Abstract
Abstract In this article, we address the problem of singular value decomposition of polynomial matrices and eigenvalue decomposition of para-Hermitian matrices. Discrete Fourier transform enables us to propose a new algorithm based on uniform sampling of polynomial matrices in frequency domain. This formulation of polynomial matrix decomposition allows for controlling spectral properties of the decomposition. We set up a nonlinear quadratic minimization for phase alignment of decomposition at each frequency sample, which leads to a compact order approximation of decomposed matrices. Compact order approximation of decomposed matrices makes it suitable in filterbank and multiple-input multiple-output (MIMO) precoding applications or any application dealing with realization of polynomial matrices as transfer function of MIMO systems. Numerical examples demonstrate the versatility of the proposed algorithm provided by relaxation of paraunitary constraint, and its configurability to select different properties.
Highlights
Polynomial matrices have been used for a long time for modeling and realization of multiple-input multipleoutput (MIMO) systems in the context of control theory [1]
Lambert [15] has utilized Discrete Fourier transform (DFT) domain to change the problem of polynomial eigenvalue decomposition (EVD) to pointwise EVD
Since EVD is obtained at each frequency separately, eigenvectors are known at each frequency up to a scaling factor
Summary
Polynomial matrices have been used for a long time for modeling and realization of multiple-input multipleoutput (MIMO) systems in the context of control theory [1]. We present polynomial EVD and SVD based on DFT formulation It transforms the problem of polynomial matrix decomposition to the problem. Of, pointwise in frequency, constant matrix decomposition At first it seems that applying inverse DFT on the decomposed matrices leads to polynomial EVD and SVD of the corresponding polynomial matrix. If at each frequency sample all singular values are in decreasing order, REARRANGE function (which is described in Algorithm 2) is only required for smooth decomposition, otherwise for spectral majorization, no further arrangement is required. First we need to compute phase angles which is indicated in the algorithm by DOGLEG function and is described in Algorithm 3
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
