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Periodic signal detection methods are widely used in applications including human detection and machinery fault diagnosis. Averaging is one of the most powerful filtering techniques for periodic signals extraction. Time domain synchronous average (TSA) and moving average (MA) are the most commonly used average techniques in engineering. TSA has the advantage at periodic signal detection by depressing noises and asynchronous signal components. MA is effective to remove noises while keeping signal periodicity. However, the TSA signal is not periodic as a measurement signal, and signal spectrum resolution degrades seriously; meanwhile, the MA filters out high-frequency signal components of interests. Detection of periodic signal among noises while keeping signal periodicity and high-frequency signal components become a challenge. To address this problem, time-synchronous moving average (TSMA) method is proposed as an improvement on TSA inspired by MA in this paper. Influences of signal overlap and properties of TSMA are investigated. Furthermore, a practical average times optimization method is given for reference. The correctness of theoretical deviations and effectiveness of the proposed method on periodic signal detection are validated using numerical simulations. At last, the proposed method is validated by an application on fault detection of the gearbox.

Time Domain Synchronous Moving Average and its Application to Gear Fault Detection