Theory, validation, and improvement of four enhancement algorithms for repetitive impulses

Analyzing vibration of rotating machinery signals is a popular methodology derived on the potent tools provided by cyclostationary process theory. Among them, the autocorrelation function (ACF), the Fourier transform (FT), the short-time Fourier transform (STFT), and the time synchronous average (TSA) are widely used for enhancing and analyze random cyclostationary components, i.e., repetitive impulses. This paper aims to thoroughly investigate these techniques through a comprehensive scientific research process. Initially, theoretical analyses are conducted to discuss their noise suppression principles, on the foundation of mean and variance analysis. Results indicate that for Gaussian random noise, the variance of the noise linked to the ACF, the FT, and TSA almost decreases linearly with signal length, while the noise variance of the short-time Fourier transform does so with window length. Therefore, longer signal lengths for the ACF, the FT, and the TSA, or extended window lengths for the STFT, improve their denoising performance. Subsequently, a series of simulated signals are generated to validate these findings, complemented by public datasets for further verification. Finally, the paper discusses and concludes with enhancement approaches derived from these four methodologies.