Sinc function

Summary

The sinc function is $\operatorname{sinc} x = \frac{\sin x}{x}$, with the value $1$ at $x = 0$. Signal processing often uses the normalised version $\frac{\sin \pi x}{\pi x}$, whose zeros are the non-zero integers. The normalised sinc function is the Fourier transform of the indicator function of an interval, and it is the interpolation kernel in the sampling theorem. Its integral over $(0, \infty)$ is the Dirichlet integral, equal to $\frac{\pi}{2}$.