If we use each of the following $1$D reconstruction filters to reconstruct a continuous function

g$($ x$)$ from a sequence of samples f $[$i$]$ using continuous$-$discontinuous convolution, for which

filterswill g$($x$)$ be C$0?$

For which filters will g$($x$)$ be C$1?$

For which filters will g$($x$)$ interpolate f $[$i$]?$

hints: the reconstructed function g$($ x$)$ is defined as g$($x$)=$i f $[$i$]$a$($x$$i$)$ for a arbitrary

sequence of samples f $[$i$]$ when each of the followings is a$($x$).$