Recent results on polyphase sequences

A polyphase sequence of length n+1, A={a_j}_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 f_A(z) of degree n and the correlation polynomial g_A(z) of degree 2n are defined. For each root α of f_A(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 f_A(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