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This paper addresses the source-filter separation problem in the context of causal/anticausal linear filter model of voice production. An algorithm based on standard signal processing tools is proposed for the class of quasi-periodic signals (voiced sounds with quasi-stationary pitch). At first, a one-period frame of an equivalent stationary infinitely periodic signal is built. A particular attention is given to the problems of windowing and temporal aliasing. Secondly, an exact pole decomposition of this signal is computed within the class of T0-periodic signals. Finally, the glottal closure instant (GCI) and the causal-anticausal factorization of the initial frame are jointly estimated from the latter decomposition. The performance of this algorithm on synthetic signals is demonstrated and the performance on real speech is discussed. In conclusion, application of this new algorithm in a complete voice analysis-synthesis system is discussed.