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Narrow-band systems and Gaussianity

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The approach to Gaussianity of the output y(t) of a narrow-band 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 functions of y(t) and of a suitable normal process, a realistic bound B on the difference F(y) -- G(y) is determined, and it is shown that B \rightarrow 0 as the bandwidth \omega _o of the system tends to zero. In the special case of the shot noise process begin{equation} y(t) = sum_i h(t - t_i) end{equation} it is shown that begin{equation} mid F(y) - G(y) mid < (omega_o/lambda) frac{1}{2} end{equation} where \lambda _i is the average density of the Poisson points t_i .

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IEEE Transactions on Information Theory  (Volume:18 ,  Issue: 1 )