−1). Their autocorrelation functions are (10, −3, 0, −1, 0, 1,−2, −1, 2, 1) and (10, 3, 0, 1, 0, −1, 2, 1, −2, −1). Properties of complementary pairs of sequences Complementary sequences have complementary spectra. As the autocorrelation function and the power spectra form a Fourier pair, complementary sequences also have complementary spectra. But as the Fourier transform of a delta function is a constant, we can write where CS is a constant. Sa and Sb are defined as a squared magnitude of the Fourier transform of the sequences. The Fourier transform can be a direct DFT of the sequences, it can be a DFT of zero padded sequences or it can be a continuous Fourier transform of the sequences which is equivalent to the Z transform for . CS spectra is upper bounded. As Sa and Sb are non-negative values we can write also If either of the sequences of the CS pair is inverted (multiplied by −1) they remain complementary. More generally if any of the sequences is multiplied by ejφ they remain complementary; If either of the sequences is reversed they remain complementary; If either of the sequences is delayed they remain complementary; If the sequences are interchanged they remain complementary; If both sequences are multiplied by the same constant (real or complex) they remain complementary; If both sequences are decimated in time by K they remain complementary. More precisely if from a complementary pair (a(k), b(k)) we form a new pair (a(Nk), b(Nk)) with skipped samples discarded then the new sequences are complementary. If alternating bits of both sequences are inverted they remain complementary. In general for arbitrary complex sequences if both sequences are multiplied by ejπkn/N (where k is a constant and n is the time index) they remain complementary; A new pair of complementary sequences can be formed as [a b] and [a −b] where [..] denotes concatenation and a and b are a pair of CS; A new pair of sequences can be formed as {a b} and {a −b} where {..} denotes interleaving of sequences. A new pair of sequences can be formed as a + b and a − b. Golay pair A complementary pair a, b may be encoded as polynomials A(z) = a(0) + a(1)z + ... + a(N − 1)zN−1 and similarly for B(z). The complementarity property of the sequences is equivalent to the condition for all