Definition
Let (a0, a1, ..., aN − 1) and (b0, b1, ..., bN − 1) be a pair of bipolar sequences, meaning that a(k) and b(k) have values +1 or −1. Let the aperiodic autocorrelation function of the sequence x be defined by
Then the pair of sequences a and b is complementary if:
for k = 1, ..., N − 1.
Or using Kronecker delta we can write:
where C is a constant.
So we can say that the sum of autocorrelation functions of complementary sequences is a delta function which is an ideal autocorrelations for many applications like radar pulse compression and spread spectrum telecommunications.
Read more about this topic: Complementary Sequences
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