Vol. 62
Latest Volume
All Volumes
PIERL 123 [2025] PIERL 122 [2024] PIERL 121 [2024] PIERL 120 [2024] PIERL 119 [2024] PIERL 118 [2024] PIERL 117 [2024] PIERL 116 [2024] PIERL 115 [2024] PIERL 114 [2023] PIERL 113 [2023] PIERL 112 [2023] PIERL 111 [2023] PIERL 110 [2023] PIERL 109 [2023] PIERL 108 [2023] PIERL 107 [2022] PIERL 106 [2022] PIERL 105 [2022] PIERL 104 [2022] PIERL 103 [2022] PIERL 102 [2022] PIERL 101 [2021] PIERL 100 [2021] PIERL 99 [2021] PIERL 98 [2021] PIERL 97 [2021] PIERL 96 [2021] PIERL 95 [2021] PIERL 94 [2020] PIERL 93 [2020] PIERL 92 [2020] PIERL 91 [2020] PIERL 90 [2020] PIERL 89 [2020] PIERL 88 [2020] PIERL 87 [2019] PIERL 86 [2019] PIERL 85 [2019] PIERL 84 [2019] PIERL 83 [2019] PIERL 82 [2019] PIERL 81 [2019] PIERL 80 [2018] PIERL 79 [2018] PIERL 78 [2018] PIERL 77 [2018] PIERL 76 [2018] PIERL 75 [2018] PIERL 74 [2018] PIERL 73 [2018] PIERL 72 [2018] PIERL 71 [2017] PIERL 70 [2017] PIERL 69 [2017] PIERL 68 [2017] PIERL 67 [2017] PIERL 66 [2017] PIERL 65 [2017] PIERL 64 [2016] PIERL 63 [2016] PIERL 62 [2016] PIERL 61 [2016] PIERL 60 [2016] PIERL 59 [2016] PIERL 58 [2016] PIERL 57 [2015] PIERL 56 [2015] PIERL 55 [2015] PIERL 54 [2015] PIERL 53 [2015] PIERL 52 [2015] PIERL 51 [2015] PIERL 50 [2014] PIERL 49 [2014] PIERL 48 [2014] PIERL 47 [2014] PIERL 46 [2014] PIERL 45 [2014] PIERL 44 [2014] PIERL 43 [2013] PIERL 42 [2013] PIERL 41 [2013] PIERL 40 [2013] PIERL 39 [2013] PIERL 38 [2013] PIERL 37 [2013] PIERL 36 [2013] PIERL 35 [2012] PIERL 34 [2012] PIERL 33 [2012] PIERL 32 [2012] PIERL 31 [2012] PIERL 30 [2012] PIERL 29 [2012] PIERL 28 [2012] PIERL 27 [2011] PIERL 26 [2011] PIERL 25 [2011] PIERL 24 [2011] PIERL 23 [2011] PIERL 22 [2011] PIERL 21 [2011] PIERL 20 [2011] PIERL 19 [2010] PIERL 18 [2010] PIERL 17 [2010] PIERL 16 [2010] PIERL 15 [2010] PIERL 14 [2010] PIERL 13 [2010] PIERL 12 [2009] PIERL 11 [2009] PIERL 10 [2009] PIERL 9 [2009] PIERL 8 [2009] PIERL 7 [2009] PIERL 6 [2009] PIERL 5 [2008] PIERL 4 [2008] PIERL 3 [2008] PIERL 2 [2008] PIERL 1 [2008]
2016-09-12
Studying the Influence of the Number Vanishing Moments of Daubechies Wavelets for the Analysis of Microstrip Lines
By
Progress In Electromagnetics Research Letters, Vol. 62, 57-64, 2016
Abstract
Using Daubechies wavelet with one, two, three, and four vanishing moments, basis functions for the efficient solution of electromagnetic integral equations are studied. Due to the vanishing moments, the moment matrices resulting in these problems are sparsified by wavelet, and consequently, the solution can be obtained rapidly. The microstrip line is examined in order to demonstrate the advantages of this suggested wavelet-moments method over the traditional moment method. To demonstrate the effectiveness and accuracy of the proposed technique, numerical results for error relative for different vanishing moments of Daubechies wavelets are presented. It is found that Daubechies wavelets with larger number of vanishing moments generally give higher accuracy.
Citation
Mohamed Bayjja, Mohamed Boussouis, and Naima Amar Touhami, "Studying the Influence of the Number Vanishing Moments of Daubechies Wavelets for the Analysis of Microstrip Lines," Progress In Electromagnetics Research Letters, Vol. 62, 57-64, 2016.
doi:10.2528/PIERL16052104
References

