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== LINEARITY == | == LINEARITY == | ||
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| + | For a system to be called Linear the following two scenarios must yield output signals that are equal to each other. | ||
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| + | 1) Signals '''<math>X_1</math>''' and '''<math>Y_1</math>''' are first multiplied by constants <math>C_1 \in \mathbb{C}</math> and <math>C_2\in \mathbb{C}</math> respectively, then added together and passed through a system that yields a signal '''<math>Z(t)</math>'''. | ||
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| + | 2) Signals '''<math>X_1</math>''' and '''<math>Y_1</math>''' each pass through a system, their results are multiplied by constants <math>C_1 \in \mathbb{C}</math> and <math>C_2\in \mathbb{C}</math> respectively, and then added together yielding a signal '''<math>W(t)</math>'''. | ||
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| + | For this system to be linear, signals '''<math>Z(t)</math>''' and '''<math>W(t)</math>''' must be equal to each other. | ||
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| + | '''<math>Z(t) = W(t)</math>''' | ||
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| + | == LINEAR SYSTEM == | ||
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| + | == NON-LINEAR SYSTEM == | ||
Revision as of 10:17, 12 September 2008
LINEARITY
For a system to be called Linear the following two scenarios must yield output signals that are equal to each other.
1) Signals $ X_1 $ and $ Y_1 $ are first multiplied by constants $ C_1 \in \mathbb{C} $ and $ C_2\in \mathbb{C} $ respectively, then added together and passed through a system that yields a signal $ Z(t) $.
and
2) Signals $ X_1 $ and $ Y_1 $ each pass through a system, their results are multiplied by constants $ C_1 \in \mathbb{C} $ and $ C_2\in \mathbb{C} $ respectively, and then added together yielding a signal $ W(t) $.
For this system to be linear, signals $ Z(t) $ and $ W(t) $ must be equal to each other.
$ Z(t) = W(t) $
