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dc.contributor.advisorParker, Sydney R.
dc.contributor.authorLenk, Peter John
dc.dateSeptember 1985
dc.date.accessioned2013-02-15T23:34:16Z
dc.date.available2013-02-15T23:34:16Z
dc.date.issued1985-09
dc.identifier.urihttp://hdl.handle.net/10945/28596
dc.descriptionApproved for public release; distribution is unlimited
dc.description.abstractThe modelling of nonlinear and multidimensional systems from input and/or output measurements is considered. Tensor concepts are used to reformulate old results and develop several new ones. These results are verified through non-trivial computer simulations. A generalized tensor formulation for the modelling of discrete-time stationary nonlinear systems is presented. Tensor equivalents of the normal equations are derived and several efficient methods for their solution are discussed. Conditions are established that ensure a diagonal correlation tensor so that a solution can be obtained directly without matrix inversion. Using a tensor formulation, a new proof of the Generalized Lattice Theory is obtained. Tensor extensions of the Levinson and Schur algorithms are presented. New two-dimensional (2-D) lattice parameter models are derived. Using the tensor form of the Generalized Lattice Theory the 2-D multi-point error order-updates are decomposed into 0(N ) single point updates. 2-D extensions of the Levinson and Schur algorithms are given. The quarter plane lattice is considered in detail, first in a general form, then in forms which reduce the computational complexity by assuming shift-invariance. Based on the 2-D lattice, a new nonlinear lattice model is developed. The model is capable of updates in the nonlinear as well as time order.
dc.description.urihttp://archive.org/details/tensorformulatio00lenk
dc.language.isoen_US
dc.rightsCopyright is reserved by the copyright owner
dc.subject.lcshPhysicsen_US
dc.titleTensor formulations for the modelling of discrete-time nonlinear and multidimensional systems.en_US
dc.typeThesisen_US
dc.contributor.corporateNaval Postgraduate School (U.S.)
dc.contributor.departmentElectrical and Computer Engineering
dc.subject.authornonlinear systemen_US
dc.subject.authornonlinear system modellingen_US
dc.subject.authorVolterra seriesen_US
dc.subject.authortensor form of Volterra seriesen_US
dc.subject.authoralternate coordinate systemsen_US
dc.subject.authormoving averageen_US
dc.subject.authorautoregressiveen_US
dc.subject.authorRLS algorithmen_US
dc.subject.authorLMS algorithmen_US
dc.subject.authormultidimensional system modellingen_US
dc.subject.authorgeneralized lattice modelsen_US
dc.subject.authorLevinson algorithmen_US
dc.subject.authorSchur algorithmen_US
dc.subject.author2-D lattice modelsen_US
dc.subject.authornonlinear lattice modelsen_US
dc.subject.authorsystolic arraysen_US
dc.description.serviceLieutenant(N), Canadian Armed Forces
etd.thesisdegree.namePh.D.en_US
etd.thesisdegree.levelDoctoralen_US
etd.thesisdegree.grantorNaval Postgraduate Schoolen_US


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