1. Poza, D. M., Microwave Engineering, 4th Ed., Wiley, Dec. 2011.

2. Francomanoa, E., A. Tortorici, et al. "Wavelet-like bases for thin-wire integral equations in electromagnetics," Journal of Computational and Applied Mathematics, Vol. 175, 77-86, Feb. 2004.
doi:10.1016/j.cam.2004.06.006

3. Gibson, W. C., The Method of Moments in Electromagnetics, 2nd Ed., Taylor & Francis, 2015.

4. Rickard, Y., "An efficient wavelet-based solution of electromagnetic field problems," Applied Numerical Mathematics, Vol. 58, No. 4, 472-485, Apr. 2008.
doi:10.1016/j.apnum.2007.01.020

5. Mallat, S., A Wavelet Tour of Signal Processing: The Sparse Way, Elsevier Inc., 2009.

6. Zhu, X., G. Lei, and G. Pan, "On application of fast and adaptive periodic Battle-Lemarie wavelets to modeling of multiple lossy transmission lines," Journal of Computational Physics, Vol. 132, 299-311, 1997.
doi:10.1006/jcph.1996.5637

7. Kunasanl, S. R. and C. Nguyen, "Efficient space-domain analysis of microstrip lines using wavelet transform," Microwave and Optical Technology Letters, Vol. 9, No. 1, May 1995.

8. Oueslat, N. and T. Aguili, "New implementation of the moment method based on the impedance operator to study the dispersion characteristics of microstrip lines," International Journal of Computer Science, Vol. 11, No. 5, Sep. 2014.

9. Harrington, R. F., Field Computation by Moment Methods, William Perkins, 1992.

10. Goswami, J. C. and A. K. Chan, Fundamentals Wavelets Theory, Algorithms, and Applications, John Wiley & Sons, 2011.
doi:10.1002/9780470926994

11. Pan, G., Wavelets in Electromagnetics and Device Modeling, John Wiley & Sons, Inc., 2003.
doi:10.1002/0471433918.ch7

12. Gupta, K. C., et al. Microstrip Lines and Slotlines, 2nd Ed., Artech House, 1996.

13. Daubechies, I., Ten Lectures on Wavelets, The Society for Industrial and Applied Mathematics, 1992.
doi:10.1137/1.9781611970104

14. Maurya, V. N. and A. K. Maurya, "Application of Haar wavelets and method of moments for computing performance characteristics of electromagnetic materials," American Journal of Applied Mathematics and Statistics, Vol. 2, No. 3, 96-105, 2014.
doi:10.12691/ajams-2-3-3

15. Metlevskis, E. and V. Urbanavicius, "Analysis of charge distribution on rectangular microstrip structures," Physical Aspects of Microwave and Radar Applications, Vol. 119, 2011.

16. Goswami, J. C., et al. "On solving first-kind integral equations using wavelets on a bounded interval," IEEE Transactions on Antennas and Propagation, Vol. 43, No. 6, Jun. 1995.
doi:10.1109/8.387178

17. Lashab, M., F. Benabdelaziz, and C. Zebiri, "Analysis of electromagnetics scattering from reflector and cylindrical antennas using wavelet-based moment method," Progress In Electromagnetics Research, Vol. 76, 357-368, 2007.
doi:10.2528/PIER07071401

18. Danesfahani, R., S. Hatamzadeh-Varmazyar, E. Babolian, and Z. Masouri, "Applying Shannon wavelet basis functions to the Method of Moments for evaluating the radar cross section of the conducting and resistive surfaces," Progress In Electromagnetics Research B, Vol. 8, 257-292, 200.

19. Davidson, D. B. and J. T. Aberle, "An introduction to spectral domain Method-of-Moments formulations," IEEE Antennas and Propagation Magazine, Vol. 46, No. 3, Jun. 2004.
doi:10.1109/MAP.2004.1374083

20. Oguzer, T., F. Kuyucuoglu, and I. Avgin, "Electromagnetic scattering from layered strip geometries: The Method of Moments study with the sinc basis," Turk. J. Elec. Eng. & Comp. Sci., Vol. 19, No. 3, 2011.

21. Oberschmid, G. and A. F. Jacob, "Battele-Lemarie wavelets for the analysis of microstrip lines," Institut fur Hochfrequenztechnik, TU Braunschwei, Annual Report, 1995.

22. Park, I., R. Mittra, and M. I. Aksun, "Numerically efficient analysis of planar microstrip configurations using closed-form Green’s functions," IEEE Transactions on Microwave Theory and Techniques, Vol. 43, No. 2, Feb. 1995.
doi:10.1109/22.348100

23. Li, Y. and S. Yangb, "Construction of symmetric or anti-symmetric B-spline wavelets and their dual wavelets," International Journal of Computer Mathematics, Vol. 88, No. 5, Mar. 2011.
doi:10.1080/00207160.2010.492213