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 .

LTI System
Input Output Reason
Time invariance
Applying the line above to

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