electron lett 1990 26 18 pp 1428 1430 that all the different cyclic time shifted versions of any sequence having an ideal periodic autocorrelation function form a complementary set a complex valued sequence x i whose k th element is s i k forms a complementary set if the sum z p of the a periodic autocorrelation function r i of all sequences from the set is equal to zero for all nonzero time shifts p that is z ue8a0 p u2211 i 0 m 1 ue89e u2211 k 0 m 1 p ue89e s i ue8a0 k ue89e s i ue8a0 k p u2211 i 0 m 1 ue89e r l ue8a0 0 p 0 0 p u2260 0 2 wherein denotes complex conjugate p is the positive time shift and r i 0 is the energy of the sequence x i when the set has only two sequences a complementary pair the two sequences of equal length m must have aperiodic autocorrelation functions whose sidelobes are equal in magnitude but opposite in sign the sum of the two autocorrelation functions has a peak of 2 m and a sidelobe level of zero in order to take advantage of this autocorrelation property in radar signals farnet e c and stevens g h u201c pulse compression radar u201d radar handbook 2 nd edition skolnik m ed mcgraw hill 1990 ch 10 the sequences.