Scaling-Basis Chirplet Transform

In this study, a novel time-frequency (TF) analysis method, referred to as the scaling-basis chirplet transform (SBCT), is developed by extending the conventional chirplet transform. This method includes a replacement kernel function that can vary the chirp rate with frequency and time by scaling the TF basis at and around the corresponding time center. This enables the corresponding chirplets to accurately match the targeted slopes for every trajectory of a multicomponent signal and within any window length. Therefore, the TF representation obtained via the SBCT can achieve significantly higher energy concentrations even for multicomponent signals with close-spaced frequencies and high levels of background noise. The effectiveness of the proposed SBCT approach was demonstrated by analyzing a numerical multicomponent signal and a vibration signal obtained from a gearbox test rig. Both numerical and experimental results showed that the SBCT can satisfactorily handle multicomponent signals with nonlinear frequency trajectories, close-spaced frequencies, and noisy backgrounds, demonstrating its superiority.