On the characterization of the amplitude and shift of N-periodic sequences

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An orthogonal transformation is used to characterize the amplitude variation and shift of a real number N-periodic sequence, where, N = 2n for some positive integer n. The amplitude variation is characterized by a set of (log2 N + 1) numbers which are invariant to shifts of the sequence. Again, (N − 1) transform coefficients are sufficient to characterize all shifts of the sequence. It is shown that the amount of shift can be detected in log2 N comparisons.

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