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Asked: 2026-05-11T13:06:38+00:00

I have a small query regarding the discrete Fourier transforms. If I understand correctly,

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I have a small query regarding the discrete Fourier transforms. If I understand correctly, then what we do is convert a polynomial to its point value representation, with n points for a polynomial that goes up to the power of n-1. But why must we evaluate it at the nth roots of unity? Wouldn’t any other n points uniquely identify this polynomial AND be much simpler?

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  1. Wouldn’t any other n points uniquely identify this polynomial AND be much simpler?

    No to both. 1) There’s no guarantee that n arbitrary points would work and 2) it wouldn’t be simpler. Turn the question around: why do you object to the roots of unity?

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