Let x$($t$)$ be a continuous time signal that is bandlimited to B$.$ Suppose a receiver receives x$($t$)$ along with two$-$delayed

echos, i$.$e$.,$ the receiver receives w$($t$)=$ x$($t$)+$ ax$($t $$ $1)+$ bx$($t $$ $2).$

a$)$ What is the continuous$-$time Fourier transform W$($F$)$ in terms of X$($F$)?$

b$)$ The receiver wants to recover x$($t$)$ from w$($t$)$ using a discrete$-$time filter HD$($f$),$ and assume that the receiver has

access to an ideal sampler, and ideal reconstruction is possible. Give a sampling frequency Fs and the corresponding

discrete$-$time filter HD$($f$)$ that does the job.