  Low-frequency quasi-periodic oscillations (LFQPOs) are commonly observed in
X-ray light curves of black hole X-ray binaries (BHXRBs); however, their origin
remains a topic of debate. In order to thoroughly investigate variations in
spectral properties on the QPO timescale, we utilized the Hilbert-Huang
transform technique to conduct phase-resolved spectroscopy across a broad
energy band for LFQPOs in the newly discovered BHXRB Swift J1727.8-1613. This
is achieved through quasi-simultaneous observations from Neutron star Interior
Composition ExploreR (NICER), Nuclear Spectroscopic Telescope ARray (NuSTAR),
and Hard X-ray Modulation Telescope (Insight-HXMT). Our analysis reveals that
both the non-thermal and disk-blackbody components exhibit variations on the
QPO timescale, with the former dominating the QPO variability. For the spectral
parameters, we observe modulation of the disk temperature, spectral indices,
and reflection fraction with the QPO phase with high statistical significance
(>5\sigma). Notably, the variation in the disk temperature is found to precede
the variations in the non-thermal and disk fluxes by ~0.4-0.5 QPO cycles. We
suggest that these findings offer further evidence that the type-C QPO
variability is a result of geometric effects of the accretion flow.
