问答题
设x(t)和y(t)分别是平稳随机过程,若
z(t)=x(t)cosωot-y(t)sinωot
【正确答案】rz(τ)=E[z(t)z(t+τ)]
=E[(x(t)cosωot-y(t)sinωot)×
(x(t+τ)cosωo(t+τ)-y(t+τ)sinωo(t+τ))]
=rx(τ)cosωotcosωo(t+τ)-rxy(τ)cosωotsinωo(t+τ)-
ryx(τ)sinωotcosωo(t+τ)+ry(τ)sinωotsinωo(t+τ)
【答案解析】
【正确答案】当rx(τ)=ry(τ),rxy(τ)=0时,则有
rz(τ)=rx(τ)cosωotcosωo(t+τ)+ry(τ)sinωotsinωo(t+τ)
=rx(τ)cosωoτ
【答案解析】