It is well known that when there is a relative motion between the transmitter (source) and receiver, a Doppler shift is observed in the spectral content of the received signal. In this paper, we investigate a scenario where the source signal itself has an innate spectral non-stationarity in addition to the non-stationarity introduced by the source motion relative to the receiver. Using only a single microphone recording, we show that these two kinds of non-stationarities are distinguishable and propose a method of separating them. Towards this, we propose a novel scheme of simulating the signal from a source traversing an arbitrary trajectory. The proposed simulation mechanism employs band-limited interpolation and nonuniform sampling to incorporate an acoustic source generating an arbitrary band-limited signal and moving along an arbitrary trajectory.