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In recent years there has been a growing interest in sparse representation of signals based on overcomplete dictionaries. Selecting few atoms that best match the signal structure, the signal is described by linear combination of these atoms. In this paper, we propose a novel overcomplete dictionary design algorithm for sparse representation of piecewise stationary signals. An effective and easy-to-use overcomplete dictionary is constructed in accordance with the parametric autocorrelation function model of piecewise stationary processes. Furthermore, a sparse decomposition algorithm in terms of nonlinear approximation is designed to obtain sparse representation of piecewise stationary signals, which has lower computational complexity and better practicability than the conventional sparse decomposition algorithms. The experimental results demonstrate that the proposed method avails for higher sparsiry of signal representation and better reconstruction performance than sparse representation of signals based on overcomplete DCT dictionary.