Neural signals encode information through oscillatory and transient components. The transient component captures rapid, non-rhythmic changes in response to internal or external events, while the oscillatory component reflects rhythmic patterns critical for processing sensation, action, and cognition. Current spectral and time-domain methods often struggle to distinguish the two components, particularly under sharp transitions, leading to interference and spectral leakage. This study introduces a novel adaptive smoothing algorithm that isolates oscillatory and transient components by dynamically up-sampling signal regions with abrupt changes. The approach leverages Euclidean distance-based thresholds to refine sampling and applies customized smoothing techniques, preserving transient details while minimizing interference. Tested on both synthetic and recorded local field potential data, the algorithm outperformed conventional methods in handling steep signal transitions, as demonstrated by lower mean-square error and improved spectral separation. Our findings highlight the algorithm's potential to enhance neural signal analysis by more accurately separating components, paving the way for more precise characterization of neural dynamics in research and clinical applications.