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The second-order analysis of the output of a discrete-time nonlinear system described by a truncated Volterra series whose input consists of a sequence of independent random variables (white noise)is considered. The main result consists of an explicit formula for the mean value of the output process in terms of the cumulants of the input and of Volterra kernels. This formula, with suitable modifications, allows the calculation of the output correlation as well as of the continuous and discrete components of the spectral distribution. Several applications are considered, and in particular the Gaussian white noise case is worked out in detail. Finally, the computational aspects of the analysis are discussed with the aim of showing that in several situations closed-form results can be obtained.