Should question 3 be
Let x(t) be a continuous-time signal with $ \left| {\mathcal X} (\omega)\right| =0 $ for $ \left| \omega\right| > \omega_s $. Can one recover the signal x(t) from the signal $ y(t)=x(t) p(t-3) $, where
$ p(t)= \sum_{k=-\infty}^\infty \delta (t- \frac{2\pi}{\omega_s} n) ? $
instead of this?
Let x(t) be a continuous-time signal with $ \left| {\mathcal X} (\omega)\right| =0 $ for $ \left| \omega)\right| > \omega_m $. Can one recover the signal x(t) from the signal $ y(t)=x(t) p(t-3) $, where
