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Recent results on polyphase sequences

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2 Author(s)
Golomb, S.W. ; Commun. Sci. Inst., Univ. of Southern California, Los Angeles, CA, USA ; Win, M.Z.

A polyphase sequence of length n+1, A={aj}j=0n, is a sequence of complex numbers, each of unit magnitude. The (unnormalized) aperiodic autocorrelation function of a sequence is denoted by C(τ). Associated with the sequence A, the sequence polynomial fA(z) of degree n and the correlation polynomial gA(z) of degree 2n are defined. For each root α of fA(z), 1/α* is a corresponding root of f*A(z-1). Transformations on the sequence A which leave |C(τ)| invariant are exhibited, and the effects of these transformations on the roots of fA(z) are described. An investigation of the set of roots A of the polynomial f A(z) has been undertaken, in an attempt to relate these roots to the behavior of C(τ). Generalized Barker (1952, 1953) sequences are considered as a special case of polyphase sequences, and examples are given to illustrate the relationship described above

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Information Theory, IEEE Transactions on  (Volume:44 ,  Issue: 2 )