  We propose a method based on the Hilbert-Huang transform (HHT) to recover the
high-energy waveform of low-frequency quasi-periodic oscillations (LFQPOs).
Based on the method, we successfully obtain the modulation of the phase-folded
light curve above 170 keV using the QPO phase reconstructed at lower energies
in MAXI J1535-571 with Insight-HXMT observations. A comprehensive simulation
study is conducted to demonstrate that such modulation indeed originates from
the QPO. Thus the highest energies turn out to significantly exceed the upper
limit of ~100 keV for QPOs reported previously using the Fourier method,
marking the first opportunity to study QPO properties above 100 keV in this
source. Detailed analyses of these high-energy QPO profiles reveal different
QPO properties between the 30-100 keV and 100-200 keV energy ranges: the phase
lag remains relatively stable, and the amplitude slightly increases below ~100
keV, whereas above this threshold, soft phase lags and a decrease in amplitude
are observed. Given the reports of a hard tail detection in broad spectroscopy,
we propose that the newly discovered QPO properties above 100 keV are dominated
by the hard tail component, possibly stemming from a relativistic jet. Our
findings also indicate a strong correlation between the QPOs originating from
the jet and corona, supporting the scenario of jet-corona coupling precssion.
We emphasize that our proposed HHT-based method can serve as an efficient
manner in expanding the high energy band for studying QPOs, thereby enhancing
our understanding of their origin.
