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Nonstationary random processes having a frequency modulated form often arise in the physical world, e.g., in acoustics as the Doppler effect and in vehicle motion over rough terrain as the height profile encountered by the vehicle as it accelerates over the surface. In this paper we propose a model to describe the generation of such processes. The model uses the notion of a 'spatial' shaping filter, and by means of a transformation yields a variable filter in the time domain, so allowing the definition of the evolutionary spectral density for the process. An application is given to demonstrate how the method may be used to predict the evolutionary spectral density as perceived by an observer due to a moving acoustic source emitting a stationary random signal. Other applications and uses of the technique are briefly described.