(New page: == Definition of a Linear System == According to Mimi, a system is called "Linear" if for any constants <math> \alpha, \beta \!</math> (part of the Complex Number domain) and for any inp...) |
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Then the response to <math>\alpha x_1(t) + \beta x_2(t)\!</math> is <math> \alpha y_1(t) + \beta y_2(t)\!</math> | Then the response to <math>\alpha x_1(t) + \beta x_2(t)\!</math> is <math> \alpha y_1(t) + \beta y_2(t)\!</math> | ||
| − | + | === Definition of Non-Linear System === | |
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The response to <math>\alpha x_1(t) + \beta x_2(t) \neq \alpha y_1(t) + \beta y_2(t)\!</math> | The response to <math>\alpha x_1(t) + \beta x_2(t) \neq \alpha y_1(t) + \beta y_2(t)\!</math> | ||
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| + | [[Homework_3_ECE301Fall2008mboutin|Back to HW3]] | ||
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| + | [[Main_Page_ECE301Fall2008mboutin|Back to ECE301 Fall 2008]] | ||
Latest revision as of 12:03, 30 January 2011
HW3, Part A: Understanding System's Properties
Definition of a Linear System
According to Mimi, a system is called "Linear" if for any constants $ \alpha, \beta \! $ (part of the Complex Number domain) and for any inputs $ x_1(t), x_2(t)\! $ (or $ x_1[n], x_2[n]\! $) yielding output $ y_1(t), y_2(t)\! $ respectively,
Then the response to $ \alpha x_1(t) + \beta x_2(t)\! $ is $ \alpha y_1(t) + \beta y_2(t)\! $
Definition of Non-Linear System
According to the previous definition of a "Linear" system, a system is called "Non-Linear" if for any constants $ \alpha, \beta \! $ (part of the Complex Number domain) and for any inputs $ x_1(t), x_2(t)\! $ (or $ x_1[n], x_2[n]\! $) yielding output $ y_1(t), y_2(t)\! $ respectively,
The response to $ \alpha x_1(t) + \beta x_2(t) \neq \alpha y_1(t) + \beta y_2(t)\! $
