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Digital zero phase start (DZPS) (Buch B., US patent 6,191,906, 2001) is a method used in timing recovery for data storage systems to jump-start the acquisition process. The DZPS sums readback signal samples and uses the arctan function. We propose a simplified DZPS, which only averages the readback signal samples and the arctan function operation can be omitted. We investigate the statistics of the two methods and find that the simplified DZPS degrades the phase estimate mean square error negligibly.