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== Example of a Non-Linear System == | == Example of a Non-Linear System == | ||
| − | + | The following system is non-linear: | |
| + | |||
| + | <math>\,y(t)=2x(t)+3\,</math> | ||
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| + | |||
| + | Proof: | ||
Revision as of 18:36, 11 September 2008
Definition of Linearity
A system is linear if for any inputs $ \,x_1(t), x_2(t)\, $ yielding outputs $ \,y_1(t), y_2(t)\, $, respectively, the response to
$ \,ax_1(t)+bx_2(t)\, $ is
$ \,ay_1(t)+by_2(t)\, $, where $ \,a,b\in \mathbb{C}, a\not= 0 ,b\not= 0\, $.
Example of a Linear System
Blah
Example of a Non-Linear System
The following system is non-linear:
$ \,y(t)=2x(t)+3\, $
Proof:
