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Ambiguity about roots of unity in discrete Fourier transform

  1. Apr 27, 2012 #1
    Hi everyone, I have a question on the discrete Fourier transform. I already know its a change of basis operator on [itex]C^N[/itex] between the usual orthonormal basis and the "Fourier" basis, which are vectors consisting of powers of the [itex]N[/itex] roots of unity.

    But if i recall correctly from complex analysis, the root of a complex number is not unique. So for example, if we look at the first entry of the first Fourier basis vector, it is [itex] e^{\frac{2 \pi i }{N}} [/itex]. But there are N solutions here. Which one is the actual first entry in the first Fourier basis vector?
  2. jcsd
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