Extraction of Periodic Signal Without External Reference by Time-Domain Average Scanning

A novel signal-analysis technique that is capable of extracting periodic signals from noisy discrete-time observations without an additional external reference is presented. It is based on a derived formulation estimating the maximally allowable synchronous error for a given attenuation threshold after the time-domain averaging. First, a continuous signal is reconstructed from the discrete samples by using cubic-spline interpolation. Second, the region that the signal fundamental frequency may lie in is finely discretized, resulting in a number of candidates of the fundamental-frequency estimate. Third, for each candidate, the continuous signal is synchronously sampled, and the resultant discrete sequence is processed with the time-domain average. Such an operation of repeated sampling and averaging is referred to as scanning. Finally, the obtained series of average waveforms and their amplitude spectra are depicted as two gray images to visualize the computational results, and the waveforms and spectra of interest are picked out for further analysis. Examples are given to confirm the validity of the approach to diagnose machine faults under complicated conditions.