Gibbs phenomenon and its applications in science and engineering

ASEE Annual Conference and Exposition, Conference Proceedings

Volumn , Issue , 2005, Pages 6867-6877

  Libii, Josué Njock ^a  

^a INDIANA UNIVERSITY PURDUE UNIVERSITY FORT WAYNE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SOFTWARE; CURRICULA; FOURIER TRANSFORMS; FUNCTIONS; PROBLEM SOLVING; SOCIETIES AND INSTITUTIONS; STUDENTS; TEACHING;

ENGINEERING STUDENTS; GIBBS PHENOMENON; PERIODIC FUNCTIONS; SCIENCE AND ENGINEERING;

ENGINEERING EDUCATION;

EID: 22544475584     PISSN: None     EISSN: 21535965     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (26)

1. D. GOTTLIEB, CHI-WANG SHU, On the Gibbs Phenomenon and Its Resolution, SIAM Review, Volume 39, Number 4, (1997), pp. 644-668. An animation of their plots can be found on World Wide Web at http://epubs.siam.org/sam-bin/dbq/ article/30139.
2. C. LANCZOS, Discourse on Fourier Series, Oliver & Boyd, Edinburgh, 1966.
3. C. C. LIN AND L. A. SEGEL, Mathematics Applied to Deterministic Problems in the Natural Sciences, Classics in Applied Mathematics, Vol. I, SIAM, Philadelphia, pp.138-143, 1988.
4. A. F. Mills, Heat Transfer, Second Edition, Prentice Hall, Upper Saddle River, New Jersey, pp. 154-274, 1999.
5. T. E. PETERSEN, Eliminating Gibb's Effect From Separation of Variables Solutions, SIAM Review, Vol. 40, No. 2, 1998, pp. 324-326.
6. J. G. PROAKIS AND DIMITRIS G. MANOLAKIS, Introduction to Digital Signal Processing, Macmillan Publishing Company, New York, pp. 551-559, 1988.
7. I. S. SOKOLNIKOFF AND R. M. REDHEFFER, Mathematics of Physics and Modern Engineering, second edition, McGraw-Hill Book Company, New York, pp. 24-27, 1966.
8. A. J. W. SOMMERFELD, Partial Differential Equations in Physics, translated by Ernst G. Straus, Academic Press, New York, N.Y., pp. 7-14, 1949.
9. I. STAKGOLD, Green's Functions and Boundary Value Problems, A Volume in Pure and Applied Mathematics, John Wiley & Sons, New York, pp.134-136, 1979.
10. A. T. Johnson, Biomechanics and Exercise Physiology, John Wiley & Sons, New York, pp.156, 331, 1991.
11. J. H. Ginsberg, Mechanical and Structural Vibrations: Theory and Applications, John Wiley & Sons, New York, pp.155-180, 2001.
12. T. W. Körner, Fourier Analysis, Cambridge University Press, pp. 62-66, 1989.
13. J. W. Gibbs, Nature, London, 59, p. 606, 1899.
14. H. Wilbraham Camb. and Dublin Math. Jour., 3, p. 198, 1848.
15. D. C. Russell, Gibbs Phenomenon, in Encyclopedic Dictionary of Physics, J. Thewlis, Editor, The Macmillan Company, New York, pp. 466-467, 1962.
16. S. C. Fan, D.Y. Zheng, F.T.K. Au, Gibbs-phenomenon-free Fourier series for vibration and stability of complex beams, AIAA Journal, vol. 39 no. 10, pp. 1977-1984, October 2001.
17. C. Pan, Gibbs phenomenon removal and digital filtering directly through the fast Fourier transform, IEEE Transactions on Signal Processing, Vol. 49, no. 2, pp. 444-448, Feb 2001.
18. Q. Li, Y. Chen, Pseudo-spectral time-domain analysis using an initial-condition excitation technique for elimination of Gibbs phenomenon, Chinese Journal of Electronics, vol. 9, no. 1, pp. 92-95, 2000.
19. Z. Zhang, C. F. Martin, Convergence and Gibbs' phenomenon in cubic spline interpolation of discontinuous functions, Journal of Computational and Applied mathematics, vol 87, no. 2, pp. 359-371, Dec. 1997.
20. S. M. Yamashiro, F. S. Grodins, Optimal Regulation of Respiratory airflow, Jour. Appl. Physiology, vol. 35, pp. 522-525, 1971.
21. J. W. Nilsson, Electric Circuits, Fourth Edition, Addison Wesley, Reading, Massachusets, pp.736-825, 1993.
22. W. M. Deen, Analysis of Transport Phenomena, Oxford University Press, New York, New York, pp. 147-151, 1998.
23. P. M. Morse and H. Feshback, Methods of Theoretical Physics, McGraw-Hill, New York, 1953.
24. M. A. Khamsi, http://www.sosmath.com/fourier/fourier3/gibbs.html
25. Interactive: http://klebanov.homeip.net/~pavel/fb//java/la_applets/Gibbs/
26. http://mathworld.wolfram.com/GibbsPhenomenon.html