The unnormalized sinc is , extended by value one at zero. The normalized form is . It is the inverse Fourier transform of a frequency interval indicator, so it describes ideal low-pass filtering and the Shannon scaling function.

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Sinc function by Wikipedia Bot 1
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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.
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