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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> | ||
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== Definition of Non-Linear System == | == Definition of Non-Linear System == | ||
Revision as of 09:09, 16 September 2008
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)\! $
