In radar astronomy, the digital backend and data recording system process and store echo signals in real-time, facilitating the monitoring of near-earth objects such as space debris, satellites, and asteroids. In this paper, a radar astronomy digital backend (RADB), designed for radar astronomy observation and data recording, is proposed. With a sampling rate of 1.12 GSps, the RADB accommodates various analog intermediate frequency (IF) front-ends. In addition to continuously recording echo signals, the RADB has three pulse storage modes and employs an architecture that combines a two-stage decimation (TSD) unit and a decimated pulse detection (DPD) unit. The TSD unit reduces the sampling frequency based on the bandwidth of the signal, after shifting the IF signal to the baseband. Compared to a single-stage decimation, the proposed TSD structure effectively reduces FIR resource consumption without compromising performance. Meanwhile, the DPD unit identifies pulse echo signals and selectively enables the backend to store data only when pulses are detected. This process further reduces the burden on data transmission and storage. Furthermore, the matched filtering pulse detection method in the DPD unit enhances triggering performance, particularly under weak signal conditions. Preliminary performance evaluations in a laboratory demonstrate that the TSD unit reduces data volume by 56 times, while the DPD unit achieves a further reduction of 20 times. Concurrently, a Moon reflection experiment is also conducted at the Yunnan Kunming Electromagnetic Environment Observation and Research Station by using a 29 m antenna. Analysis and processing of stored data validate the effectiveness of the proposed design.