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 (log2N + 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 log2N comparisons.