(New page: == Linearity == A system is said to be linear if it satisfies the properties of scaling and superposition. Thus, the following holds true for all linear systems: :Suppose there are two in...) |
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Revision as of 04:31, 9 September 2008
Linearity
A system is said to be linear if it satisfies the properties of scaling and superposition. Thus, the following holds true for all linear systems:
- Suppose there are two inputs
- $ \,x1(t) $
- $ \,x2(t) $
- with outputs
- $ \,y1(t) = C\left\{x1(t)\right\} $
- $ \,y2(t) = C\left\{x2(t)\right\} $
- A linear system must satisfy the condition
- $ \,ay1(t) + by2(t) = C\left\{ax1(t) + bx2(t)\right\} $