The Sinc Function (``Cardinal Sine'')

   sinc$$(t) \mathrel{\stackrel{\mathrm{\Delta}}{=}}\left\{\begin{array}{ll} \frac{\sin(\pi t)}{\pi t}, & t\ne 0 \\ [5pt] 1, & t=0 \\ \end{array} \right.$$

Sinc Function

The sinc function is the impulse response of the ideal lowpass filter which cuts off at half the sampling rate