  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.
