Epochs are instants of significant excitation of vocal-tract system in speech production process. In this paper, we attempt to extract information about epochs from phase spectra of speech signals. The phase spectrum of speech is modelled as the response of an allpass (AP) filter, and the resulting error signal is used for epoch extraction. The parameters of AP model are estimated by imposing sparsity constraints on the error signal. The error signal, thus obtained, exhibits prominent peaks at epoch locations. The epochal candidates obtained from the error signal are refined using a dynamic programming algorithm. The performance of the proposed method is consistent across genders and is comparable with the state-of-the-art methods. © 2015, Springer Science+Business Media New York.