To address the insufficient extraction accuracy of the traditional discrete Fourier transform method and the low processing speed of the Levenberg-Marquardt (L-M) algorithm in ring-down time extraction, a periodic discrete Fourier transform (PDFT) algorithm is proposed. By applying the Fourier transform to periodic ring-down signals, the common characteristic frequency of the decay signal is extracted from the frequency domain, enabling the direct and highly accurate extraction of the ring-down time constant. By analyzing the relationship among extraction accuracy, fitting rate, and the number of periods, the optimal number of periods is determined to be 20. The accuracy, precision, and fitting rate of the PDFT algorithm are analyzed via simulations, and an ammonia detection system based on cavity ring-down spectroscopy (CRDS) is constructed to experimentally validate the simulation results. Experimental results demonstrate that the PDFT algorithm improves accuracy by a factor of 1.79 and fitting rate by a factor of 6.76 compared to the conventional L-M algorithm. Additionally, Allan deviation analysis reveals a detection limit below 1×10^-9 under optimal integration time. These results highlight the promising potential of the PDFT algorithm for real-time gas sensing in CRDS systems.