Falls among the elderly are a common and serious health risk that can lead to physical injuries and other complications. To promptly detect and respond to fall events, radar-based fall detection systems have gained widespread attention. In this paper, a deep learning model is proposed based on the frequency spectrum of radar signals, called the convolutional bidirectional long short-term memory (CB-LSTM) model. The introduction of the CB-LSTM model enables the fall detection system to capture both temporal sequential and spatial features simultaneously, thereby enhancing the accuracy and reliability of the detection. Extensive comparison experiments demonstrate that our model achieves an accuracy of 98.83% in detecting falls, surpassing other relevant methods currently available. In summary, this study provides effective technical support using the frequency spectrum and deep learning methods to monitor falls among the elderly through the design and experimental validation of a radar-based fall detection system, which has great potential for improving quality of life for the elderly and providing timely rescue measures.