(New page: If X1(t) -> system => y1(t) and X2(t) -> system => y2(t) implies a*X1(t)+ b*X2(t) -> system => a*y1(t) + b*y2(t) for any complex number a,b then the system is called linear. ---- E.g...) |
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| − | If X1(t) -> system => y1(t) | + | If X1(t) -> system => y1(t) and X2(t) -> system => y2(t)implies a*X1(t)+ b*X2(t) -> system => a*y1(t) + b*y2(t) |
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| − | and X2(t) -> system => y2(t) | + | |
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| − | implies a*X1(t)+ b*X2(t) -> system => a*y1(t) + b*y2(t) | + | |
for any complex number a,b | for any complex number a,b | ||
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E.g. | E.g. | ||
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y(t)=<math>x^2 (t)</math> is non-linear | y(t)=<math>x^2 (t)</math> is non-linear | ||
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| + | Since a*y1(t) + b*y2(t)=<math>(a*X1(t)+ b*X2(t))^2= (a*X1(t))^2+ 2*(a*X1(t)*(b*X2(t)) + (b*X2(t))^2 | ||
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y(t)=2(x)t is linear | y(t)=2(x)t is linear | ||
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| + | Since a*y1(t) + b*y2(t)=2*(a*X1(t)+ b*X2(t))= 2*a*X1(t)+ 2*b*X2(t) | ||
Revision as of 15:04, 10 September 2008
If X1(t) -> system => y1(t) and X2(t) -> system => y2(t)implies a*X1(t)+ b*X2(t) -> system => a*y1(t) + b*y2(t)
for any complex number a,b
then the system is called linear.
E.g.
y(t)=$ x^2 (t) $ is non-linear
Since a*y1(t) + b*y2(t)=$ (a*X1(t)+ b*X2(t))^2= (a*X1(t))^2+ 2*(a*X1(t)*(b*X2(t)) + (b*X2(t))^2 y(t)=2(x)t is linear Since a*y1(t) + b*y2(t)=2*(a*X1(t)+ b*X2(t))= 2*a*X1(t)+ 2*b*X2(t) $
