The response of linear systems to non-Gaussian noise

A fairly broad class of problems deals with the way certain properties of noise are altered on passage through a linear system. Fig. l defines these properties. If any n instants of time are chosen and if boundary value problems of the zero crossing type are omitted, the specification of the n dimensional probability distribution yields the most complete statistical information. Very often, however, this information is difficult or impossible to find and it is useful to obtain properties (2) and (3) of Fig. 1 without actually knowing property (1). Briefly, an nth order random process is defined by no more than an n dimensional probability distribution. Given a higher order distribution, it can be reduced to order n. The example in Fig. 1 shows how, for a 2nd degree (a Markoff) process, a trivariate form can be expressed in terms of bivariate and lower forms. A stationary process is one whose statistical properties do not depend on the choice of time reference.