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<p>The convolution-based windowed free metaplectic transform (CWFMT) is a novel time-frequency analysis tool. In this paper, we first develop the relationship of the CWFMT with the Fourier transform (FT), the Short-time Fourier transform (STFT) and the free metaplectic transform (FMT). Second, we establish inequalities associated with the CWFMT including Pitt’s inequality and the Hausdorff–Young inequality. Finally, we demonstrate some new results concerning several generalizations of the uncertainty principles associated with the proposed transform.</p>

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Inequalities and uncertainty principles in the framework of convolution-based windowed free metaplectic transform

  • 期刊论文

  • 发表日期：

    2026年5月8日

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  • Huzaifa Jan,
  • M. Younus Bhat

摘要

The convolution-based windowed free metaplectic transform (CWFMT) is a novel time-frequency analysis tool. In this paper, we first develop the relationship of the CWFMT with the Fourier transform (FT), the Short-time Fourier transform (STFT) and the free metaplectic transform (FMT). Second, we establish inequalities associated with the CWFMT including Pitt’s inequality and the Hausdorff–Young inequality. Finally, we demonstrate some new results concerning several generalizations of the uncertainty principles associated with the proposed transform.