As we have seen in this chapter, the concept of an eigenfunction is an extremely importa...

As we have seen in this chapter, the concept of an eigenfunction is an extremely important tool in the study of LTI systems. The same can be said for linear, but time-varying, systems. Specifically, consider such a system with input x(t) and output y(t). We say that a signal ∅(t) is an eigenfunction of the system if

That is, if .

(a) Suppose that we can represent the input x(t) to our system as a linear combination of eigenfunctions ;

(b) that is,