A Discrete Cosine Adaptive Harmonic Wavelet Packet and Its Application to Signal Compression
Nandini Basumallick, S. V. Narasimhan
.
DOI: 10.4236/jsip.2010.11007   PDF    HTML     5,181 Downloads   8,868 Views   Citations

Abstract

A new adaptive Packet algorithm based on Discrete Cosine harmonic wavelet transform (DCHWT), (DCAHWP) has been proposed. This is realized by the Discrete Cosine Harmonic Wavelet transform (DCHTWT) which exploits the good properties of DCT viz., energy compaction (low leakage), frequency resolution and computational simplicity due its real nature, compared to those of DFT and its harmonic wavelet version. Hence the proposed wavelet packet is advantageous both in terms of performance and computational efficiency compared to those of existing DFT harmonic wavelet packet. Further, the new DCAHWP also enjoys the desirable properties of a Harmonic wavelet transform over the time domain WT, viz., built in decimation without any explicit antialiasing filtering and easy interpolation by mere concatenation of different scales in frequency (DCT) domain with out any image rejection filter and with out laborious delay compensation required. Further, the compression by the proposed DCAHWP is much better compared to that by adaptive WP based on Daubechies-2 wavelet (DBAWP). For a compression factor (CF) of 1/8, the ratio of the percentage error energy by proposed DCAHWP to that by DBAWP is about 1/8 and 1/5 for considered 1-D signal and speech signal, respectively. Its compression performance is better than that of DCHWT, both for 1-D and 2-D signals. The improvement is more significant for signals with abrupt changes or images with rapid variations (textures). For compression factor of 1/8, the ratio of the percentage error energy by DCAHWP to that by DCHWT, is about 1/3 and 1/2, for the considered 1-D signal and speech signal, respectively. This factor for an image considered is 2/3 and in particular for a textural image it is 1/5.

Share and Cite:

N. Basumallick and S. Narasimhan, "A Discrete Cosine Adaptive Harmonic Wavelet Packet and Its Application to Signal Compression," Journal of Signal and Information Processing, Vol. 1 No. 1, 2010, pp. 63-76. doi: 10.4236/jsip.2010.11007.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] C. Sidney Burrus, R. A. Gopinath and H. T. Guo, “Introduction to Wavelets and Wavelet Transforms: A Primer,” Prentice-Hall, Inc., Upper Saddle River, 1998.
[2] P. S. Addison, “The Illustrated Wavelet Transform Hand- Book,” Institute of Physics Publishing, London, 2002.
[3] R. R. Coifman and M. V. Wickerhauser, “Entropy-Based Algorithms for Best Basis Selection,” IEEE Transactions on Information Theory, Vol. 38, No. 2, March 1992, pp. 713-718.
[4] B. Liu, “Adaptive Harmonic Wavelet Transform with Applications in Vibration Analysis,” Journal of Sound and Vibration, Vol. 262, No. 1, 2003, pp. 45-64.
[5] M. Kivanc Mihcak, K. Ramchandran and P. Moulin, “Adaptive Wavelet Packet Image Coding Using an Estimation-Quantization Framework,” Proceedings of International Conference on Image Processing, Chicago, USA, Vol. 1, 1998, pp. 92-96.
[6] M. Musaruddin and A. Z. Kouzani, “Embedding Data in Images Using Wavelet Packets,” International Conference IEEE TENCO, Vol. 2, 21-24 November 2004, pp. 120- 123.
[7] D. E. Newland, “Harmonic Wavelet Analysis,” Proceedings: Mathematical and Physical Sciences, Vol. 444, No. 1917, 1993, pp. 203-225.
[8] S. V. Narasimhan and M. Harish, “A New Spectral Estimator Based on Discrete Cosine Transform and Modified Group Delay,” Signal Processing, Vol. 86, No. 7, 2006, pp. 1586-1596.
[9] S. V. Narasimhan, M. Harish, A. R. Haripriya and N. Basumallick, “Discrete Cosine Harmonic Wavelet Transform and Its Application to Signal Compression and Spectral Estimation Using Modified Group Delay,” Signal, Image and Video Processing, Vol. 3, No. 1, February 2009, pp. 85-99.
[10] S. V. Narasimhan, A. R. Haripriya and B. K. Shreyamsha Kumar, “Improved Wigner-Ville Distribution Performance Based on Dct/Dft Harmonic Wavelet Transform and Modified Magnitude Group Delay,” Signal Processing, Vol. 88, No. 1, 2008, pp. 1-18.
[11] S. V. Narasimhan and A. Adiga, “Shift Invariant Discrete Cosine Harmonic Wavelet Transform and Its Application to Denoising,” Proceedings, IEEE International Conference INDICON, Bangalore, 2007.
[12] S. V. Narasimhan and S. Veena, “Signal Processing Principles and Implementation,” Alpha Science, Harrow, UK and Narosa publishers, New Delhi, India, 2008.
[13] T. Gulzow, T. Ludwig and U. Heute “Spectral-Subtrac- tion Speech Enhancement in Multirate Systems with and without Non-Uniform and Adaptive Bandwidths,” Signal Processing, Vol. 83, No. 8, 2003, pp. 1613-1631.

Copyright © 2024 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.