Narrow-band systems and Gaussianity
- 1 January 1972
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 18 (1) , 20-27
- https://doi.org/10.1109/tit.1972.1054731
Abstract
The approach to Gaussianity of the outputy(t)of a narrow-band systemh(t)is investigated. It is assumed that the inputx(t)is ana-dependent process, in the sense that the random variablesx(t)andx(t + u)are independent foru > a. WithF(y)andG(y)the distribution functions ofy(t)and of a suitable normal process, a realistic boundBon the differenceF(y) -- G(y)is determined, and it is shown thatB \rightarrow 0as the bandwidth\omega_oof 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_iis the average density of the Poisson pointst_i.Keywords
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