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In this paper, we propose single-channel speech separation by using a sparse decomposition method. First, the model for the periodic signals with time-varying amplitude is introduced to approximate speech signals. The sparse decomposition is proposed with this signal model and a sparsity measure. The sparsity measure is defined as a sum of the l2 norms of the resultant periodic subsignals to find the shortest path to the approximation. By this penalty of the sparsity, the proposed decomposition extracts significant periodic components from a mixture and has ability of the source estimation for mixtures of periodic signals. In experiments, we apply the proposed decomposition to speech mixtures and demonstrate speech separation with codebooks of the speakers. In additionally, comparison with MaxVQ method that performs separation on the frequency spectrum domain is also demonstrated. Comparing with the MaxVQ, our method is less sensitive to the codebook design and requires less computational costs.