基于曲面拟合的时频分解方法及应用

Time-frequency Decomposition Based on Curved Surface Fitting and Its Application

对基于基信号的时频分解法和时频分布级数法的原理进行了分析,在此基础上,提出一种新的时频分解方法。该方法的核心是根据信号特征选定时频聚集性好的基函数作为原信号的扩展函数簇,用基函数的时频分布曲面逐步拟合分解得到残余信号时频分布级数,从而确定基函数的参数值。该方法的曲面拟合过程就是信号结构的匹配过程,与具有较高时频聚集性的基函数结构相似程度较大的信号分量总是先被拟合出来,然后才是与基函数相差较大的噪声分量。基于这一点,用分解出的前几个分量对信号进行重构,可达到非平稳信号噪声抑制的目的。计算机仿真和工程实践证明了该方法的可行性和有效性。

The theory of time-frequency decomposition was analyzed based on elementary functions and the time-frequency distribution series, then a novel time-frequency decomposition algorithm was presented. According to the input signal characteristics, a kind of appropriate elementary function was selected with great concentration in the time frequency （TF） domain, and the input signal was decomposed into a linear combination of these functions. The elementary functions＇ parameters and coefficients were calculated by using elementary function＇s TF curved surface to fit the TFDS of the remained signals after decomposing step by step. The process of curved surface fitting was equal to the process of component matching. The signal dominating elements which have the great resemblance with elementary functions, were fitted out firstly. Repeating the fitting procedure, the residue is the non-stationary noise having great difference from the function. Selecting the fore elements to reconstruct, the noise can be suppressed. The simulation result and engineering experiments indicate that the algorithm is very effective.