随机信号自相关函数S(t)=X(t)coswt-Y(t)sinwtX(t)Y(t)为平稳随机过程.且X(t)Y(t)的自相关与互相关函数已知.W为固定值求S(t)的自相关函数!很着急

Answer 1

Rss(t1,t2)=E{[x(t1)coswt1-y(t1)sinwt1][x(t2)coswt2-y(t2)sinwt2]}
=coswt1coswt2E[x(t1)]E[x(t2)]-coswt1sinwt2E[x(t1)]E[y(t2)]-coswt2sinwt1E[x(t2)]E[y(t1)]+sinwt1sinwt2E[y(t1)]E[y(t2)]
=coswt1coswt2Rx(t1,t2)-coswt1sinwt2Rxy(t1,t2)-coswt2sinwt1Ryx(t1,t2)+sinwt1sinwt2Ry(t1,t2)