Journal of Nuclear Science, Engineering and Technology (JONSAT)
In cooperation with the Iranian Nuclear Society

Application of the Fourier and Wavelet Transforms in Noise Reduction of the out of the Ordinary Data

Document Type : Research Paper

Authors

M.A Tafreshi
Y Sadeghi
Abstract
In this article the noise reduction of the experimental data by the Fourier and the wavelet transforms has been investigated. Using both simulated and experimental data (from the plasma focus facility, Dena), the sensitive features of the application of the Fourier transform are visualized and discussed. Then, the main idea of the wavelet transform and the results of the noise reduction with this transform are presented. Due to this investigation, for the cases such as the current derivative of the Dena facility, where the reliability of the Fourier transform can be doubtful, the wavelet transform can be considered as a more accurate alternative approach.

Highlights

  1. 1.    M.A. Tafreshi, M. Farrahi et. al, “Dena a new PF device,” Nukleonika, 46 (Supplement1), S85-S87 (2001).

 

  1. 2.    V. Siahpoush, S. Sobhanian, M.A. Tafreshi, et. al, “A model for plasma evolution in Filippov type plasma focus facilities,” Iranian Journal of Science & Technology, Transaction A, Vol. 27, No. A2, Summer (2003).

 

  1. 3.    V. Siahpoush, M.A. Tafreshi, S. Sobhanian, S. Khorram, “Adaptation of Sing Lee’s model to the Filippov type plasma focus geometry,” Plasma Phys and Control, Fusion 47 1065-1075 (2005).

 

  1. 4.    C. Kittel, “Introduction to solid state physics,” 5th edition, John Wiley & Sons, ISBN 0-471-49024-5 (1976).

 

  1. 5.    R.C. Gonzales, P. Wintz, “Digital Image Processing,” addison-wesley publishing, ISBN: 0-201-11026-1 (1987).

 

  1. 6.    M.E. Van Valkenburg, “Network Analysis,” Prentice-Hall (1955).

 

  1. 7.    A.B. Carlson, “Communication Systems,” Mc-Graw-Hill, New York (1968).

 

  1. 8.    J.B. Thomas, “Statistical Communication Theory,” Wiley, New York (1969).

 

  1. 9.    J.W. Cooley, P.A.W. Lewis, P.D. Welch, “Historical Notes on the Fast Fourier Transform,” IEEE Trans. On Audio and Electroacoustics, Vol. AU-15, No. 2. 76-79 (1967).

 

 

 

 

 

 

 

 

 
 

43
 

 

 

 

 

 


  1. 10.              J.W. Cooley, P.A.W. Lewis, P.D. Welch, “Application of the Fast Fourier Transform to Computation of Fourier Integrals,” IEEE Trans. on Audio and Electroacoustics, Vol. AU-15, No. 2, 79-84 (1967).

 

11. J.W. Cooley and J.W. Tukey, “An Algorithm for the Machine Calculation of Complex Fourier Series,” Math of Comput, Vol. 19, 297-301 (1965).

 

  1. 12.              S. Mellat, “A theory for multi-resolution signal decomposition: the wavelet representation,” IEEE Trans. on Pattern Anal. And Machine Intelligence, Vol.11, No.7, 674-693 (1989).

 

  1. 13.              G.P. Nason, B.W. Silverman, “The stationary wavelet transform and some statistical applications,” Lecture Notes in Statistics, 103, 281-299 (1995).

 

14. R.A. DeVore, B. Jawerth, B.J. Lucier, “Image compression through wavelet transform coding,” IEEE Trans. on Inf. Theory, Vol. 38, 719-746 (1992).

 

  1. 15.              P. Flandrin, “Wavelet analysis and synthesis of fractional Brownian motion,” IEEE Trans. on Inf. Theory, Vol. 38, 910-917 (1992).

 

“Wavelet Analysis,”م.ا. تفرشی، ی. صادقی، پژوهشکده فیزیک پلاسما و گداخت هسته‌ای، گزارش علمی-فنی، شماره 6-84013 (1384).

Keywords

Noise
Fourier Transform
Wavelet
Plasma Focus
  1. 1.    M.A. Tafreshi, M. Farrahi et. al, “Dena a new PF device,” Nukleonika, 46 (Supplement1), S85-S87 (2001).

 

  1. 2.    V. Siahpoush, S. Sobhanian, M.A. Tafreshi, et. al, “A model for plasma evolution in Filippov type plasma focus facilities,” Iranian Journal of Science & Technology, Transaction A, Vol. 27, No. A2, Summer (2003).

 

  1. 3.    V. Siahpoush, M.A. Tafreshi, S. Sobhanian, S. Khorram, “Adaptation of Sing Lee’s model to the Filippov type plasma focus geometry,” Plasma Phys and Control, Fusion 47 1065-1075 (2005).

 

  1. 4.    C. Kittel, “Introduction to solid state physics,” 5th edition, John Wiley & Sons, ISBN 0-471-49024-5 (1976).

 

  1. 5.    R.C. Gonzales, P. Wintz, “Digital Image Processing,” addison-wesley publishing, ISBN: 0-201-11026-1 (1987).

 

  1. 6.    M.E. Van Valkenburg, “Network Analysis,” Prentice-Hall (1955).

 

  1. 7.    A.B. Carlson, “Communication Systems,” Mc-Graw-Hill, New York (1968).

 

  1. 8.    J.B. Thomas, “Statistical Communication Theory,” Wiley, New York (1969).

 

  1. 9.    J.W. Cooley, P.A.W. Lewis, P.D. Welch, “Historical Notes on the Fast Fourier Transform,” IEEE Trans. On Audio and Electroacoustics, Vol. AU-15, No. 2. 76-79 (1967).

 

 

 

 

 

 

 

 

 
 

43
 

 

 

 

 

 


  1. 10.              J.W. Cooley, P.A.W. Lewis, P.D. Welch, “Application of the Fast Fourier Transform to Computation of Fourier Integrals,” IEEE Trans. on Audio and Electroacoustics, Vol. AU-15, No. 2, 79-84 (1967).

 

11. J.W. Cooley and J.W. Tukey, “An Algorithm for the Machine Calculation of Complex Fourier Series,” Math of Comput, Vol. 19, 297-301 (1965).

 

  1. 12.              S. Mellat, “A theory for multi-resolution signal decomposition: the wavelet representation,” IEEE Trans. on Pattern Anal. And Machine Intelligence, Vol.11, No.7, 674-693 (1989).

 

  1. 13.              G.P. Nason, B.W. Silverman, “The stationary wavelet transform and some statistical applications,” Lecture Notes in Statistics, 103, 281-299 (1995).

 

14. R.A. DeVore, B. Jawerth, B.J. Lucier, “Image compression through wavelet transform coding,” IEEE Trans. on Inf. Theory, Vol. 38, 719-746 (1992).

 

  1. 15.              P. Flandrin, “Wavelet analysis and synthesis of fractional Brownian motion,” IEEE Trans. on Inf. Theory, Vol. 38, 910-917 (1992).

 

“Wavelet Analysis,”م.ا. تفرشی، ی. صادقی، پژوهشکده فیزیک پلاسما و گداخت هسته‌ای، گزارش علمی-فنی، شماره 6-84013 (1384).

Journal of Nuclear Science, Engineering and Technology (JONSAT)
Volume 26, Issue 2 - Serial Number 37
September 2006
Pages 39-43

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