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<math>ax_1(t)+bx_2(t) -> [System] -> aY_1(t) + bY_2(t)</math> | <math>ax_1(t)+bx_2(t) -> [System] -> aY_1(t) + bY_2(t)</math> | ||
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<math>a_1(t)+x_2(t) -> [System] -> y_1(t) + Y_2(t) -> [a b] -> aY_1(t) + bY_2(t)</math> | <math>a_1(t)+x_2(t) -> [System] -> y_1(t) + Y_2(t) -> [a b] -> aY_1(t) + bY_2(t)</math> | ||
The outcome of people ways are equal so it is Linear. | The outcome of people ways are equal so it is Linear. | ||
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== Non-Linear System Example == | == Non-Linear System Example == | ||
Revision as of 13:48, 12 September 2008
Linearity is defined as a system that contains superposition in the book(Signals and Systems 2nd ed. Oppenheim, 53). How I see it is if the input signal has a magnitude applied to it the output should have a magnitude applied to it. Also if two signals are added it would be as if each signal had went through the system and then had been added.
Linear System Example
$ Y(t) = x(t) $
$ ax_1(t)+bx_2(t) -> [System] -> aY_1(t) + bY_2(t) $
$ a_1(t)+x_2(t) -> [System] -> y_1(t) + Y_2(t) -> [a b] -> aY_1(t) + bY_2(t) $
The outcome of people ways are equal so it is Linear.
Non-Linear System Example
$ Y(t) = x(t)+5 $
$ x_1(t) x_2(t) -> [System] -> Y_1(t) Y_2(t) -> [a b] -> aY_1(t) bY_2(t) = ax_1(t)+a5 $
