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<p>This paper is devoted to the investigation of several tighter uncertainty principles (UPs) for the continuous Bendlet transform (CBT) and continuous quaternion Bendlet transform (CQBT), respectively, by using the coordinate form for both complex and quaternion signals. We mainly focus on the tighter Heisenberg–Weyl UPs in spatial and directional settings for the CBT and CQBT. Remarkably, these new UPs possess more stringent lower bounds by comparing with the classical UPs.</p>

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Tighter uncertainty principles associated with Bendlet and quaternion-Bendlet transforms

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月4日

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  • Cen Li,
  • Xinyu Wang,
  • Shenzhou Zheng

摘要

This paper is devoted to the investigation of several tighter uncertainty principles (UPs) for the continuous Bendlet transform (CBT) and continuous quaternion Bendlet transform (CQBT), respectively, by using the coordinate form for both complex and quaternion signals. We mainly focus on the tighter Heisenberg–Weyl UPs in spatial and directional settings for the CBT and CQBT. Remarkably, these new UPs possess more stringent lower bounds by comparing with the classical UPs.