自适应最稀疏时频分析方法的分解能力研究

Research on the Decomposing Ability of the Adaptive and Sparsest Time-Frequency Analysis Method

自适应最稀疏时频分析(adaptive and sparsest time-frequency analysis,ASTFA)方法将信号分解转化为最优化问题,在优化的过程中实现信号的自适应分解.为了研究ASTFA的分解能力,在定义分解能力评价指标(Evaluation Index of Decomposition Capacity,EIDC)的基础上,以双谐波分量合成信号模型来研究幅值比、频率比、初始相位差对ASTFA的影响.同时,将ASTFA方法与经验模态分解(Empirical Mode Decomposition,EMD)、局部特征尺度分解(Local Characteristic-scale Decomposition,LCD)进行对比分析.研究结果表明,ASTFA方法的分解能力基本不受幅值比的影响,可分解的极限频率比较大,不受初始相位差的影响,该方法的分解能力具有明显的优越性.

The signal decomposition is translated into optimization problem in the adaptive and sparsest time--frequency analysis （ASTFA） method, and the signal can be decomposed adaptively in the optimization. In order to research the ASTFA decomposition capability, based on the evaluation index of decomposition capacity （EIDC）, this paper studied the effect of amplitude ratio, the frequency ratio and initial phase difference by using the decomposition model with the double harmonic component synthetic signal. And then, the ASTFA was compared with the Empirical Mode Decomposition （EMD） and Local Characteristic-scale Decomposition （LCD）. The results show that the decomposition capacity of the ASTFA is not influenced by the amplitude ratio or the initial phase difference, and the decomposed ultimate frequency ratio is larger. The decomposition capacity of the ASTFA method has the obvious superiority.