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== Example of a Non-Linear System == | == Example of a Non-Linear System == | ||
Let <math>y(t)=x^2(t) \!</math>. Then: | Let <math>y(t)=x^2(t) \!</math>. Then: | ||
| − | + | <br> | |
[[Image:Nonlinsystempjcannon2_ECE301Fall2008mboutin.JPG]] | [[Image:Nonlinsystempjcannon2_ECE301Fall2008mboutin.JPG]] | ||
| + | <br> | ||
Thus, the system <math>y(t)=x^2(t)\!</math> is non-linear. | Thus, the system <math>y(t)=x^2(t)\!</math> is non-linear. | ||
Revision as of 12:53, 11 September 2008
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.
