We investigate the singular value decomposition of a rectangular matrix that is analytic on the complex unit circumference, which occurs, e.g., with the matrix of transfer functions representing a broadband multiple-input multiple-output channel. Our analysis is based on the Puiseux series expansion of the eigenvalue decomposition of analytic para-Hermitian matrices on the complex unit circumference. We study the case in which the rectangular matrix does not admit a full analytic singular value factorization, either due to partly multiplexed systems or to sign ambiguity. We show how to find an SVD factorization in the ring of Puiseux series where each singular value and the associated singular vectors present the same period and multiplexing structure, and we prove that it is always possible to find an analytic pseudo-circulant factorization, meaning that any arbitrary arrangements of multiplexed systems can be converted into a parallel form. In particular, one can show that the sign ambiguity can be overcome by allowing non-real holomorphic singular values.

翻译：我们研究了在复单位圆周上解析的矩形矩阵的奇异值分解，此类矩阵常见于描述宽带多输入多输出信道的传递函数矩阵。我们的分析基于复单位圆周上解析para-Hermitian矩阵特征值分解的Puiseux级数展开。针对矩形矩阵因部分复用系统或符号歧义而无法实现完全解析奇异值分解的情形，我们探索了解决方案。我们展示了如何在Puiseux级数环中构造奇异值分解，使得每个奇异值及其关联奇异向量具有相同的周期结构与复用结构，并证明总能找到解析伪循环分解，即任意复用系统的排列均可转化为并联形式。特别地，研究表明允许非实数全纯奇异值可克服符号歧义问题。