$8.(10\backslash \%)$ A baseband system facing an ideal channel and AWGN with PSD $\backslash (=$N$\_\{0\}/2\backslash )$ is considered. Please give a design of the transmitter filter and the receiver filter such that the cascade of the filters, denoted as $\backslash ($ P$($f$)\backslash ),$ is a raised$-$cosine spectrum, and the error probability is minimized. $($Note: Express your design in terms of the given functions.$)$