关键词: Morlet小波, 容许条件, 逆变换, 时-频分析, S变换

Abstract: 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.

Key words: Morlet wavelet, admissible condition, inverse transform, time-frequency analysis, S transform