Decomposition of the nodal conductance matrix of a planar resistive grid and derivation of its eigenvalues and eigenvectors using the kronecker product and sum with application to cnn image filters

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dc.authorid0000-0001-8590-1518
dc.contributor.authorTavşanoğlu, Ahmet Vedaten_US
dc.date.accessioned2016-12-27T07:37:49Z
dc.date.available2016-12-27T07:37:49Z
dc.date.issued2016-12
dc.departmentIşık Üniversitesi, Mühendislik Fakültesi, Elektrik-Elektronik Mühendisliği Bölümüen_US
dc.departmentIşık University, Faculty of Engineering, Department of Electrical-Electronics Engineeringen_US
dc.description.abstractIt is shown that an (M× N)-node planar resistive grid can be decomposed into two sub-grids; one made up of M N-node horizontal and the other of N M-node vertical linear resistive grids which corresponds to decomposing its nodal conductance matrix (NCM) into the Kronecker sum of the NCMs of horizontal and vertical linear grids. This enables the analytical expressions of the eigenvalues and eigenvectors of the NCMs of the sub-grids as well as those of the planar resistive grid to be expressed in terms of those of the two linear grids, whose analytical expressions are well known. For a Cellular Neural Network (CNN) Gabor-type filter (GTF) we define generalized nodal conductance matrices (GNCMs) that correspond to the NCMs of the resistive sub-grids, show that each Kronecker decomposition has a counterpart in CNN GTF and prove that each GNCM, its counterpart NCM and the corresponding temporal state matrices are related through unitary diagonal similarity transformations. Consequently, we prove that the eigenvalues of the temporal state matrix of a spatial band-pass CNN GTF are the same as those of its counterpart spatial low-pass CNN image filter, hence their temporal transient behaviors are similar in settling to a forced response.en_US
dc.description.versionPublisher's Versionen_US
dc.identifier.citationTavşanoğlu, A. V. (2016). Decomposition of the nodal conductance matrix of a planar resistive grid and derivation of its eigenvalues and eigenvectors using the kronecker product and sum with application to CNN image filters. IEEE Transactions on Circuits and Systems I: Regular Papers, 63(12), 2169-2179. doi:10.1109/TCSI.2016.2617918en_US
dc.identifier.doi10.1109/TCSI.2016.2617918
dc.identifier.endpage2179
dc.identifier.issn1549-8328
dc.identifier.issn1558-0806
dc.identifier.issue12
dc.identifier.scopus2-s2.0-85002863221
dc.identifier.scopusqualityQ1
dc.identifier.startpage2169
dc.identifier.urihttps://hdl.handle.net/11729/1156
dc.identifier.urihttp://dx.doi.org/10.1109/TCSI.2016.2617918
dc.identifier.volume63
dc.identifier.wosWOS:000389338300008
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.indekslendigikaynakScience Citation Index Expanded (SCI-EXPANDED)en_US
dc.indekslendigikaynakConference Proceedings Citation Index – Science (CPCI-S)en_US
dc.institutionauthorTavşanoğlu, Ahmet Vedaten_US
dc.institutionauthorid0000-0001-8590-1518
dc.language.isoenen_US
dc.peerreviewedYesen_US
dc.publicationstatusPublisheden_US
dc.publisherIEEEen_US
dc.relation.ispartofIEEE Transactions on Circuits and Systems I: Regular Papersen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectCNN low-pass and Gabor-type filtersen_US
dc.subjectKronecker producten_US
dc.subjectNodal conductance matrixen_US
dc.subjectResistive griden_US
dc.subjectBandpass filtersen_US
dc.subjectCellular neural networksen_US
dc.subjectGabor filtersen_US
dc.subjectLinear transformationsen_US
dc.subjectLow pass filtersen_US
dc.subjectMatrix algebraen_US
dc.subjectAnalytical expressionsen_US
dc.subjectConductance matrixen_US
dc.subjectEigenvalues and eigenvectorsen_US
dc.subjectLow-passen_US
dc.subjectSimilarity transformationen_US
dc.subjectTransient behavioren_US
dc.subjectEigenvalues and eigenfunctionsen_US
dc.titleDecomposition of the nodal conductance matrix of a planar resistive grid and derivation of its eigenvalues and eigenvectors using the kronecker product and sum with application to cnn image filtersen_US
dc.typeArticleen_US
dspace.entity.typePublication

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