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Convolution Theorems for Quaternion Fourier Transform: Properties and Applications

Author

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  • Mawardi Bahri
  • Ryuichi Ashino
  • Rémi Vaillancourt

Abstract

General convolution theorems for two-dimensional quaternion Fourier transforms (QFTs) are presented. It is shown that these theorems are valid not only for real-valued functions but also for quaternion-valued functions. We describe some useful properties of generalized convolutions and compare them with the convolution theorems of the classical Fourier transform. We finally apply the obtained results to study hypoellipticity and to solve the heat equation in quaternion algebra framework.

Suggested Citation

  • Mawardi Bahri & Ryuichi Ashino & Rémi Vaillancourt, 2013. "Convolution Theorems for Quaternion Fourier Transform: Properties and Applications," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, November.
    • Handle: RePEc:hin:jnlaaa:162769
    DOI: 10.1155/2013/162769
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    Cited by:

    1. Siddiqui Saima & Bingzhao Li & Samad Muhammad Adnan, 2022. "New Sampling Expansion Related to Derivatives in Quaternion Fourier Transform Domain," Mathematics, MDPI, vol. 10(8), pages 1-12, April.
    2. Mohammad Younus Bhat & Aamir H. Dar & Mohra Zayed & Altaf A. Bhat, 2023. "Convolution, Correlation and Uncertainty Principle in the One-Dimensional Quaternion Quadratic-Phase Fourier Transform Domain," Mathematics, MDPI, vol. 11(13), pages 1-14, July.

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