Linear Systems
Because we are engineers we will use a picture to describe a linear system:
Where $ a \! $ and $ b\! $ are real or complex. The system is defined as linear if $ z(t)=w(t)\! $
In other words, if in one scenario we have two signals put into a system, multiplied by a variable, then summed together, the output should equal the output of a second scenario where the signals are multiplied by a variable, summed together, then put through the same system. If this is true, then the system is defined as linear.
Example of a Linear System
Let $ y(t)=x(t) \! $. Then:
Thus, the system $ y(t)=x(t)\! $ is linear.
Example of a Non-Linear System
Let $ y(t)=x^2(t) \! $. Then:
Thus, the system $ y(t)=x^2(t)\! $ is non-linear.
