Signal detection theory, a fundamental concept in various scientific disciplines, involves mandatory measuring of the signal features. This theory finds applications in telecommunications, radar technology, medical devices, automation and process control, geophysical research, biometric systems, and security systems, emphasizing its broad significance. Likewise, drone detection in the radio-frequency domain is necessary for signal detection and ensures efficient and reliable communication, surveillance, and security. The recent conflict between Russia and Ukraine has underscored the crucial role of drones in modern warfare. Our research can improve the detection of any malicious drones that pose a threat, thereby underlining the significance of the proposed methodology in modern electronic warfare. This is a specialized approach to drone signal detection based on two-stage classification with two key components: a method based on spectrogram energy detection and deep learning classification. Energy detection on the spectrograms is particularly effective when the signal's energy characteristics differ significantly from the surrounding noise. The practical applicability of our proposed method was evaluated using the publicly available VTI_DroneSET dataset, which contains a diverse range of signals from three types of drones. Furthermore, we conducted tests with the VTI_DroneUSRP dataset and signals from the NI-USRP-2954 receiver, demonstrating the effectiveness and practicality of the proposed method in real situations. The successful detection and identification of Wi-Fi, Bluetooth, and drone signals in both ISM frequency bands were performed, proving the method's reliability. The proposed approach improved execution times and energy savings, indicating that applying the energy detector on the spectrograms in a two-stage classification significantly enhances the performance of ADRO applications for real-time drone detection. Furthermore, we conducted a comparative analysis of different deep learning algorithms at the outset of two-stage classification, which is a potential basis for adopting this approach.