Timing jitter performance in binary optical preamplifier direct detection system is investigated through both the analytical method and computer simulation method. The presented analytical method is based on the moment generating function (MGF) and has taken into account the influence of optical filter on the optical pulse shape. It can be used to optimize the timing jitter performance for linear clock extraction scheme for any type of optical filter and narrow bandpass electrical filter. The presented computer simulation method is capable of dealing with any nonlinear clock extraction scheme and also the impact of laser phase noise on timing jitter performance.