This paper demonstrates that various sound-absorbing/reflective materials or structures can be effectively characterized over a wide band of frequency by the sum of only a few damped harmonic oscillators. This method is physically sound in the sense that each damped harmonic oscillator corresponds to the natural resonance of the impedance boundary as it is numerically advantageous to afford a simple, recursive, efficient, and unconditionally stable boundary algorithm for computational aero-acoustics applications. The time-domain damped-harmonic-oscillator impedance characterization method is finally validated by accurate predictions of reflected pulses from impedance boundaries physically formed of Helmholtz resonators or various exits of a circular pipe.