 Sinc function

The unnormalized sinc is $\mathrm{sinc}(x)=\sin x/x$, extended by value one at zero. The normalized form is $\sin (\pi x)/(\pi x)$. It is the inverse Fourier transform of a frequency interval indicator, so it describes ideal low-pass filtering 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.