The approach to Gaussianity of the output y(t) of a narrowband system h(t) is investigated. It is assumed that the input x(t) is an a-dependent process in the sense that the random variables x(t) and x(t+u) are independent for u a. With F(y) and G(y) the distribution function of y(t) and of a suitable normal process, a realistic bound B of the difference F(y) - G(y) is determined and it is shown that B approaches 0 as the bandwidth omega sub 0 of the system tends to zero.
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