Meteorological Radar Echoes with Rayleigh Distribution

In meteorological radar applications, the Rayleigh distribution serves as a fundamental statistical model for characterizing echo signal properties, including time-frequency analysis, power spectral density, and spectral distribution. The Rayleigh distribution represents a transformed normal distribution particularly suitable for modeling signal propagation in weak to moderate multipath fading environments. For radar data processing implementation, time-frequency analysis typically employs algorithms like Short-Time Fourier Transform (STFT) or Wavelet Transform to resolve simultaneous temporal and spectral variations, enabling comprehensive signal interpretation. Power spectral density analysis, commonly computed using periodogram or Welch's method, reveals spectral characteristics by quantifying signal power distribution across frequencies. Spectral distribution analysis employs histogram-based or parametric estimation techniques to identify dominant frequency bands, which is crucial for optimizing radar signal processing algorithms and enhancing target detection capabilities in meteorological applications.