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In this paper, we model a spatially varying channel where a source is moving along a random trajectory with respect to a fixed re- ceiver. The aim is to compute the power spectral density corre- sponding to the channel impulse response as a function of tempo- ral and spatial frequencies. The trajectory of the source follows an autoregressive model where the poles of the system control the smoothness of the path. Theoretical results are presented for the AR2 case and generalized to any ARn systems. Simulations results are shown and compared to the presented theory. The stochas- tic plenacoustic function analyzed in this paper also models time- varying channels governed by the wave equation, like they appear in acoustic echo cancellation or ultra wide band communication channels.