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<p>This paper introduces a novel biquaternion offset linear canonical transform-based Wigner-Ville distribution to unlock the potential of complex signal analysis.The Wigner-Ville distribution (WVD) associated with the biquaternion offset linear canonical transform (BiQOLCT), termed WVD-BiQOLCT, represents a significant advancement in signal processing within biquaternion algebra. This novel hybrid transform synergizes the strengths of both WVD and BiQOLCT, offering enhanced analytical capabilities. Our research commences with an exploration of the WVD-BiQOLCT’s core characteristics, including its nonlinear nature, invertibility, shift properties, and adherence to the Plancherel formula. The paper’s primary contribution lies in extending several pivotal uncertainty principles to the WVD-BiQOLCT framework, namely the logarithmic, Hardy’s, and Beurling’s uncertainty principles. Some potential applications are also presented at the end.</p>

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Wigner-Ville distribution associated with the biquaternion offset Linear canonical transform

  • 期刊论文

  • 发表日期：

    2026年1月16日

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  • Aijaz Ahmad Dar,
  • Owais Ahmad

摘要

This paper introduces a novel biquaternion offset linear canonical transform-based Wigner-Ville distribution to unlock the potential of complex signal analysis.The Wigner-Ville distribution (WVD) associated with the biquaternion offset linear canonical transform (BiQOLCT), termed WVD-BiQOLCT, represents a significant advancement in signal processing within biquaternion algebra. This novel hybrid transform synergizes the strengths of both WVD and BiQOLCT, offering enhanced analytical capabilities. Our research commences with an exploration of the WVD-BiQOLCT’s core characteristics, including its nonlinear nature, invertibility, shift properties, and adherence to the Plancherel formula. The paper’s primary contribution lies in extending several pivotal uncertainty principles to the WVD-BiQOLCT framework, namely the logarithmic, Hardy’s, and Beurling’s uncertainty principles. Some potential applications are also presented at the end.