Source-filter models for sound resynthesis are useful in applications including compression of audio data and restoration of noisy recordings. Driven by actual recordings of sounding objects, resynthesis methods require system identification and excitation source estimation. Such methods may be entirely data-driven, but they may also incorporate a priori knowledge of systems or excitations. This paper proposes a method of estimating the excitation of percussively struck resonant objects from sound recordings, constraining the excitation to be time-limited. The constraint serves to use prior knowledge of the short duration of the excitations of percussive sounds, improving estimation when compared to other methods of unconstrained estimation and inverse filtering. Evaluated examples and simulations demonstrate the proposed method's robustness to noise and applicability to the analysis and resynthesis of acoustic recordings.