The analysis of acoustic data from the ocean is a valuable tool to study free ranging cetaceans and anthropogenic noise. Due to the typically large volume of acquired data, there is a demand for automated analysis techniques. Many cetaceans produce acoustic pulses (echolocation clicks) with a pulse repetition interval (PRI) remaining nearly constant over several pulses. Analyzing these pulse trains is challenging because they are often interleaved. This article presents an algorithm that estimates a pulse's PRI with respect to neighboring pulses. It includes a deinterleaving step that operates via a spectral dissimilarity metric. The sperm whale (SW) produces trains with PRIs between 0.5 and 2 s. As a validation, the algorithm was used for the PRI-based identification of SW click trains with data from the NEMO-ONDE observatory that contained other pulsed sounds, mainly from ship propellers. Separation of files containing SW clicks with a medium and high signal to noise ratio from files containing other pulsed sounds gave an area under the receiver operating characteristic curve value of 0.96. This study demonstrates that PRI can be used for the automated identification of SW clicks and that deinterleaving via spectral dissimilarity contributes to algorithm performance.