  The high-mass X-ray binary SMC X-1 is an eclipsing binary with an orbital
period of 3.89 d. This system exhibits a superorbital modulation with a period
varying between ~40 d and ~65 d. The instantaneous frequency and the
corresponding phase of the superorbital modulation can be obtained by a
recently developed time-frequency analysis technique, the Hilbert-Huang
transform (HHT). We present a phase-resolved analysis of both the spectra and
the orbital profiles with the superorbital phase derived from the HHT. The
X-ray spectra observed by the Proportional Counter Array onboard the Rossi
X-ray Timing Explorer are fitted well by a blackbody plus a Comptonized
component. The plasma optical depth, which is a good indicator of the
distribution of material along the line of sight, is significantly
anti-correlated with the flux detected at 2.5-25 keV. However, the relationship
between the plasma optical depth and the equivalent width of the iron line is
not monotonic: there is no significant correlation for fluxes higher than ~35
mCrab but clear positive correlation when the intensity is lower than ~20
mCrab. This indicates that the iron line production is dominated by different
regions of this binary system in different superorbital phases. To study the
dependence of the orbital profile on the superorbital phase, we obtained the
eclipse profiles by folding the All Sky Monitor light curve with the orbital
period for different superorbital states. A dip feature, similar to the
pre-eclipse dip in Her X-1, lying at orbital phase ~0.6-0.85, was discovered
during the superorbital transition state. This indicates that the accretion
disk has a bulge that absorbs considerable X-ray emission in the stream-disk
interaction region. The dip width is anti-correlated with the flux, and this
relation can be interpreted by the precessing tilted accretion disk scenario.
