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The study proposes a novel time-frequency analysis technique, titled time-frequency synchroextracting transform which enhances the accuracy of synchroextracting transform. The synchroextracting transform is a powerful postprocessing method that sharpens the energy distribution of spectrogram. However, its limitation is the sole use of time or frequency factors that cannot accurately portray signals containing both 'slowvarying' and 'fast-changing' components. The proposed method applies the synchroextracting procedure in both time and frequency dimensions to improve the energy concentration. A fast Fourier transform--based algorithm is also provided for efficient implementation. The proposed method is validated via numerical and empirical data. Compared with advanced methods including synchrosqueezing transform and synchroextracting transform, the proposed method is suitable to analyse wider range of signals and has better noise robustness than the original synchroextracting transform.

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Speed estimation is crucial to monitor the conditions of rotational machinery. Most speed measurements are carried out by installing encoders or tachometers inside the machines. In many cases, such method could be cumbersome or even inaccessible. This paper proposes a vibration-based speed estimation method. The vibration sensors are often cheaper and easier to install than angle encoders. In the proposed method, the continuous wavelet transform (CWT) is used as a preprocessing technique to extract the signal of importance. Then, the time-varying autoregressive (TAR) model is applied to analyze the rotational frequency. Additionally, the paper presents a fast algorithm for implementation. The proposed method is validated by both synthetic and empirical data.