3. Gaussian Noise

The stochastic processes of almost exclusive interest in modeling channel noise are the Gaussian processes. Gaussian processes are stochastic processes for which the random variables N(t1), N(t2), . . . , N(tk) are jointly Gaussian for all t1, . . . , tk and all k > 0. Today we start by giving a more complete discussion of jointly Gaussian random variables. We restrict our attention to zero mean jointly Gaussian rv’s and zero mean Gaussian processes, both because a mean can be trivially added to a zero mean fluctuation, and because zero mean processes are used to model noise.