Analytic Constructions of Periodic and Non-periodic Complementary Sequences

An analytic approach for the generation of non-periodic and periodic complementary sequences is advanced for lengths that are powers of two.The periodic complementary sequences can be obtained using symmetric or anti-symmetric extensions.The properties of their autocorrelation functions are studied.The non-periodic complementary sequences are the intersection between anti-symmetric and symmetric periodic sequences.These non-periodic and periodic complementary sequences are identified to be special cases of non-periodic and periodic (or cyclic) orthogonal wavelet transforms.This relationship leads to the novel approach.