Fourier Series, Eigenvalue Problems, and Green's Function

doi:10.1117/3.467443.ch8

Book: Mathematical Techniques for Engineers and Scientists

Author(s): Larry C. Andrews, Ronald L. Phillips

Published: 2003

https://doi.org/10.1117/3.467443.ch8

Author Affiliations +

Abstract

In this chapter we introduce the method of Fourier series for the analysis of periodic waveforms (e.g., power signals). This approach reduces the signal being studied to a spectral representation in which the distribution of power is found to be concentrated at specific frequencies that are harmonically related to a fundamental frequency. In addition, we discuss the related notion of eigenvalue problem for homogeneous boundary value problems, the eigenfunctions of which are used to develop generalized Fourier series. Last, the method of Green's function is introduced for solving nonhomogeneous problems (including eigenvalue problems). By representing the Green's function in a "bilinear" representation, we amalgamate the theory of Fourier series and eigenvalue problems with that of the Green's function method.