Part D: Time Invariance

When a system is time invariant, any time shifting on the input signal will result in the same shifting of the output signal.

In other words (pictures),

Partd1 ECE301Fall2008mboutin.JPG

implies

Partd2 ECE301Fall2008mboutin.JPG


Example of a Time-Invariant System

An example of a time-invariant system is $ x(t) = \frac{1}{t} $.

As you can see from the graph, $ y $2$ (t) $ (the blue dotted graph) is the same graph of </math>1$ (t) $ (the green graph), but shifted to the right by $ t $0$ =2 $. Untitled6 ECE301Fall2008mboutin.jpg


Example of a System That Is Not Time-Invariant

An example of a system that is not time-invariant would be $ x(t) = (1-t)*(t-1) $.

The graph below shows that the resulting signal is not a shifted input signal. Untitled7 ECE301Fall2008mboutin.jpg

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Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett