Linear time-invariant (LTI) continuous-time system

A system is linear if it obeys linear superposition: a superposition of input signals results in an output that is the superposition of the responses of the system to each input signal.

A system is time-invariant (shift-invariant in discrete-time) if, when an input signal is delayed, the response is not changed except that it is delayed by the same amount. Intuitively, time-invariance holds if there is nothing about the definition of the system that is changing with time.

Both properties have to be obeyed for all input signals, and for every possible delay. Let's look at these properties in pictoral form.

Continuous-time linear time-invariant system

Discrete-time linear shift-invariant system

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Example: Continuous-time differentiator system

Example: Discrete-time first difference system

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