The 2p order Heisenberg-Pauli-Weyl uncertainty principles related to the offset linear canonical transform

2025/06/12 by Peng, Jia-Yin, Li, Bing-Zhao
#FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.2507.00010

Abstract

The uncertainty principle is one of the fundamental tools for time-frequency analysis in signal processing, revealing the intrinsic trade-off between time and frequency resolutions. With the continuous development of various advanced time-frequency analysis methods based on the Fourier transform, investigating uncertainty principles associated with these methods has become one of the most interesting topics. This paper studies the uncertainty principles related to the offset linear canonical transform, including the Plancherel-Parseval-Rayleigh identity, the 2p order Heisenberg-Pauli-Weyl uncertainty principle and the sharpened Heisenberg-Weyl uncertainty principle. Numerical simulations are also proposed to validate the derived results.

Citations

• Multidimensional Fractional Wavelet Transforms and Uncertainty Principles
• Uncertainty principles for the short-time linear canonical transform of complex signals
• Uncertainty principles for the windowed offset linear canonical transform
• The Fourier Transform and its Applications.

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