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Assume we have a series v[k] of length M=16. It's shifted to the right in a circular manner by k0=2 samples.

Which phase difference between the DFT spectrum of the original signal and that of the shifted version is to be expected?

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The phase shift will be a factor of $e^{j2\pi k_0 m/M}$, where $m$ is the DFT bin number

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