Sinc function

The sinc function, also known as the interpolation function or filtering function, is the product of a sine function and a monotonically decreasing function. It is defined by:

${\displaystyle \operatorname {sinc} \left(x\right)={\frac {\sin \left(x\right)}{x}}}$

or:

${\displaystyle \operatorname {sinc} \left(x\right)={\frac {\sin \left(\pi x\right)}{\pi x}}}$

It has a removable singularity at the origin. Sinc(0)=1, despite the division by zero.

The sinc function oscillates with decreasing amplitude. Applications of the sinc function are found in communication theory, control theory, and optics.

See also: trigonometric function