 Sinc function

The unnormalized sinc function is $\mathrm{sinc}(x)=\sin x/x$, extended by value one at zero. The normalized sinc function is $\sin (\pi x)/(\pi x)$, with the same removable value. These arise, with convention-dependent scaling, as inverse Fourier transforms of frequency-interval indicator functions, so they describe ideal low-pass filters and the Shannon scaling function.

The sinc function is a mathematical function defined in relation to the sine function. There are two commonly used definitions for the sinc function: 1. **Normalized sinc function**: \[ \text{sinc}(x) = \frac{\sin(\pi x)}{\pi x} \quad \text{for } x \neq 0 \] \[ \text{sinc}(0) = 1 \] 2.