(→Example) |
(→Example) |
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== Example == | == Example == | ||
| − | |||
Let: | Let: | ||
| − | x1(t)=t, x2(t)= | + | x1(t)=t, x2(t)=2t; |
| − | + | System: y(t)=3*x(t) | |
| − | + | Thus, y1(t)=3t,y2(t)=6t | |
| − | + | So say a,b are any non-zero constant | |
| − | + | a*x1(t)->system->3at | |
| + | + --->Output= 3at+6bt -----(1) | ||
| + | b*x2(t)->system->6bt | ||
| + | |||
| + | |||
| + | a*y1(t)=3at | ||
| + | + ---->Output= 3at+6bt ----------(2) | ||
| + | b*y2(t)=6bt | ||
| + | |||
| + | (1)=(2),so linear | ||
Revision as of 16:56, 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
Let:
x1(t)=t, x2(t)=2t;
System: y(t)=3*x(t)
Thus, y1(t)=3t,y2(t)=6t
So say a,b are any non-zero constant
a*x1(t)->system->3at
+ --->Output= 3at+6bt -----(1)
b*x2(t)->system->6bt
a*y1(t)=3at
+ ---->Output= 3at+6bt ----------(2)
b*y2(t)=6bt
(1)=(2),so linear
