(Linear System)
(Example)
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== Example ==
 
== Example ==
 
<pre>
 
<pre>
For function y=2t+1, its derivitive y'=2
+
Let:
y' is a constant
+
    x1(t)=t, x2(t)=t+1;
Thus y=2t+1 is a linear system.
+
    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
For function y=sin(t), y'=cos(t)
+
y' is not a constant
+
Thus y=sin(t) is a non-linear system.
+
 
+
 
</pre>
 
</pre>

Revision as of 15:28, 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

Alumni Liaison

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