We demonstrate a cavity ringdown spectrometer that affords a frequency resolution higher than the conventional limit imposed by the bandwidth of a pulsed laser source. A Fabry-Perot etalon at the exit of a ringdown cavity disperses the frequency components of a broadband ringdown signal spatially, permitting a narrow-linewidth spectral measurement based on single-exponential decay signals. A proof of principle experiment is presented with the P(9) transition of the [50]-10(0)0(0) band of C2H2 This technique is expected to be useful for in situ monitoring molecular concentration.