Time–frequency analysis (TFA) facilitates the extraction of instantaneous frequency (IF) features from non-stationary signals. Transient Extraction Transform (TET) produces highly concentrated time–frequency representations (TFRs) for pulse-like fault vibration signals. Nevertheless, in noisy environments characterized by strong impulsive-like infinite-variance processes with a low characteristic exponent α, the performance of TET degrades significantly. First, an adaptive fractional-order low-order statistical function (AFLOF) is defined, which adaptively determines optimal parameter values based on noise impulse level. Subsequently, a robust transient extraction transform (RTET) based on AFLOF is proposed to accommodate various α-stable distribution environments defined by characteristic metrics, thereby facilitating the efficient acquisition of time–frequency features from rapidly varying signals. To mitigate the blurring effects faced by conventional TET algorithms in linear TFA-like scenarios, a robust generalized instantaneous extraction transform (RGTET) is further constructed. The computational framework of RGTET is rigorously derived, along with its corresponding inverse transform expression. Compared with existing methods, RGTET demonstrates superior adaptive performance in parameter adaptation. Finally, the proposed methods are applied to analyze pulse-like mechanical fault vibration signals and conduct time–frequency analysis of continuous signals under complex background noise conditions. The results demonstrate the robustness and adaptability of the proposed RTET and RGTET methods.
Long et al. (Fri,) studied this question.