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== Example == | == Example == | ||
− | + | A)LINEAR | |
− | + | Let: | |
− | y | + | 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*x1(t)+b*x2(t)=at+2bt->system->Output=3*(at+2bt)= 3at+6bt ----------(2) | |
− | + | ||
− | + | ||
− | + | (1)=(2),so linear. | |
+ | |||
+ | B)NON-LINEAR | ||
+ | Let: | ||
+ | x1(t)=t, x2(t)=2t; | ||
+ | System: y(t)=x(t)^2 | ||
+ | Thus, y1(t)=t^2,y2(t)=4t^2 | ||
+ | |||
+ | So say a,b are any non-zero constant | ||
+ | a*x1(t)->system->a*t^2 | ||
+ | + --->Output= a*t^2+4b*t^2 -----(3) | ||
+ | b*x2(t)->system->b*4t^2 | ||
+ | |||
+ | a*x1(t)+b*x2(t)=at+2bt->system->Output=(at+2bt)^2 ----------(4) | ||
+ | |||
+ | (3)!=(4),so non-linear. |
Latest revision as of 17:02, 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
A)LINEAR
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*x1(t)+b*x2(t)=at+2bt->system->Output=3*(at+2bt)= 3at+6bt ----------(2)
(1)=(2),so linear.
B)NON-LINEAR
Let: x1(t)=t, x2(t)=2t; System: y(t)=x(t)^2 Thus, y1(t)=t^2,y2(t)=4t^2
So say a,b are any non-zero constant a*x1(t)->system->a*t^2 + --->Output= a*t^2+4b*t^2 -----(3) b*x2(t)->system->b*4t^2
a*x1(t)+b*x2(t)=at+2bt->system->Output=(at+2bt)^2 ----------(4)
(3)!=(4),so non-linear.