I can easily find the Fourier transform of rect(x) to be [itex]2sinc(2\pi k)[/itex] using particular conventions (irrelevant here). But when I attempt to inverse Fourier transform the sinc function, I find I have to resort to contour integration and Cauchy principal values. This is troubling to me. It appears as if the usual definition of a Fourier transform is inadequate here, and could possibly lead to incorrect results in another context. Can anyone shed any light on this?