Sinc function

The $\sin$ -over-argument ripple shape, $\sin(a\omega)/\omega$ , that is a rectangular pulse's Fourier transform.

A sinc function is a function of the shape $\sin(a\omega)/\omega$ (up to a scale constant): it oscillates forever, crossing zero at evenly spaced points, inside a shrinking $1/|\omega|$ envelope. It is the Fourier transform of a rectangular pulse -- the never-ending ripple a sharp edge in time always costs in frequency.

Examples

The Fourier transform of the rectangular pulse on $[-a,a]$ is $2\sin(a\omega)/\omega$ , a sinc function.