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<p>We introduce a generalized quaternion Fourier transform termed the linear canonical space-time transform (LCST). The uncertainty principles and convolution theorem are the prominent results that play a significant role in the development of the LCST, both theoretically and in its applications. This study explores the convolution theorem and then establish two uncertainty principles associated with the proposed transformation. In addition, we rigorously derive a new point-wise Heisenberg-type uncertainty inequality for the LCST and special cases of this new Heisenberg principle are also presented.</p>

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Linear canonical space-time transform: convolution theorem and uncertainty principles

  • 期刊论文

  • 发表日期：

    2026年5月7日

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  • Mawardi Bahri,
  • Nasrullah Bachtiar,
  • Muhammad Nur,
  • Amran Rahim

摘要

We introduce a generalized quaternion Fourier transform termed the linear canonical space-time transform (LCST). The uncertainty principles and convolution theorem are the prominent results that play a significant role in the development of the LCST, both theoretically and in its applications. This study explores the convolution theorem and then establish two uncertainty principles associated with the proposed transformation. In addition, we rigorously derive a new point-wise Heisenberg-type uncertainty inequality for the LCST and special cases of this new Heisenberg principle are also presented.