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The separation of pathological discontinuous adventitious sounds (DAS) from vesicular sounds (VS) is of great importance to the analysis of lung sounds, since DAS are related to certain pulmonary pathologies. An automated way of revealing the diagnostic character of DAS by isolating them from VS, based on their nonstationarity, is presented in this paper. The proposed algorithm combines multiresolution analysis with hard thresholding in order to compose a wavelet transform-based stationary-nonstationary filter (WTST-NST). Applying the WTST-NST filter to fine/coarse crackles and squawks, selected from three lung sound databases, the coherent structure of DAS is revealed and they are separated from VS. When compared to other separation tools, the WTST-NST filter performed more accurately, objectively, and with lower computational cost. Due to its simple implementation it can easily be used in clinical medicine.