改进的Morlet小波及其变换

提出了一个改进的Morlet小波，并在此基础上给出了Morlet小波变换的完全重构公式，这个重构公式不需要Morlet小波满足小波容许条件，使得Morlet小波变换在理论上趋于完善。改进后的Morlet小波其尺度参数替换为小波主频参数，参数有明确的物理意义，用它作为核函数的小波变换把时间信号映射到时间-频率域。重构公式的提出可拓宽Morlet小波的应用范围，引进了一个由Morlet小波变换及其逆变换构建的时-频滤波器并将其用于地震信号处理以提高其分辨率。从理论上分析了Morlet小波变换与S变换的区别，并用实际算例验证了分析结果。

Improved Morlet wavelet and its complete transform

The paper proposes an improved Morlet wavelet, and introduces a complete reconstruction formula of Morlet wavelet transform based on the improved Morlet wavelet. This reconstruction formula frees the constraint of wavelets satisfying the admissible condition, and it makes Morlet wavelet transformation more complete in theory. Owing to the wavelet’s dominant frequency instead of its scale parameter in improved Morlet wavelet, the parameter has clear physical meaning, and wavelet transform takes the improved Morlet wavelet as kernel function map time signal to time-frequency domain. This reconstruction formulacan widens the application of Morlet wavelets. The paper shows a time-frequency filter built upon Mortlet wavelet transform and its inverse transform and employs it improving seismic signal resolution. The paper analyzes differences of Morlet wavelet transform and S transform from theory and verifies these differences by practical application.