Smoothed Affine Wigner Transform

Coarse-scale representations and smoothed Wigner transforms

Smoothed Wigner transforms have been used in signal processing, as a regularized version of the Wigner transform, and have been proposed as an alternative to it in the homogenization and / or semiclassical limits of wave equations. We derive explicit, closed formulations for the coarse-scale representation of the action of pseudodifferential operators. The resulting ``smoothed operators'' are in general of infinite order. The formulation of an appropriate framework, resembling the Gelfand-Shilov spaces, is necessary. Similarly we treat the ``smoothed Wigner calculus''. In particular this allow…

平滑Wigner变换的精确方程与波传播的均匀化

Exact equations for smoothed Wigner transforms and homogenization of wave propagation

本文提出平滑Wigner变换并推导其精确方程，用于消除干涉项，以有效模拟波传播问题，并通过薛定谔方程的渐近模型进行数值验证。

半经典（高频）波传播数值模拟中的平滑Wigner变换

Smoothed Wigner transforms in the numerical simulation of semiclassical (high-frequency) wave propagation

针对半经典波传播数值模拟难题，提出基于平滑Wigner变换的相空间方法，相比传统Wigner变换和原方程全数值解显著提高计算效率。