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

TL;DR

This paper explores uncertainty principles related to the offset linear canonical transform, extending fundamental time-frequency analysis tools and validating results through numerical simulations.

Contribution

It establishes new uncertainty principles for the offset linear canonical transform, including identities and inequalities, with validation via numerical simulations.

Findings

Derived new uncertainty principles for the offset linear canonical transform.

Established identities like Plancherel-Parseval-Rayleigh for this transform.

Validated theoretical results through numerical simulations.

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.