$1$ II We defined three "Types" $($or "Cases"$)$ of linear phase FIR filters: Type IV Order odd Symmetry symmetric symmetric of h$[$n$]$ symmetric symmetric Each of these $$Types$"$ has a transfer function defined as H$?($z$)=$ h$[0]+$h$[1]$z$-1+...$ h$[$N$]$z$-$N$.$ even odd even anti$-$ anti$-$ Show each of the following: a$.$ A Type$-$II linear$-$phase FIR filter's H$^2(2)$ has a factor $(1+$z$-1)$ b$.$ A Type$-$III linear$-$phase FIR filter's H$?($z$)$ has a factor $(1+$z$-)$ c$.$ A Type$-$IV linear$-$phase FIR filter's H$^2($z$)$ has a factor $(1-$z$-1)$