Module 2 : Signals in Frequency Domain
Lecture 12 : Introduction to Transformations
   

Now, the eigenvalue can also be thought of as the projection of the impulse response h(t) of the system along the signal , i.e may be regarded as the inner product between the input signal and the impulse response h(t).

This special property of the complex exponential function with respect to LSI systems is one of the inspirations for trying to represent signals in terms of complex exponentials. We shall see soon the consequences of this property.