In recent years, the rapid growth of the Internet of Things technologies and the widespread adoption of 5G wireless networks have led to an exponential increase in the number of radiation devices operating in complex electromagnetic environments. A key challenge in managing and securing these devices is accurate identification and classification. To address this challenge, specific emitter identification techniques have emerged as a promising solution that aims to provide reliable and efficient means of identifying individual radiation devices in a unified and standardized manner. This research proposes an approach that leverages transient energy spectrum analysis using the General Linear Chirplet Transform to extract features from RF devices. A dataset comprising nine RF devices is utilized, with each sample containing 900 attributes and a total of 1080 equally distributed samples across the devices. These features are then used in a classification modeling framework. To overcome the limitations of conventional machine learning methods, we introduce a hybrid deep learning model called the CNN-Bi-GRU for learning the identification of RF devices based on their transient characteristics. The proposed approach provided a 10-fold cross-validation performance with a precision of 99.33%, recall of 99.53%, F1-score of 99.43%, and classification accuracy of 99.17%. The results demonstrate the promising classification performance of the CNN-Bi-GRU approach, indicating its suitability for accurately identifying RF devices based on their transient characteristics and its potential for enhancing device identification and classification in complex wireless environments.