  We present the time-frequency analysis results based on the Hilbert-Huang
transform (HHT) for the evolution of a 4-Hz low-frequency quasi-periodic
oscillation (LFQPO) around the black hole X-ray binary XTE J1550-564. The
origin of LFQPOs is still debated. To understand the cause of the peak
broadening, we utilized a recently developed time-frequency analysis, HHT, for
tracking the evolution of the 4-Hz LFQPO from XTE J1550 564. By adaptively
decomposing the ~4-Hz oscillatory component from the light curve and acquiring
its instantaneous frequency, the Hilbert spectrum illustrates that the LFQPO is
composed of a series of intermittent oscillations appearing occasionally
between 3 Hz and 5 Hz. We further characterized this intermittency by computing
the confidence limits of the instantaneous amplitudes of the intermittent
oscillations, and constructed both the distributions of the QPO's high and low
amplitude durations, which are the time intervals with and without significant
~4-Hz oscillations, respectively. The mean high amplitude duration is 1.45 s
and 90% of the oscillation segments have lifetimes below 3.1 s. The mean low
amplitude duration is 0.42 s and 90% of these segments are shorter than 0.73 s.
In addition, these intermittent oscillations exhibit a correlation between the
oscillation's rms amplitude and mean count rate. This correlation could be
analogous to the linear rms-flux relation found in the 4-Hz LFQPO through
Fourier analysis. We conclude that the LFQPO peak in the power spectrum is
broadened owing to intermittent oscillations with varying frequencies, which
could be explained by using the Lense-Thirring precession model.
