Singular Spectrum Analysis-Based Hierarchical Multiresolution Analysis with Exploitation of Frequency Selectivities of Desirable Grouped Functions

Abstract

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.