Linear Time Invariant System
Linear Time Invariant Systems (LTI Systems)
A linear time invariant system is one that is linear (superposition and proportionality apply) and one that doesn't change with time. For example a circuit with fixed capacitors, resistors, and inductors having an input and an output is linear and time invariant. If a capacitor changed value with time, then it would not be time invariant.
Eigenfunctions and Eigenvalues of an LTI Systems
It is an interesting exercise to show that are eigenfunctions of any LTI system. The eigenvalues are .
|Applying the line above to|
Note that the last line is obtained by doing a change of variables, then recognizing the Fourier Transform.