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<p>The objective of this paper is to extend some uncertainty inequalities for the fractional quaternion Fourier transform. We investigate the sharp Hausdorff-Young inequality for the fractional quaternion Fourier transform and utilize it to build the MS inequality related to this transform. We establish the Donoho-Stark uncertainty principle and Shannon inequalities. These results are very significant in the field of uncertainty principles. They show that a nonzero signal and its transform can not be both timelimited and bandlimited in the fractional quaternion domain with two different indexes.</p>

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Quantitative uncertainty principles associated with the fractional quaternion fourier transform

  • 期刊论文

  • 发表日期：

    2025年7月28日

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  • Fatima Elgadiri,
  • Abdellatif Akhlidj

摘要

The objective of this paper is to extend some uncertainty inequalities for the fractional quaternion Fourier transform. We investigate the sharp Hausdorff-Young inequality for the fractional quaternion Fourier transform and utilize it to build the MS inequality related to this transform. We establish the Donoho-Stark uncertainty principle and Shannon inequalities. These results are very significant in the field of uncertainty principles. They show that a nonzero signal and its transform can not be both timelimited and bandlimited in the fractional quaternion domain with two different indexes.