Impulse train

An infinite row of evenly spaced unit Dirac impulses, used to model sampling as multiplication.

An impulse train, $p(t)=\sum_{n=-\infty}^{\infty}\delta(t-n\,\Delta t)$ , is an infinite row of unit impulses spaced $\Delta t$ apart. Multiplying a continuous signal by an impulse train models the act of sampling it, concentrating the product entirely at the sample instants.

Examples

Multiplying $f(t)$ by an impulse train spaced $\Delta t$ apart produces a signal that is nonzero only at $t=n\Delta t$ .