Consider two signals $x_1(t)$ and $x_2(t)$ that are band$-$limited to frequencies ${}_1$ and ${}_2,$ respectively. A product signal $w(t)=x_1(t)x_2(t)$ is obtained by multiplying signals $x_1(t)$ and $x_2(t).w(t)$ is sampled by a periodic impulse train yielding the signal

$w_s(t)={\displaystyle \underset{n=-}{\overset{}{}}}w(nT)(t-nT)$