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Abstract and Applied Analysis
Volume 2013, Article ID 162769, 10 pages
http://dx.doi.org/10.1155/2013/162769
Research Article

Convolution Theorems for Quaternion Fourier Transform: Properties and Applications

1Department of Mathematics, Hasanuddin University, Makassar 90245, Indonesia
2Division of Mathematical Sciences, Osaka Kyoiku University, Osaka 582-8582, Japan
3Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada K1N 6N5

Received 1 June 2013; Revised 1 September 2013; Accepted 7 September 2013

Academic Editor: Narcisa C. Apreutesei

Copyright © 2013 Mawardi Bahri et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [17 citations]

The following is the list of published articles that have cited the current article.

  • Mawardi Bahri, and Ryuichi Ashino, “Relationship between quaternion linear canonical and quaternion fourier transforms,” 2014 International Conference on Wavelet Analysis and Pattern Recognition, pp. 116–121, . View at Publisher · View at Google Scholar
  • Mawardi Bahri, “On Two-Dimensional Quaternion Wigner-Ville Distribution,” Journal of Applied Mathematics, vol. 2014, pp. 1–13, 2014. View at Publisher · View at Google Scholar
  • Mawardi Bahri, Muh. Irwan, Syamsuddin Toaha, and Muh. Saleh, “Correlation theorem for two-sided quaternion fourier transform,” Applied Mathematical Sciences, no. 41-44, pp. 1999–2005, 2014. View at Publisher · View at Google Scholar
  • Mawardi Bahri, “Product theorem for quaternion fourier transform,” International Journal of Mathematical Analysis, vol. 8, no. 1-4, pp. 81–87, 2014. View at Publisher · View at Google Scholar
  • Mawardi Bahri, and Ryuichi Ashimo, “Convolution and correlation theorems for continuous reduced biquaternion wavelet transform,” International Conference on Wavelet Analysis and Pattern Recognition, vol. 2015-, pp. 81–86, 2015. View at Publisher · View at Google Scholar
  • Mawardi Bahri, “A Modified Uncertainty Principle for Two-Sided Quaternion Fourier Transform,” Advances in Applied Clifford Algebras, 2015. View at Publisher · View at Google Scholar
  • Kit Ian Kou, and Xiao-Xiao Hu, “Quaternion Fourier and linear canonical inversion theorems,” Mathematical Methods in the Applied Sciences, vol. 40, no. 7, pp. 2421–2440, 2016. View at Publisher · View at Google Scholar
  • Mawardi Bahri, and Ryuichi Ashino, “Logarithmic uncertainty principle for quaternion linear canonical transform,” International Conference on Wavelet Analysis and Pattern Recognition, vol. 2016-, pp. 140–145, 2016. View at Publisher · View at Google Scholar
  • Mawardi Bahri, and Ryuichi Ashino, “A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform,” Abstract and Applied Analysis, vol. 2016, pp. 1–11, 2016. View at Publisher · View at Google Scholar
  • Guangsheng Ma, and Jiman Zhao, “Multilinear localization operators associated to quaternion Fourier transforms,” Trends in Mathematics, no. 9783319475110, pp. 107–118, 2017. View at Publisher · View at Google Scholar
  • Cuiming Zou, Kit Ian Kou, and Joao Morais, “Prolate spheroidal wave functions associated with the quaternionic Fourier transform,” Mathematical Methods in the Applied Sciences, 2017. View at Publisher · View at Google Scholar
  • Resnawati, and Selvy Musdalifah, “Modified convolution theorem for one-sided quaternion linear canonical transform,” Journal of Physics: Conference Series, vol. 943, pp. 012012, 2018. View at Publisher · View at Google Scholar
  • Mawardi Bahri, and Ryuichi Ashino, “Duality property of two-sided quaternion fourier transform,” International Conference on Wavelet Analysis and Pattern Recognition, vol. 2018-, pp. 1–6, 2018. View at Publisher · View at Google Scholar
  • Shrideh K. Q. Al-Omari, and D. Baleanu, “Quaternion fourier integral operators for spaces of generalized quaternions,” Mathematical Methods in the Applied Sciences, 2018. View at Publisher · View at Google Scholar
  • Mawardi Bahri, and Ryuichi Ashino, “A Convolution Theorem Related to Quaternion Linear Canonical Transform,” Abstract and Applied Analysis, vol. 2019, pp. 1–9, 2019. View at Publisher · View at Google Scholar
  • Kamel Brahim, and Emna Tefjeni, “Uncertainty principle for the two sided quaternion windowed Fourier transform,” Journal of Pseudo-Differential Operators and Applications, 2019. View at Publisher · View at Google Scholar
  • Brahim Kamel, and Emna Tefjeni, “Uncertainty principle for the two-sided quaternion windowed Fourier transform,” Integral Transforms and Special Functions, pp. 1–21, 2019. View at Publisher · View at Google Scholar