averaging and differencing filters ha$[$n$]=0\mathrm{.}5$$[$n$]+0\mathrm{.}5$$[$n $1]$ and hd$[$n$]=0\mathrm{.}5$$[$n$]0\mathrm{.}5$$[$n $1].($a$)$ Derive the frequency response functions for both filters. $($b$)$ What is the overall frequency response of the two filters in series? That is$,$ what is the frequency response of ha$[$n$]$ hd$[$n$]?($c$)$ What is the overall frequency response of ten copies of ha$[$n$]$ in series?