Article Sidebar

Submitted
September 17, 2013
Accepted
October 25, 2014
Published
October 25, 2014
Download
PDF
Statistic
Read Counter : 709 Download : 326

Downloads

Download data is not yet available.

Main Article Content

Abstract

The non-commutativity of the Clifford multiplication gives different aspects from the classical Fourier analysis.We establish main properties of convolution theorems for the Clifford Fourier transform. Some properties of these generalized convolutionsare extensions of the corresponding convolution theorems of the classical Fourier transform.

DOI : http://dx.doi.org/10.22342/jims.20.2.143.125-140

Keywords

Clifford convolution Clifford algebra Clifford Fourier transform

Article Details

Author Biographies

Mawardi Bahri, Hasanuddin University

Department of Mathematics

Ryuichi Ashino, Osaka Kyoiku University

Mathematical Sciences

Rémi Vaillancourt, University of Ottawa

Department of Mathematics and Statistics
How to Cite
Bahri, M., Ashino, R., & Vaillancourt, R. (2014). CONVOLUTION THEOREMS FOR CLIFFORD FOURIER TRANSFORM AND PROPERTIES. Journal of the Indonesian Mathematical Society, 20(2), 125–140. https://doi.org/10.22342/jims.20.2.143.125-140
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. Mawardi, B. and Hitzer, E.,
  2. Clifford Fourier transformation and uncertainty principle for
  3. the Clifford geometric algebra Cl_{3,0},
  4. Adv. Appl. Clifford Algebr., 16(1) (2006), 41--61.
  5. Mawardi, B., Adji, S. and Zhao, J.,
  6. Clifford algebra-valued wavelet transform on multivector fields,
  7. Adv. Appl. Clifford Algebr., 21(1) (2011), 13--30.
  8. Hitzer, E.,
  9. Quaternion Fourier transform on quaternion fields and generalizations,
  10. Adv. Appl. Clifford Algebr., 17(3) (2007), 497--517.
  11. Hitzer, E. and Mawardi, B.,
  12. Clifford Fourier transform on multivector fields and uncertainty principle
  13. for dimensions n = 2 (mod 4) and n = 3 (mod 4),
  14. Adv. Appl. Clifford Algebr., 18}(3-4) (2008), 715--736.
  15. Brackx, F., Delanghe, R. and Sommen, F.,
  16. Clifford Analysis,
  17. Research Notes in Mathematics, 76.
  18. Pitman, Boston, MA, 1982.
  19. Sommen, F.,
  20. A product and an exponential function in hypercomplex function theory,
  21. Applicable Anal., 12(1) (1981), 13--26.
  22. De Bie, H., De Schepper, N. and Sommen, F.,
  23. The class of Clifford-Fourier transforms,
  24. J. Fourier Anal. Appl., 17(6) (2011), 1198--1231.
  25. De Bie, H. and De Schepper, N.,
  26. The fractional Clifford-Fourier transforms,
  27. Complex Anal. Oper. Theory, 6(5) (2012), 1047--1067.
  28. Ebling, J. and Scheuermann, G.,
  29. Clifford Fourier transform on vector fields,
  30. IEEE Transactions on Visualization and Computer Graphics, 11(4) (2005), 469--479.
  31. Bahri, M.,
  32. Clifford windowed Fourier transform applied to linear time-varying systems,
  33. Appl. Math. Sci. (Ruse), 6(58) (2012), 2857--2864.
  34. Bracewell, R. N.,
  35. The Fourier Transform and its Applications},
  36. McGraw-Hill International Editions, Singapore, 2000.
  37. Bujack, R., Scheuermann, G. and Hitzer, E.,
  38. A general geometric Fourier transform convolution theorem,
  39. Adv. Appl. Clifford Algebr., 23(1) (2013), 15--38.
  40. Sangwine, S. J.,
  41. Color images edge detector based on quaternion convolution,
  42. Electronics Letters, 34(10) (1998), 969--971.
  43. Batard, T., Berthier, M. and Saint-Jean, C.,
  44. Clifford-Fourier transform for color image processing,
  45. In: Geometric Algebra Computing in Engineering and Computer Science,
  46. pp. 135--162, Springer London, 2010.
  47. Fu, Y., Kahler, U. and Cerejeiras, P.,
  48. The Balian-Low theorem for the windowed quaternionic Fourier transform,
  49. Adv. Appl. Clifford Algebr., 22(4) (2012), 1025--1040.