Passive acoustic sensing is a cost-effective solution for monitoring moving targets such as vessels and aircraft, but its performance is hindered by complex propagation effects like multi-path reflections and motion-induced artefacts. Existing filtering techniques do not properly incorporate the characteristics of the environment or account for variability in medium properties, limiting their effectiveness in separating source and reflection components. This paper proposes a method for separating target signals from their reflections in a spectrogram. Temporal filtering is applied to cepstral coefficients using an adaptive band-stop filter, which dynamically adjusts its bandwidth based on the relative intensity of the quefrency components. The method improved the signal-to-noise ratio (SNR) and log-spectral distance (LSD) across velocities ranging from 10 to 100 metres per second in aircraft noise with simulated motion. It also enhanced the performance of ship-type classification in underwater tasks by 2.28 and 2.62 Matthews Correlation Coefficient percentage points for the DeepShip and VTUAD v2 datasets, respectively. These results demonstrate the potential of the proposed pipeline to improve acoustic target classification and time-delay estimation in multi-path environments, with future work aimed at amplitude preservation and multi-sensor applications.