Applied and Computational Harmonic Analysis ( IF 2.6 ) Pub Date : 2018-07-23 , DOI: 10.1016/j.acha.2018.07.003 Daniel J. Katz , Sangman Lee , Stanislav A. Trunov
We consider the class of Rudin–Shapiro-like polynomials, whose norms on the complex unit circle were studied by Borwein and Mossinghoff. The polynomial is identified with the sequence of its coefficients. From the norm of a polynomial, one can easily calculate the autocorrelation merit factor of its associated sequence, and conversely. In this paper, we study the crosscorrelation properties of pairs of sequences associated to Rudin–Shapiro-like polynomials. We find an explicit formula for the crosscorrelation merit factor. A computer search is then used to find pairs of Rudin–Shapiro-like polynomials whose autocorrelation and crosscorrelation merit factors are simultaneously high. Pursley and Sarwate proved a bound that limits how good this combined autocorrelation and crosscorrelation performance can be. We find infinite families of polynomials whose performance approaches quite close to this fundamental limit.
中文翻译:
Rudin–Shapiro多项式的互相关
我们考虑类Rudin–Shapiro的多项式,其 Borwein和Mossinghoff研究了复杂单位圆上的范数。多项式 用序列识别 其系数。来自多项式的范数,可以很容易地计算出其相关序列的自相关优因数,反之亦然。在本文中,我们研究了与Rudin–Shapiro类多项式相关的序列对的互相关特性。我们为互相关优因数找到了一个明确的公式。然后使用计算机搜索来找到对数类似的Rudin–Shapiro多项式,其自相关和互相关优因数同时很高。Pursley和Sarwate证明了一个局限性,它限制了这种自相关和互相关组合性能的好坏。我们发现多项式的多项式的性能接近该基本极限。