$8\mathrm{.}21.($a$)$ Figure P$8\mathrm{.}21-1$ shows two periodic sequences, $,[$n$]$ and z$[$n$],$ with period N $=7.$ Finda sequence $$,[$n$]$ whose DFS is equal to the product of the DFS of $,[$n$]$ and the DFSof i$2$ln$],$ i$.$e$.,$