Prior to reading this module, the reader should already have some experience with linear algebra and should specifically be familiar with the eigenvectors and eigenvalues of linear operators. A linear time invariant system is a linear operator defined on a function space that commutes with every time shift operator on that function space. Thus, we can also consider the eigenvector functions, or eigenfunctions, of a system. It is particularly easy to calculate the output of a system when an eigenfunction is the input as the output is simply the eigenfunction scaled by the associated eigenvalue. As will be shown, discrete time complex exponentials serve as eigenfunctions of linear time invariant systems operating on discrete time signals.

Comments:"My introduction to signal processing course at Rice University."