(color online) Detecting weak and shortly-lived signal from strong noise background. (a) Pure noise time sequence , D = 0.5 (red curve), and signal in the time interval ( to ) with , ω = 0.02, A = 0.006 (green curve). (b) Time sequence of weak signal contaminated with strong noise with and given in panel (a), from which one can hardly find any trace of . (c) computed by Eq. (1) for A = 0.006 with finite time length . Note, signal exists in time interval , which cannot be observed in the plots. (d) The same as panel (c) with longer signal interval, . during the signal interval is considerably above that in the rest times. Now signal in interval with can be evidently extracted.