The development of time-frequency analysis techniques allow astronomers to successfully deal with the non-stationary time series that originate from unstable physical mechanisms. We applied a recently developed time-frequency analysis method, the Hilbert-Huang transform (HHT), to two non-stationary phenomena: the superorbital modulation in the high-mass X-ray binary SMC X-1 and the quasi-periodic oscillation (QPO) of the AGN RE J1034+396. From the analysis of SMC X-1, we obtained a Hilbert spectrum that shows more detailed information in both the time and frequency domains. Then, a phase- resolved analysis of both the spectra and the orbital profiles was presented. From the spectral analysis, we noticed that the iron line production is dominated by different regions of this binary system in different superorbital phases. Furthermore, a pre-eclipse dip lying at orbital phase ~ 0.6 - 0.85 was discovered dur- ing the superorbital transition state. We further applied the HHT to analyze the QPO of RE J1034+396. From the Hilbert spectrum and the O - C analysis results, we suggest that it is better to divide the evolu- tion of the QPO into three epochs according to their different periodicities. The correlations between the QPO periods and corresponding uxes were also different in these three epochs. The change in periodicity and the relationships could be interpreted as the change in oscillation mode based on the diskoseismology model.

ABSTRACT
1. NON-STATIONARY PHENOMENA
2. HILBERT-HUANG TRANSFORM
3. SUPERORBITAL MODULATION IN SMC X-1
    3.1. Time-Frequency Analysis
    3.2. Superorbital Phase-resolved Analysis
4. THE QPO IN RE J1034+396
5. SUMMARY & FUTURE WORK
REFERENCES

• Chin-Ping Hu(Graduate Institute of Astronomy, National Central University)
• Yi Chou(Graduate Institute of Astronomy, National Central University)
• Ting-Chang Yang(Graduate Institute of Astronomy, National Central University)
• Yi-Hao Su(Graduate Institute of Astronomy, National Central University)
• Hung-En Hsieh(Graduate Institute of Astronomy, National Central University)
• Ching-Ping Lin(Graduate Institute of Astronomy, National Central University)
• Po-Sheng Chuang(Graduate Institute of Astronomy, National Central University)
• Nai-Hui Liao(Graduate Institute of Astronomy, National Central University)