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== Example of a Linear System == | == Example of a Linear System == | ||
Let <math>y(t)=x(t) \!</math>. Then: | Let <math>y(t)=x(t) \!</math>. Then: | ||
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| + | <math>y_1(t)=x_1(t) y_2(t)=x_2(t) ax_1(t) bx_2(t) ax_1(t)+bx_2(t) \!</math> | ||
Revision as of 11:33, 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:
$ y_1(t)=x_1(t) y_2(t)=x_2(t) ax_1(t) bx_2(t) ax_1(t)+bx_2(t) \! $
