An innovative approach is introduced in this study for optimizing power distribution within a hybrid energy storage system, which encompasses batteries and supercapacitors. The method involves utilizing an adaptive wavelet technique within the energy management system dedicated to the EV. This technique customizes the wavelet decomposition level based on the supercapacitor's state of charge. As a result, optimal power sharing between the two real sources incorporated in a small-scale EV emulator is achieved. Notably, the approach adjusts the wavelet decomposition level during transient high peaks and when the supercapacitor has high reserves to alleviate battery workload. Through experimental validation and comparative analysis with three other frequency-based techniques, it is demonstrated that the adaptive wavelet control strategy significantly extends battery lifetime. This extension is achieved by reducing the root mean square (RMS) current by 34 % compared to fixed cut-off frequency approaches. Consequently, this minimizes losses and safeguards the battery from high peaks, resulting in a substantial decrease of 44.53 %. These results underscore the substantial potential of the adaptive wavelet approach as a suitable solution for effective energy management in hybrid electric vehicles.