The Radon and Hilbert transform and their applications to convectively coupled waves (CCWs) are reviewed. The Hilbert Transform is used to compute the wave envelope, whereas the Radon transform is used to estimate the phase and group velocities of CCWs. Together, they provide an objective method to understand CCW propagation. Results reveal phase speeds and group velocities for fast waves (mixed Rossby‐gravity, westward and eastward inertio‐gravity, and Kelvin) that are consistent with previous studies and with Matsuno's equatorial wave dispersion curves. However, slowly‐propagating tropical depression‐like systems and equatorial Rossby waves exhibit wave envelopes that propagate faster than the individual wave crests, which is not predicted by dry shallow water theory.

中文翻译：

---

Radon 和 Hilbert 变换及其在大气波中的应用

回顾了氡和希尔伯特变换及其在对流耦合波 (CCW) 中的应用。希尔伯特变换用于计算波包络，而拉东变换用于估计 CCW 的相速度和群速度。它们共同提供了一种理解 CCW 传播的客观方法。结果揭示了快波（混合罗斯贝重力、向西和向东惯性重力以及开尔文）的相速度和群速度，这与之前的研究和松野的赤道波色散曲线一致。然而，缓慢传播的热带低压类系统和赤道罗斯贝波表现出的波包络传播速度比单个波峰传播得更快，这是干燥浅水理论无法预测的。