white noise #stochastic_processes Definition Assume E[X(t)]=0E[X(t)] = 0, then X(t)X(t) is white noise if R(t1,t2)=E[X(t1)X(t2)]=0R(t_1, t_2) = E[X(t_1) X(t_2)] = 0 for any t1,t2t_1, t_2 can write as R(t1,t2)=q(t1)δ(t1−t2)R(t_1, t_2) = q(t_1) \delta(t_1 - t_2) for some function suppose q(t1)=qq(t_1) = q constant, then R(t1,t2)=qδ(t2−t1)R(t_1, t_2) = q \delta(t_2 - t_1), thus X(t)X(t) is WSS (where R(t1,t2)R(t_1, t_2) is autocorrelation)