HW 2.c Hetong Li ECE301Fall2008mboutin - Rhea

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