  Gamma-ray bursts (GRBs) have variable lightcurves. Although most models
attribute the observed variability to one physical origin (e.g. central engine
activity, clumpy circumburst medium, relativistic turbulence), some models
invoke two physically distinct variability components. We develop a method,
namely, the stepwise filter correlation (SFC) method, to decompose the
variability components in a GRB lightcurve. Based on a low-pass filter
technique, we progressively filter the high frequency signals from the
lightcurve, and then perform a correlation analysis between each adjunct pair
of filtered lightcurves. Our simulations suggest that if a mock lightcurve
contains a slow variability component superposed on a rapidly varying time
sequence, the correlation coefficient as a function of the filter frequency
would display a prominent dip feature around the frequency of the slow
component. Through simulations, we demonstrate that this method can identify
significant clustering structures of a lightcurve in the frequency domain, and
proved that it can catch superposed signals that are otherwise not easy to
retrieve based on other methods (e.g. the power density spectrum analysis
method). We apply this method to 266 BATSE bright GRBs. We find that the
majority of the bursts have clear evidence of such a superposition effect. We
perform a statistical analysis of the identified variability components, and
discuss the implications for GRB physics.
