The sinc function is defined by

This analytic expression corresponds to the continuous inverse Fourier transform
of a rectangular pulse of width 2*π* and height 1:

The space of functions bandlimited in the frequency range $$\omega =(-\pi ,\pi ]$$ is spanned by the countably infinite set of sinc functions shifted
by integers. Thus, you can reconstruct any such bandlimited function
*g*(*t*) from its samples at integer
spacings: