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<p>Following the idea of the fractional space-time Fourier transform, a linear canonical space-time transform for 16-dimensional space-time <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="6_2025_1386_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="37" /> </InlineMediaObject> <EquationSource Format="TEX">\(C\ell _{3,1}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>C</mi> <msub> <mi>ℓ</mi> <mrow> <mn>3</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mrow> </math></EquationSource> </InlineEquation>-valued signals is investigated in this paper. First, the definition of the proposed linear canonical space-time transform is given, and some related properties of this transform are obtained. Second, the convolution operator and the corresponding convolution theorem are proposed. Third, the convolution theorem associated with the two-sided linear canonical space-time transform is derived.</p>

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Linear Canonical Space-Time Transform and Convolution Theorems

  • 期刊论文

  • 发表日期：

    2025年5月21日

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  • Yi-Qiao Xu,
  • Bing-Zhao Li

摘要

Following the idea of the fractional space-time Fourier transform, a linear canonical space-time transform for 16-dimensional space-time \(C\ell _{3,1}\) C ℓ 3 , 1 -valued signals is investigated in this paper. First, the definition of the proposed linear canonical space-time transform is given, and some related properties of this transform are obtained. Second, the convolution operator and the corresponding convolution theorem are proposed. Third, the convolution theorem associated with the two-sided linear canonical space-time transform is derived.