Suppose we sample the signal x$($t$)=23$ cos$(100$t$)+$ cos$(200$t$)$ at a sampling frequency of fs $=200$ samples$/$second to obtain a discrete$-$time signal x$[$n$].($a$)$ Give the mathematical formula for x$[$n$].($b$)$ Design an FIR filter that removes the components at $0$Hz and $50$Hz$,$ but preserves the signal at $100$Hz$.$ Hint: Design two filters to be put in series, one that eliminates $0$Hz components and another that eliminates $50$Hz components, and make sure the overall frequency response at the discrete$-$time frequency corresponding to $100$Hz has magnitude $1.$