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

On the Periodicity of Singular Vectors and the Holomorphic Block-Circulant SVD on the Unit Circumference