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<p>Recently, the octonion Fourier transform (OFT) has been proposed and utilized in image processing. This transformation is intimately related to the three-dimensional Clifford Fourier transform. Similar to the Clifford Fourier transform, the uncertainty principle is recognized as an important result in the OFT. The present study explores Heisenberg-type inequality associated with the OFT. This uncertainty principle describes how an octonion-valued signal and its OFT relates. Variations on the uncertainty inequality are then established. Finally, we establish a new form of Heisenberg uncertainty principle for octonion linear canonical transform (OLCT). This result refines Heisenberg inequality for the OLCT in literature.</p>

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Some Heisenberg Uncertainty Principles for Octonion Fourier Transform and A New Form of Heisenberg Inequality for Octonion Linear Canonical Transform

  • 期刊论文

  • 发表日期：

    2026年7月3日

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  • Mawardi Bahri,
  • Manab Kundu

摘要

Recently, the octonion Fourier transform (OFT) has been proposed and utilized in image processing. This transformation is intimately related to the three-dimensional Clifford Fourier transform. Similar to the Clifford Fourier transform, the uncertainty principle is recognized as an important result in the OFT. The present study explores Heisenberg-type inequality associated with the OFT. This uncertainty principle describes how an octonion-valued signal and its OFT relates. Variations on the uncertainty inequality are then established. Finally, we establish a new form of Heisenberg uncertainty principle for octonion linear canonical transform (OLCT). This result refines Heisenberg inequality for the OLCT in literature.