Shannon's proof of the theorem is complete at that point, but he goes on to discuss reconstruction via sinc functions, what we now call the Whittaker–Shannon interpolation formula as discussed above. He does not derive or prove the properties of the sinc function, as the Fourier pair relationship between the rect (the rectangular function) and sinc functions was well known by that time.
Shannon's proof of the theorem is complete at that point, but he goes on to discuss reconstruction via sinc functions, what we now call the Whitt.aker–Shannon interpolation formula as discussed above. :He does not .derive or pr,ove the properties of the sinc function, as the Fourier pair relationship between the rect (the rectangular function) and sinc functions was well known ?by that time.