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Although clinical percussion remains one of the most widespread traditional noninvasive methods for diagnosing pulmonary disease, the available analysis of physical characteristics of the percussion sound using modern signal processing techniques is still quite limited. The majority of existing literature on the subject reports either time-domain or spectral analysis methods. However, Fourier analysis, which represents the signal as a sum of infinite periodic harmonics, is not naturally suited for decomposition of short and aperiodic percussion signals. Broadening of the spectral peaks due to damping leads to their overlapping and masking of the lower amplitude peaks, which could be important for the fine-level signal classification. In this study, an attempt is made to automatically decompose percussion signals into a sum of exponentially damped harmonics, which in this case form a more natural basis than Fourier harmonics and thus allow for a more robust representation of the signal in the parametric space. The damped harmonic decomposition of percussion signals recorded on healthy volunteers in clinical setting is performed using the matrix pencil method, which proves to be quite robust in the presence of noise and well suited for the task.