An approach is presented to evaluate the impulse response of an annular piston, which is mounted in an infinite planar rigid baffle. Since the impulse response is defined to be the time-dependent force on the ring, which results from an impulsive velocity of the ring, the impulse response and radiation impedance of the ring are a Fourier transform pair. A closed-form expression for the impulse response of a ring of any size is developed from the well-known double surface integral representation of the radiation impedance. Various integral and asymptotic expressions for the radiation impedance of the ring are derived from the impulse response, and the results are shown to be in agreement with those of earlier investigators. Several numerical results are also presented to show the effect of changing the ring size on the impulse response, and on the radiation resistance and reactance of the ring.