# Linear Time Invariant System

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### 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 .

Input | Output | Reason |
---|---|---|

Given | ||

Time invariance | ||

Proportionality | ||

Superposition | ||

Applying the line above to |

Note that the last line is obtained by doing a change of variables, then recognizing the Fourier Transform.