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When radar receivers adopt digital channelization, it is prone to generating a cross-channel split signal, the rabbit ear effect, and a transition band repeated signal, leading to errors in radar signal sorting or identification. The pulse-splitting model and detection method proposed in this paper can model split pulses and identify them in radar pulse streams, facilitating the merging of split pulses to enhance sorting and identification performance. Firstly, the mechanism of splitting pulse generation is deeply analyzed, and the splitting site theory is proposed. Then, the split pulse signal model and the split pulse number statistical model based on geometric distribution are constructed, which are used to guide the construction of simulation data of split pulse flow with different characteristics. Furthermore, a time-domain convergence degree (TCD) index is proposed to characterize the pulse split phenomenon. At the same time, in order to avoid a large number of threshold searching problems in pulse-splitting detection, an empirical formula for the pulse-splitting detection threshold based on the TCD is given to quickly determine whether there is a pulse train split problem. The selected measured radar pulse stream is verified to follow a geometric distribution at a significance level of 0.05. The proposed method achieved a detection accuracy of at least 99.55% on the simulation dataset and at least 95.68% on the experimental dataset, validating the rationality of pulse-splitting modeling and the effectiveness of the detection method.