$(30$ points$)$Given real joint stationary processes X$($t$)$and Y$($t$)$: aY$($t$)+$A$.=$ X$($t$)-$pdx$$d$3$y$($t$),$and the power spectrum of X$($t$)$is Sx$(\backslash$omega $),$d$3$td$2$t$(1)$Calculate the transfer function Hy$($w$)$ and the cross$-$power spectrum of Sxy$(\backslash$omega and Syx$($w$)($represented by a$,\backslash$beta and Sx$($w$)).(15$ points$)2\backslash$beta w$2+2(2)$if the input X$($t$)$is a white noise with power spectrum q$,$ and Sy$($w$)=04-02+1$ calculate a$,$B$,$g$($value only, do not consider the units$).(15$ points$)$