The most crucial transmission components utilized in rotating machinery are gears and bearings. In a gearbox, the bearings support the force acting on the gears. Compound Faults in both the gears and bearings may cause heavy vibration and lead to early failure of components. Despite their importance, these compound faults are rarely studied since the vibration signals of the compound fault system are strongly dominated by noise. This work proposes an intelligent approach to fault identification of a compound gear-bearing system using a novel Bessel kernel-based Time-Frequency Distribution (TFD) called the Bessel transform. The Time-frequency images extracted using the Bessel transform are used as an input to the Convolutional Neural Network (CNN), which classifies the faults. The effectiveness of the proposed approach is validated with a case study, and a testing efficiency of 94% is achieved. Further, the proposed method is compared with the other TFDs and found to be effective.