基于窗口理论的时频分析方法研究

Research on time-frequency analysis based on window theory

通过对比短时Fourier变换、连续小波变换、S变换、广义S变换等时频分析方法发现,从窗的维度看,它们具有统一的内积形式,差别在于窗函数中σ(f)的取值。通过分析相应方法中σ(f)随信号频率的变化规律,以及随之产生的时窗与时频分辨率问题,解释广义S变换的相对优越性。将广义S变换应用于四类薄互层模型,研究薄互层时频特性与地质特性的对应关系,指导地层旋回方向的预测。

By comparing the short time Fourier transform, continuous wavelet transform, S transform, gener- alized S transform and so on, the authors find that they have common inner product forms, and the difference is that the value of window function. The authors analyze the variation regulation of tr（f） along with the signal frequency, and the resulting question between window and time-frequency resolution to explain the relative superiority of the generalized S transform. Lastly, the generalized S transform are used in four kinds of thin interbed models to study the relation between time-frequency characteristics and geological characteristics, which is helpful to predict the di- rection of stratigraphic cycles.