  The high-mass X-ray binary (HMXB) SMC X-1 exhibits a superorbital modulation
with a dramatically varying period ranging between ~40 d and ~60 d. This
research studies the time-frequency properties of the superorbital modulation
of SMC X-1 based on the observations made by the All-Sky Monitor (ASM) onboard
the Rossi X-ray Timing Explorer (RXTE).We analyzed the entire ASM database
collected since 1996. The Hilbert-Huang Transform (HHT), developed for
non-stationary and nonlinear time series analysis, was adopted to derive the
instantaneous superorbital frequency. The resultant Hilbert spectrum is
consistent with the dynamic power spectrum while it shows more detailed
information in both the time and frequency domains. The RXTE observations
manifest that the superorbital modulation period was mostly betweenn ~50 d and
~65 d, whenas it changed to ~45 d around MJD 50,800 and MJD 54,000. Our
analysis further indicates that the instantaneous frequency changed in a time
scale of hundreds of days between ~MJD 51,500 and ~MJD 53,500. Based on the
instantaneous phase defined by HHT, we folded the ASM light curve to derive a
superorbital profile, from which an asymmetric feature and a low state with
barely any X-ray emissions (lasting for ~0.3 cycles) were observed. We also
calculated the correlation between the mean period and the amplitude of the
superorbital modulation. The result is similar to the recently discovered
relationship between the superorbital cycle length and the mean X-ray flux for
Her X-1.
