Title: Application and graphical interpretation of a new two-dimensional quaternion fractional Fourier transform
Author(s): Khinal Parmar, V. R. Lakshmi Gorty
Pages: 561-575
Cite as:
Khinal Parmar, V. R. Lakshmi Gorty, Application and graphical interpretation of a new two-dimensional quaternion fractional Fourier transform, Int. J. Anal. Appl., 19 (4) (2021), 561-575.

Abstract


In this paper, a new two-dimensional quaternion fractional Fourier transform is developed. The properties such as linearity, shifting and derivatives of the quaternion-valued function are studied. The convolution theorem and inversion formula are also established. An example with graphical representation is solved. An application related to two-dimensional quaternion Fourier transform is also demonstrated.

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References


  1. M. Bahri, A.K. Amir, C. Lande, The quaternion domain Fourier transform and its application in mathematical statistics, IAENG Int. J. Appl. Math. 48 (2018), 1-7. Google Scholar

  2. M. Bahri, R. Ashino, R. Vaillancourt, Continuous quaternion Fourier and wavelet transforms, Int. J. Wavelets Multiresolut. Inf. Process. 12 (2014), 1460003. Google Scholar

  3. T. B¨ulow, M. Felsberg, G. Sommer, Non-commutative hyper complex Fourier transforms of multidimensional signals, In: G. Sommer (eds) Geometric Computing with Clifford Algebras, Springer, Berlin, Heidelberg, 2001. Google Scholar

  4. D. Cheng, K.I. Kou, Plancherel theorem and quaternion Fourier transform for square integrable functions, Complex Var. Elliptic Equ. 64 (2019), 223–242. Google Scholar

  5. B. Davies, Integral transforms and their Applications, Springer, New York, 1978. Google Scholar

  6. T.A. Ell, Quaternion-Fourier transforms for analysis of two-dimensional linear time-invariant partial differential systems, in: Proceedings of 32nd IEEE Conference on Decision and Control, IEEE, San Antonio, TX, USA, 1993: pp. 1830–1841. Google Scholar

  7. T.A. Ell, S.J. Sangwine, Hypercomplex Fourier Transforms of Color Images, IEEE Trans. Image Process. 16 (2007), 22–35. Google Scholar

  8. X. Guanlei, W. Xiaotong, X. Xiaogang, Fractional quaternion Fourier transform, convolution and correlation, Signal Processing. 88 (2008), 2511–2517. Google Scholar

  9. E.M.S. Hitzer, Quaternion Fourier Transform on Quaternion Fields and Generalizations, Adv. Appl. Clifford Alg. 17 (2007), 497–517. Google Scholar

  10. A.C. Lewis, William Rown Hamilton, Lectures on quaternions (1853), in: Landmark Writings in Western Mathematics 1640-1940, Elsevier, 2005: pp. 460–469. Google Scholar

  11. P. Lian, Uncertainty principle for the quaternion Fourier transform, J. Math. Anal. Appl. 467 (2018), 1258–1269. Google Scholar

  12. L. Romero, R. Cerutti, L. Luque, A new Fractional Fourier Transform and convolutions products, Int. J. Pure Appl. Math. 66 (2011), 397-408. Google Scholar

  13. R. Roopkumar, Quaternionic one-dimensional fractional Fourier transform, Optik, 127 (2016), 11657-11661. Google Scholar

  14. A.H. Zemanian, Generalized integral transformations, John Wiley Sons Inc., New York, 1968. Google Scholar


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