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now for <math>aY1(t)+bY2(t)=\ a10t+b10t^2=aX1(t)+bX2(t)</math> | now for <math>aY1(t)+bY2(t)=\ a10t+b10t^2=aX1(t)+bX2(t)</math> | ||
| + | |||
| + | thus the given system<math>Y(t)=\ 5X(t)</math> | ||
==Examples of non linear system== | ==Examples of non linear system== | ||
Revision as of 11:10, 11 September 2008
Linear system
A system is said to be linear if it satisfies the principle of superposition i.e if for an input A the system gives an output X and for an input B the system gives output then for an input ( a*A + b*B ) the system should yield the output as ( a*X + b*B ). Where a and b are any complex numbers.
Examples of linear system
$ X1(t)=\ 2t $
$ X2(t)=\ 2t^2 $
assume the function $ Y(t)=\ 5X(t) $
$ Y1(t)=\ 10t $
$ Y2(t)=\ 10t^2 $
now for $ aY1(t)+bY2(t)=\ a10t+b10t^2=aX1(t)+bX2(t) $
thus the given system$ Y(t)=\ 5X(t) $
