Pseudorandom number generators | Sequences and series | Signal processing

Complementary sequences

In applied mathematics, complementary sequences (CS) are pairs of sequences with the useful property that their out-of-phase aperiodic autocorrelation coefficients sum to zero. Binary complementary sequences were first introduced by Marcel J. E. Golay in 1949. In 1961–1962 Golay gave several methods for constructing sequences of length 2N and gave examples of complementary sequences of lengths 10 and 26. In 1974 R. J. Turyn gave a method for constructing sequences of length mn from sequences of lengths m and n which allows the construction of sequences of any length of the form 2N10K26M. Later the theory of complementary sequences was generalized by other authors to polyphase complementary sequences, multilevel complementary sequences, and arbitrary complex complementary sequences. Complementary sets have also been considered; these can contain more than two sequences. (Wikipedia).

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Related pages

Pseudorandom binary sequence | Polyphase sequence | Maximum length sequence | Binary Golay code | Lambek–Moser theorem | Autocorrelation | Shapiro polynomials | Power of two | Interleave sequence | Pulse compression | Sequence | Ternary Golay code | Fourier transform | Hadamard code | Kronecker delta