THEKERNEL OF N- DIMENSIONAL FRACTIONAL FOURIER TRANSFORM

Authors

  • Zakia Abdul Wahid Department of Mathematics, University of Balochistan Quetta, Pakistan
  • Saleem Iqbal Department of Mathematics, University of Balochistan Quetta, Pakistan
  • Farhana Sarwar Department of Mathematics F.G. Girls Degree College, Madrissa Road, Quetta, Cantt, Pakistan
  • Abdul Rehman Department of Mathematics, University of Balochistan Quetta, Pakistan

DOI:

https://doi.org/10.29121/ijetmr.v7.i1.2020.495

Keywords:

Fourier Transform, Fractional Fourier Transform, N-Dimensional Fractional Fourier Transform, Kernel of N- Dimensional Fractional Fourier Transform

Abstract

In this paper we have developed the kernel of N-dimensional fractional Fourier transform by extending the definition of first dimensional fractional Fourier transform. The properties of kernel up to N- dimensional are also presented here which is missing in the literature of fractional Fourier transform. The properties of kernel of fractional Fourier transforms up to N- dimensional will help the researcher to extend their research in this aspect.

Downloads

Download data is not yet available.

References

Almeida, L.B. (1994). The Fractional Fourier Transform and Time-Frequency Representation. IEEE Transactions on signal Processing, Vol. 42, No. 11. DOI: https://doi.org/10.1109/78.330368

Zayed, A. L. (DECEMBER 1996). On the Relationship Between the Fourier and Fractional Fourier Transforms Letters, Vol. 3, No. 12. DOI: https://doi.org/10.1109/97.544785

V. Ashok Narayanana, 1. K. (2003). The fractional Fourier transform: theory,implementation and error analysis. Microprocessors and Microsystems 27, 511–521. DOI: https://doi.org/10.1016/S0141-9331(03)00113-3

NAMIAS, V. (1980). The Fractional Order Fourier Transform and its Application to Quantum Mechanics. J. Inst. Maths Applies, 241-265. DOI: https://doi.org/10.1093/imamat/25.3.241

Ervin Sejdi´c, I. D. (2011). Fractional Fourier transform as a signal processing tool: An overview of recent developments. Time Frequency signal analysis. Vol. 91 No. 6,.

Singh, R. S. (2005). Fractional Fourier transform: A novel tool for signal processing. J. Indian Inst. Sci, 85, 11–26.

Almanasrah, A. A. (2000). “Fractional Fourier Transforms.”. In The Transforms and Applications Handbook: Second Edition. Boca Raton: CRC Press LLC.

Sulbaran, A. B. (2004). Computation of the Fractional Fourier Transform. Celestijnenlaan 200A, B-3001 Leuven.

Ervin Sejdic´ a, ,. I. (2011). Fractional Fourier transform as a signal processing tool: An overview of recent developments. signal processing 91, 1351-1369. DOI: https://doi.org/10.1016/j.sigpro.2010.10.008

Zhengjun Liua, *. Q. (2009). A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains. Optics Communications 282, 1536–1540. DOI: https://doi.org/10.1016/j.optcom.2009.01.002

Wolf, R. S. (2000). Fractional Fourier transform in two dimensions. J. Opt. Soc. Am. A, Vol. 17, No. 12.

Bracewell,R. N. (2000). The Fourier Transform and Its Applications, 3 rd ed., Boston, McGraw Hill,

Şahin, A. (Two Dimensional Fractional Fourier Transform and its Optical Impementation.

V.D. Sharma. (August 2013). Operational Calculus on Generalized Two-Dimensional Fractional Fourier Transform. International Journal of Engineering and Innovative Technology (IJEIT), Volume 3, Issue 2,.

Sharma, V. D. (2012). Applications of Generalized Two-Dimensional Fractional Fourier transform. International Journal of Science and Research (IJSR) ISSN (Online): 2319-7064 Impact Factor (2012): 3.358.

Lei Gao1, L. Q. (2012). 2D-FRFT based rotation invariant digital image watermarking. IEEE International Symposium on Multimedia.

Sharma, V. D. (2014). Operators on the Distributional Generalized Two-Dimensional Fractional Fourier Transform. International Journal of Modern Mathematical Sciences, 9(1): 39-45.

Downloads

Published

2020-01-31

How to Cite

Wahid, Z. A., Iqbal, S., Sarwar, F., & Rehman, A. (2020). THEKERNEL OF N- DIMENSIONAL FRACTIONAL FOURIER TRANSFORM. International Journal of Engineering Technologies and Management Research, 7(1), 36–41. https://doi.org/10.29121/ijetmr.v7.i1.2020.495