论文标题
全通函数，用于镜像有理矩阵函数的复杂偶联根对
All-Pass Functions for Mirroring Pairs of Complex-Conjugated Roots of Rational Matrix Functions
论文作者
论文摘要
我们构建具有实值系数的有理全通矩阵函数，用于镜像有理矩阵的复合偶联的确定根对。例如，在证明频谱分解定理的情况下，或者最近在有关可能不可固化或可能是非毒物矢量自回归移动平均值（VARMA）模型的文献中，出现了此问题。通常，尚不明显的是，通用矩阵函数（因此，全通矩阵函数最初具有真实价值的系数转换为合理的矩阵），它反映了单位圆的复杂偶联根具有实值的系数。幼稚的构造导致具有复杂值系数的全通函数，这意味着留下了实值参数空间（通常与估计相关）。
We construct rational all-pass matrix functions with real-valued coefficients for mirroring pairs of complex-conjugated determinantal roots of a rational matrix. This problem appears, for example, when proving the spectral factorization theorem, or, more recently, in the literature on possibly non-invertible or possibly non-causal vector autoregressive moving average (VARMA) models. In general, it is not obvious whether the all-pass matrix function (and as a consequence the all-pass transformed rational matrix with initally real-valued coefficients) which mirrors complex-conjugated roots at the unit circle has real-valued coefficients. Naive constructions result in all-pass functions with complex-valued coefficients which implies that the real-valued parameter space (usually relevant for estimation) is left.
