Can we ever reconstruct a a signal by its sampling? No, we generally never can but we can approximate.
1. The easiest way to "reconstruct" a signal is by zero-order interpolation which looks like step functions.
$ x(t) = \sum^{\infty}_{k = -\infty} x(kT) (u[t-kT]-u[t-(k+1)T]) $
2. To step it up we can use 1st order interpolation. She gave an example about a kid going to an interview and they asked him if he has ever heard o splines and peace-wise polynomial functions and that is what this is.
