To accurately restore interdecadal oscillations from the length of day variation ({Delta}LOD) and the polar motion (PM), we propose a normal time-frequency transform (NTFT) combing with curve fitting scheme. Compared with the NTFT, the combined NTFT with a boundary extreme point mirror-image-symmetric extension (BEPME) process, and singular spectrum analysis (SSA) in some simulated tests, the superiority and reliability of this new scheme have been confirmed; and we further verified the validity of it in a mature case analysis from the Earths free oscillation modes 0S0 and 1S0. After then, we use it to restore the ~5.9yr oscillation (referred to as SYO) and ~8.5yr oscillation (referred to as EYO) from the {Delta}LOD and the PM records. Our results reconfirm that the SYO and EYO in the {Delta}LOD (and PM) have no stable damping trend (which is different from results in some previous studies), and for the first time, we find that the SYOs (and EYOs) contained in the {Delta}LOD and the PM show very good consistency. Such consistency demonstrates that the SYOs/EYOs in the {Delta}LOD and the PM must come from the same source. As the external excitation sources of the Earth rotation contain no such oscillations, we suggest that core motions are possible sources.
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