Is it possible for continuous fourier transform of a function to have values only on finite number of frequencies? Or do these values necessarily impulse values, not complex numbers?
2026-03-30 07:09:27.1774854567
Is it possible for continuous fourier transform of a function to have values only on finite number of frequencies?
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Suppose $g$ is the Fourier transform of some $f$, and that $g$ is zero everywhere except a finite set $\{x_n\}$, where it is finite. Then $g$ is a function (i.e. "not a distribution"*) that is zero a.e.; what happens if you integrate a function that is zero a.e.?
In particular, what if you take the inverse Fourier transform of $g$?
*: of course, functions are distributions, but hopefully my meaning is understood and you will allow me to be informal here.