This paper proposes a singular spectrum analysis (SSA)-based hierarchical multiresolution analysis (HMA) with the exploitation of the frequency selectivities of the desirable grouped functions. To perform the HMA, the SSA components are grouped based on the desirable grouped functions. Similar procedures are applied to the sum of the SSA components in a group in the previous level of decomposition. Computer numerical simulation results show that the SSA components in the next level of decomposition are localized within the passband of the sum of the SSA components in the corresponding group in the previous level of decomposition if its intrinsic mode functions (IMFs) or the ideal filters are employed as the desirable grouped functions. Moreover, unlike the empirical mode decomposition (EMD)-based HMA, the total number of the SSA components in each level of decomposition can be chosen.

中文翻译：

---

基于奇异谱分析的分层多分辨率分析，利用所需分组函数的频率选择性

本文提出了一种基于奇异频谱分析 (SSA) 的分层多分辨率分析 (HMA)，利用所需分组函数的频率选择性。为了执行 HMA，SSA 组件根据所需的分组功能进行分组。类似的过程适用于前一个分解级别中组中 SSA 组件的总和。计算机数值模拟结果表明，如果本征模式函数（IMF）或理想滤波器为下一级分解中的 SSA 分量，则下一级分解中的 SSA 分量位于上一级分解中相应组中 SSA 分量之和的通带内。用作理想的分组函数。此外，与基于经验模式分解 (EMD) 的 HMA 不同，