Distribution of the Sum of Clipped Waveforms in Terms of the Multivariate Input-Amplitude Distribution

For an arbitrary multivariate input-amplitude distribution, it is shown that the density of the sum of clipped versions of the input waveforms is linearly related to the sums of the clipped moments of each order. This linear dependence implies that the vector of clipped-moment sums must lie within an N-dimensional tetrahedral restriction region in a moment space and provides a necessary condition on the multivariate input distribution. Previous derivations of the density and moments of the sum of clipped waveforms were restricted to the case in which the components of the input vector were statistically independent.