Sinc Function / Sampling Function 取樣函數

There are two definitions for the Sinc function:

When x ≠ 0,

for mathematics,

    sinc(x) = sin(x)/x (unnormalized sinc function)

for digital signal processing,

    sinc(x) = sin(πx)/πx (normalized sinc function)

When x = 0,

    sinc(x) = sinc(0) = 1 for both mathematics and DSP.

In DSP, sinc(x) is also called the sampling function:

    Sa(πx) = sin(πx)/πx = sinc(x)