Investigating vibrations in mechanical transmission systems to detect and identify the causes of abnormal vibrations remains a prominent focus for researchers. Within industrial transmission systems, rolling bearings play a pivotal role. Utilizing the envelope spectrum of vibration signals to diagnose faults in rolling bearings proves highly reliable due to the bearings' mechanical properties. Under constant shaft rotational speed, most envelope analysis methods can accurately identify faults at the characteristic frequency of rolling bearings. However, numerous transmission systems operate at variable rotational speeds due to technological demands and load fluctuations. In such scenarios, the vibration signals of rolling bearings undergo frequency modulation, rendering conventional vibration analysis methods like envelope spectrum analysis ineffective. Time-frequency analysis is a valuable diagnostic tool for identifying faults in rolling bearings under these conditions. Nonetheless, its practical application, particularly with large-scale data, necessitates high-performance computers capable of processing extensive multi-dimensional matrices. To overcome this challenge, this paper introduces a novel tool based on the Synchrosqueezing Transform (SST) and other resampling techniques. The proposed method additionally incorporates advanced techniques for extracting frequency curves from non-stationary signals to detect the fault characteristic frequencies (FCFs) of rolling bearings. The effectiveness of this approach is showcased through both a simulated example and an experimental instance. Furthermore, a comprehensive comparison of the novel method with existing techniques is provided.