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== Example == | == Example == | ||
<pre> | <pre> | ||
| − | + | Let: | |
| − | + | x1(t)=t, x2(t)=t+1; | |
| − | + | y1(t)=2*1(t)= 2*t, y2(t)=x(t)+1= t+2; | |
| − | + | a=2, b=3; | |
| − | + | so, a*x1(t)+b*x2(t)=2*t+3*(t+1)=5*t+6 | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
</pre> | </pre> | ||
Revision as of 16:28, 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)=t+1;
y1(t)=2*1(t)= 2*t, y2(t)=x(t)+1= t+2;
a=2, b=3;
so, a*x1(t)+b*x2(t)=2*t+3*(t+1)=5*t+6
