TY - JOUR

T1 - APPROXIMATION OF PHYSICAL MEASUREMENT DATA BY DISCRETE ORTHOGONAL EIGENFUNCTIONS OF LINEAR DIFFERENTIAL OPERATORS

AU - Harker, Matthew

AU - O'Leary, Paul

PY - 2017

Y1 - 2017

N2 - We present a new method for computing the eigenfunctions of a linear differential operator such that they satisfy a discrete orthogonality constraint, and can thereby be used to efficiently approximate physical measurement data. Classic eigenfunctions, such as those of Sturm-Liouville problems, are typically used for approximating continuous functions, but are cumbersome for approximating discrete data. We take a matrix-based variational approach to compute eigenfunctions based on physical problems which can be used in the same manner as the DCT or DFT. The approach uses sparse matrix methods, so it can be used to compute a small number of eigenfunctions. The method is verified on common eigenvalue problems, and the approximation of real-world measurement data of a bending beam by means of its computed mode-shapes.

AB - We present a new method for computing the eigenfunctions of a linear differential operator such that they satisfy a discrete orthogonality constraint, and can thereby be used to efficiently approximate physical measurement data. Classic eigenfunctions, such as those of Sturm-Liouville problems, are typically used for approximating continuous functions, but are cumbersome for approximating discrete data. We take a matrix-based variational approach to compute eigenfunctions based on physical problems which can be used in the same manner as the DCT or DFT. The approach uses sparse matrix methods, so it can be used to compute a small number of eigenfunctions. The method is verified on common eigenvalue problems, and the approximation of real-world measurement data of a bending beam by means of its computed mode-shapes.

KW - eigenfunctions

KW - discrete orthogonality

KW - approximation of measurement data

U2 - 10.1139/tcsme-2017-513

DO - 10.1139/tcsme-2017-513

M3 - Article

VL - 41.2017

SP - 804

EP - 824

JO - Transactions of the Canadian Society for Mechanical Engineering, CSME = Transactions de la Société Canadienne de Génie Mécanique

JF - Transactions of the Canadian Society for Mechanical Engineering, CSME = Transactions de la Société Canadienne de Génie Mécanique

SN - 0315-8977

IS - 5

ER -