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:

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

or:

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

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

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