THEKERNEL OF N- DIMENSIONAL FRACTIONAL FOURIER TRANSFORM
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.
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.
Copyright (c) 2020 Zakia Abdul Wahid, Saleem Iqbal, Farhana Sarwar, Abdul Rehman
This work is licensed under a Creative Commons Attribution 4.0 International License.
License and Copyright Agreement
In submitting the manuscript to the journal, the authors certify that:
- They are authorized by their co-authors to enter into these arrangements.
- The work described has not been formally published before, except in the form of an abstract or as part of a published lecture, review, thesis, or overlay journal.
- That it is not under consideration for publication elsewhere.
- That its release has been approved by all the author(s) and by the responsible authorities – tacitly or explicitly – of the institutes where the work has been carried out.
- They secure the right to reproduce any material that has already been published or copyrighted elsewhere.
- They agree to the following license and copyright agreement.
Authors who publish with International Journal of Engineering Technologies and Management Research agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY-SA 4.0) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors can enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or edit it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) before and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
For More info, please visit CopyRight Section