The high-mass X-ray binary SMC X-1 exhibits a superorbital modulation with a dramatically varying period ranging between similar to 40 days and similar to 60 days. 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 as it shows more detailed information in both the time and frequency domains. The RXTE observations show that the superorbital modulation period was mostly between similar to 50 days and similar to 65 days, whereas it changed to similar to 45 days around MJD 50,800 and MJD 54,000. Our analysis further indicates that the instantaneous frequency changed to a timescale of hundreds of days between similar to MJD 51,500 and similar to 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 similar to 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.
