We will now introduce two new terms -  "Eigenvalue" and "Eigensignal". These concepts will be used later along with the concept of inner product of signals to introduce the Fourier series.

"Eigen" is a German word meaning "one's own". In the context of Signals & Systems, eigensignals and eigenvalues are described as follows :-

Consider a system with impulse response h(t). A signal x(t) applied to this system produces an output y(t) which is same as the input signal x(t) except for multiplication by a scalar. Then, the signal x(t) is known as an Eigensignal of the system and the multiplication factor is called the Eigenvalue corresponding to the eigensignal. Mathematically,

Here, x(t) is the eigensignal and A is the eigenvalue corresponding to the eigensignal x(t). (Note that A is a constant)