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The first arrival time of seismic P- and S- waves affects the determination of the beginning of an earthquake by the Earthquake Early Warning System for High-speed Rail (HSREEWs). Accordingly, we propose an approach to picking P- and S-waves arrival time for HSREEWs. This approach can treat the continuous seismic signals in real-time without prior knowledge of whether an earthquake occurs. Firstly, we replace the fixed time window of the S transform (ST) with the dynamic window of the generalized S transform (GST) to make the necessary time of signal processing more flexible. Meanwhile, the GST extends the sequential signal to the time-frequency domain (TF), and combines the TF polarization to construct four three-component polarization filters. Accordingly, the P-wave and S-wave can be separated from the seismic waveform by those filters, which effectively avoids the phenomenon that the S-wave phase is difficult to determine because of the interference of S-wave overlapping in the coda region. Secondly, based on the instantaneous frequency of seismic signal, we construct a new STA/LTA (GSPA-STA/LTA) with the characteristic function (CF) of constrained TF spectrum to pick the first arrivals of the P- and S-waves, and provide the corresponding automatic picking algorithm. Finally, we analyze 504 seismic events larger than Ms40 near the Japanese Tohoku Shinkansen to comprehensively verify the effectiveness of our approach. Since the P-wave and S-wave are first separated, the subsequent process just has to identify the first arrival times of their respective components. The approach has a good practical value in maintaining the safe operation of high-speed rail under earthquake, which meets the industry demands for speed, scale and accuracy in HSREEWs. • The proposed generalized S-transform (GST) has better time resolution and better frequency resolution. • Four three-component polarization filters are constructed for separating the P- and S-waves in time-frequency domain. • A new STA/LTA with constrained time-frequency spectrum is designed for picking the arrival times. • The proposed approach has better performance on picking the arrival times of the P- and S-waves than revised STA/LTA, VAR-AIC, PphasePicker et al. [ABSTRACT FROM AUTHOR]