Analytic Constructions of Periodic and Non-periodic Complementary Sequences


IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A    No.11    pp.3272-3282
Publication Date: 2006/11/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.11.3272
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
correlation,  discrete Fourier transforms,  orthogonal functions,  sequences,  transforms,  wavelet transforms,  

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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.