(→Linear System) |
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A system is called "Linear" | A system is called "Linear" | ||
if for any constants a,b and for any inputs x1(t),x2(t),(x1[n],x2[n]) | if for any constants a,b and for any inputs x1(t),x2(t),(x1[n],x2[n]) | ||
| − | yielding output y1(t),y2(t) | + | yielding output y1(t),y2(t),respectively, the respond to a*x1(t)+b*x2(t) is a*y1(t)+b*y2(t) |
== Example == | == Example == | ||
Revision as of 15:20, 12 September 2008
Linear System
A system is called "Linear" if for any constants a,b and for any inputs x1(t),x2(t),(x1[n],x2[n]) yielding output y1(t),y2(t),respectively, the respond to a*x1(t)+b*x2(t) is a*y1(t)+b*y2(t)
Example
For function y=2t+1, its derivitive y'=2 y' is a constant Thus y=2t+1 is a linear system. For function y=sin(t), y'=cos(t) y' is not a constant Thus y=sin(t) is a non-linear system.
