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.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Fourier transform of rect(x)

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