Problem $1(20$ points$)$

Consider a baseband signal $y(t)$ with bandwidth $B($i$.$e$.,Y(f)=0,|f|>B).$ The signal is sampled at a rate of $R$ samples per second to obtain the sequence of samples $s[k],k=0,+-1,+-2$dots, with $s[0]=y(0).$

Define $s[k]$ from $y(t).$

For which values of $B$ is it possible to perfectly recover the original signal $y(t)$ from $s[k]?$ Define a system that performs recovery. All the blocks and signals in the system have to be specified completely.

If for reconstruction we can only use i$)$ sums of shifted versions of the pulse $p(t)$ defined below, with each shifted version weighted by the value of one of the samples, and ii$)$ an equalizer, for which values of a can we perform recovery whenever recovery is possible using the system in $2)?$ Define the system that performs recovery. All the blocks and signals in the system have to be specified completely.