components in the wavelet domain,” IEEE International Conference on Acoustics, Speech and Signal Processing, Vol. 2, pp. 1323–1326, 1997.
[5] P. V. Tuan and G. Kubin, “DWT-Based classification of acoustic-phonetic classes and phonetic units,” International Conference on Spoken Language Processing, 2004.
[6] E. P. A. Montuori, “Real time performance measures of low delay perceptual audio coding,” Journal of Electrical Engineering, Vol. 56, No. 3–4, pp. 100–105, 2005.
[7] I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Communications on Pure and Applied Mathematics, Vol. 41, No. 7, pp. 909–996 , November 1998.
[8] S. Mallat, “A theory for multiresolution signal decomposition: The wavelet representation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 11, No. 7, pp. 674–693, July 1989.
[9] A. Grossman and J. Morlet, “Decompositions of Hardy functions into square integrable wavelets of constant shape,” SIAM Journals on Mathematical Analysis, Vol. 15, No. 4, pp. 723–736, July 1984.
[10] R. Coifman and M. Wickerhauser, “Entropy-based algorithms for best basis selection,” IEEE Transactions on Information Theory, Vol. 38, No. 2, March 1992.
[11] R. Learned, “Wavelet packet based transient signal classification,” Master’s Thesis, Massachusetts Institute of Technology, 1992.
[12] M. Wickerhauser, “Lectures on wavelet packet algorithms,” Technical Report, Department of Mathematics, Washington University, 1992.
[13] R. Priebe and G. Wilson, “Applications of ‘matched’ wavelets to identification of metallic transients,” Proceedings of the IEEE–SP International Symposium, Victoria, British Columbia, Canada, October 1992.
[14] E. Serrano and M. Fabio, “The use of the discrete wavelet transform for acoustic emission signal processing,” Proceedings of the IEEE–SP International Symposium, Victoria, British Columbia, Canada, October 1992.
[15] T. Brotherton, T. Pollard, R. Barton, A. Krieger, and L. Marple, “Applications of time frequency and time scale analysis to underwater acoustic transients,” Proceedings of the IEEE–SP International Symposium, Victoria, British Columbia, Canada, October 1992.
[16] K. P. Soman and K. I. Ramachandran, “Insight into wavelets: From theory to practice,” 2nd Edition, PHI, 2005.
[17] P. P. Vaidyanathan, “Multirate systems and filter banks,” Prentice Hall, New Jersey, 1992.
[18] M. V. Wickerhauser, “INRIA lectures on wavelet packet algorithms,” Lecture Notes, pp. 31–99, June 1991.
[19] MATLAB7.0.

comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.