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that the product of their normalization factors be An uncommon normalization of for both the DFT and IDFT makes the transform-pair unitary.

can also be evaluated outside the domain , and that extended sequence is -periodic. Accordingly, other sequences of indices are sometimes used, such as (if is even) and (if is odd), which amounts to swapping the left and right halves of the result of the transform.

DFT including sampling interval

Using the standard definition

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