N-dimensional Fractional Fourier Transform and its Eigenvalues and Eigenfunctions

  • Inayat Ullah Department of Mathematics, University of Balochistan, Quetta 87300, Pakistan
  • Saleem Iqbal Department of Mathematics, University of Balochistan, Quetta 87300, Pakistan
  • Farhana Sarwar Department of Mathematics F.G.Girls Degree College, Madrissa Road , Quetta, Cantt, 87300, Pakistan
  • Abdul Rehman Department of Mathematics, University of Balochistan, Quetta 87300, Pakistan
Keywords: Fourier transform, Fractional Fourier Transform, Eigenvalues, Eigenfunctions

Abstract

In this paper, we have  established the N- dimentional fractional Fourier transform and its mathematical expression in a easier manner and discus the  eigenvalues and eigenfunctions of   -dimensional fractional Fourier transform.

References

N. Wiener. Hermitian polynomials and Fourier analysis. J. Math. Phys., 8:70{73, 1929.

H. Kober, Wurzeln aus der Hankel-, Fourier- und aus anderen stetigen transfornationen, Q. J Math.(Oxford), 10, 45–59 (1939).

E.U. Condon. Immersion of the Fourier transform in a continuous group of functional transformations. Proc.National Academy Sciences, 23:158{164, 1937.

V. Namias, “The fractional order Fourier transform and its application to quantum mechanics”, IMA Journal of Applied Mathematics, 25(3) 241-265(1980)

A.C. McBride and F.H. Kerr. On Namias's fractional Fourier transforms. IMA J. Appl. Math., 39:159- 175, 1987.

L.B. Almeida. The fractional Fourier transform and time-frequency representation.IEEE Trans. Sig. Proc., 42:3084-3091, 1994

http://en.wikipedia.org/wiki/Eigenface

Y.Karuna and R. Dhuli et.el “ Complete analysis of the eigen functions of Fourier transform” International Conference on Computer Communication and Informatics , India (ICCCI -2013)

] R.C. Gonzalez, R.E. Woods, and S.L. Eddins. Digital image processing using MATLAB. Prentice Hall Upper Saddle River, NJ, 2004.

Published
2020-01-06
Section
Articles