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Research Articles

On the fractional space-time Fourier transforms

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Pages 127-150 | Received 06 Apr 2023, Accepted 13 Nov 2023, Published online: 13 Dec 2023

References

  • Almeida LB. The fractional Fourier transform and time-frequency representations. IEEE Trans Signal Process. 1994;42(11):3084–3091. doi: 10.1109/78.330368.
  • Mendlovic D, Ozaktas HM. Fractional Fourier transforms and their optical implementation-I. J Opt Soc Am A. 1993;10:1875–1881. doi: 10.1364/JOSAA.10.001875
  • Namias V. The fractional order Fourier transform and its application to quantum mechanics. J Inst Math Appl. 1980;25:241–265. doi: 10.1093/imamat/25.3.241
  • Ozaktas HM, Kutay MA, Candan C. Fractional fourier transform. In: Poularikas AD, editor. Transforms and applications handbook. Boca Raton: CRC Press; 2010. p. 632–659.
  • Ran T, Bing D, Yue W. Research progress of the fractional Fourier transform in signal processing. Sci China Ser F. 2006;49:1–25.
  • Sejdić E, Djurović I, Stanković L. Fractional Fourier transform as a signal processing tool: an overview of recent developments. Signal Process. 2011;91:1351–1369. doi: 10.1016/j.sigpro.2010.10.008
  • Doran C, Lasenby A. Geometric algebra for physicists. Cambridge: Cambridge University Press; 2003.
  • Hestenes D. Space-time algebra. 2nd ed. Basel: Birkhäuser; 2015.
  • Hitzer E, Nitta T, Kuroe Y. Applications of Clifford's geometric algebra. Adv Appl Clifford Algebra. 2013;23:377–404. doi: 10.1007/s00006-013-0378-4
  • Hitzer E, Sangwine SJ. The orthogonal 2D planes split of quaternions and steerable quaternion Fourier transformations. Vol. 27, Trends in mathematics. Basel: Birkhauser; 2013. p. 15–39.
  • Sommer G. Geometric computing with Clifford algebras. Berlin, Heidelberg, New York: Springer-Verlag; 2001.
  • Hitzer E. Special relativistic Fourier transformation and convolutions. Math Meth Appl Sci. 2019;42:2244–2255. doi: 10.1002/mma.v42.7
  • El Haoui Y, Hitzer E, Fahlaoui S. Heisenberg's and Hardy's uncertainty principles for special relativistic space-time Fourier transformation. Adv Appl Clifford Algebras. 2020;30:69. doi: 10.1007/s00006-020-01093-5
  • Shi H, Yang H, Li Z, et al. Fractional Clifford–Fourier transform and its application. Adv Appl Clifford Algebras. 2020;30. doi: 10.1007/s00006-020-01094-4.
  • El Haoui Y, Fahlaoui S. Donoho–Stark's uncertainty principles in real Clifford algebras. Adv Appl Clifford Algebras. 2019;29. doi: 10.1007/s00006-019-1015-7.
  • Ozaktas HM, Kutay MA, Mendlovic D. Introduction to the fractional Fourier transform and its applications. In: Hawkes PW, editor. Advances in imaging and electron physics. Vol. 106. San Diego (CA): Academic Press; 1999. p. 239–291.
  • Linares F, Ponce G. Introduction to nonlinear dispersive equations. New York (NY): Springer; 2009.
  • Hitzer E. Directional uncertainty principle for quaternion Fourier transform. Adv Appl Clifford Algebras. 2010;20:271–284. doi: 10.1007/s00006-009-0175-2
  • Hitzer E, Mawardi B. Clifford Fourier transform on multivector fields and uncertainty principles for dimensions n=2(mod4) and n=3(mod4). Adv Appl Clifford Algebras. 2008;18:715–736. doi: 10.1007/s00006-008-0098-3
  • Mawardi B, Hitzer E. Clifford Fourier transform and uncertainty principle for the Clifford geometric algebra Cℓ(3,0). Adv Appl Clifford Algebras. 2006;16:41–61. doi: 10.1007/s00006-006-0003-x
  • Shah FA, Teali AA, Tantary AY. Linear canonical wavelet transform in quaternion domains. Adv Appl Clifford Algebras. 2021;31. doi: 10.1007/s00006-021-01142-7.
  • Mustard D. Fractional convolution. J Aust Math Soc Ser B. 1998;40:257–265. doi: 10.1017/S0334270000012509

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