Used for centuries in the clinical practice, audible percussion is a method of eliciting sounds by tapping various areas of the human body either by finger tips or by a percussion hammer. Despite its advantages, pulmonary diagnostics by percussion is still highly subjective, depends on the physician's skills, and requires quiet surroundings. Automation of this well-established technique could help amplify its existing merits while removing the above drawbacks. In this work, clinical percussion signals from normal volunteers are decomposed into a sum of exponentially damped sinusoids (EDS) whose parameters are determined using the Matrix Pencil Method. Some EDS represent transient oscillation modes of the thorax/abdomen excited by the percussion event, while others are associated with the noise. It is demonstrated that relatively few EDS are usually enough to accurately reconstruct the original signal. It is shown that combining the frequency and damping parameters of these most significant EDS allows for efficient classification of percussion signals into the two main types historically known as "resonant" and "tympanic." This classification ability can provide a basis for the automated objective diagnostics of various pulmonary pathologies including pneumothorax. The algorithm can be implemented on an embedded platform for the battlefield and other emergency applications.