@prefix dcat: . @prefix dct: . @prefix foaf: . @prefix vcard: . @prefix xsd: . a dcat:Dataset ; dct:description """ In this thesis, we focus on a particular type of matrices: Laurent polynomial matrices whose elements are Laurent polynomials, ie polynomials with positive and negative powers of $ z $. Such polynomials cannot be associated to a causal filter but they occur when considering the spectrum of finite impulse response filter output. First, we present the properties of Laurent polynomials and Laurent polynomial matrices. We define the L-Smith form which is an extension of the classical Smith form of a polynomial matrix and give a precise definition of the degree and the order of these matrices (sometimes confused notions in the literature). We then study para-Hermitian matrices and para-unitary matrices which are respectively equal to their para-conjugated or whose inverse is equal to the para-conjugated. We develop their properties in terms of particular degree and factorization. In system theory and signal processing, many factorizations of matrices with constant coefficients are involved: QR factorizations (using an orthogonal and a triangular matrix), LU (using two triangular matrices: one lower and one upper), SVD (singular value decomposition using two unitary matrices) EVD (eigenvalue decompositions). In particular, the spectral theorem shows that every hermitian matrix can be diagonalized using a unitary matrix. The Cholesky factorization of a hermitian positive definite matrix uses a triangular matrix and its conjugate transpose. These factorizations cannot be extended to polynomial matrices because the coefficients of these matrices do not belong to a field but a ring (that of Laurent polynomials). We show that in the general case, a polynomial EVD decomposition of a para-Hermitian matrix which is positive definite on the unit circle does not exist, but one can almost-diagonalize these matrices using para-unitary matrices which are continuous on the unit circle. Finally, we show what role para-unitary matrices factorizations plays in blind equalization of convolutive multivariable systems. """ ; dct:identifier "tel-00805547" ; dct:issued "2026-05-12T00:19:47.895722"^^xsd:dateTime ; dct:language "fr" ; dct:modified "2026-05-12T00:19:47.895726"^^xsd:dateTime ; dct:publisher ; dct:title "Matrices polynomiales et égalisation de canal" ; dcat:contactPoint [ a vcard:Organization ; vcard:fn "CCSD" ] ; dcat:distribution ; dcat:keyword "egalisation", "equalization", "habilitation-a-diriger-des-recherches", "infoeu-reposemanticsother", "infoinfo-tscomputer-science-cssignal-and-image-processing", "matrices-polynomiales", "mimo-systems", "polynomial-matrices", "signal-processing", "spiautoengineering-sciences-physicsautomatic", "spisignalengineering-sciences-physicssignal-and-image-processing", "systemes-multivariables", "traitement-du-signal" ; dcat:landingPage . a dcat:Distribution ; dct:format "HTML" ; dct:issued "2026-05-12T00:19:47.952136"^^xsd:dateTime ; dct:modified "2026-05-12T00:19:47.866363"^^xsd:dateTime ; dct:title "Matrices polynomiales et égalisation de canal" ; dcat:accessURL . a foaf:Agent ; foaf:name "test_moissonnage_selune" . a foaf:Document .