Impulse-train sampling is a method of [sampling](Sampling) [continuous signal](Continuous%20signals) in time that uses [impulses](Impulses) spaced at regular intervals in time. In order to procede we define an _impulse train_ as $p(t)$ such that $p(t) = \sum_{-\infty}^{\infty}\delta(t-nT)$ where $\delta(t-nT)$ is an [impulse](impulses#^bf920a) function and $T$ is referred to as the _sampling period_ since it defines the distance in time between consecutive impulses. This impulse train is multiplied by the original signal, $x(t)$ in order to obtain an new impulse train, $x_p(t) = x(t)p(t).$ #MathematicalFoundations/SignalProcessing