(→Example) |
(→Example) |
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| Line 14: | Line 14: | ||
a*x1(t)-> system ->2at<br> | a*x1(t)-> system ->2at<br> | ||
b*x2(t)-> system ->10bt<br> | b*x2(t)-> system ->10bt<br> | ||
| − | Therefore, the output is 2at + 10bt | + | Therefore, the output is 2at + 10bt <-- answer A |
| − | a*x1(t)+b*x2(t)=at+5bt-> system ->Output=2*(at+2bt)= 2at + 10bt | + | a*x1(t)+b*x2(t)=at+5bt-> system ->Output=2*(at+2bt)= 2at + 10bt <-- answer B |
| + | answer A = answer B, proves that it's a linear system | ||
Revision as of 17:38, 12 September 2008
What Is a Linear System
A linear system has to satisfy these contions:
If the inputs x1(t),x2(t),(x1[n],x2[n]) multiplied/divided by any constant a,b, then the output y1(t),y2(t),(y1[n],y2[n]) will yield a*x1(t)+b*x2(t) --> a*y1(t)+b*y2(t) and respectively
Example
Given:
x1(t)=t, x2(t)=5
System: y(t)=2*x(t)
Thus, y1(t)=2t,y2(t)=10t
So say a,b are any non-zero constant
a*x1(t)-> system ->2at
b*x2(t)-> system ->10bt
Therefore, the output is 2at + 10bt <-- answer A
a*x1(t)+b*x2(t)=at+5bt-> system ->Output=2*(at+2bt)= 2at + 10bt <-- answer B
answer A = answer B, proves that it's a linear system
