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'''Linear System''': | '''Linear System''': | ||
| − | A system is said to be linear if 1) the magnitude of the | + | A system is said to be linear if 1) the magnitude of the system output is proportional to the system input, |
| − | 2)it handles two | + | 2)it handles two simultaneous inputs independantly and they do not interact within the system.i.e. if input x produces output X, and input y produces output Y, then an input of x + y will produce an output of X + Y |
| + | Eg: Y(t)=t X(t) | ||
| + | Proof: Y1(t)=t X1(t)....1 | ||
| + | Y2(t)=t X2(t)....2 | ||
| + | Let X3(t) be a linear combination of X1(t) and X2(t) | ||
| + | X3(t)=aX1(t)+bX2(t) | ||
| + | |||
| + | Correspondingly the output can also be represented as the linear combination | ||
| + | Y3(t)=aY1(t)+bY2(t) | ||
| + | |||
| + | NONLINEAR SYSTEMS: | ||
| + | |||
| + | Y[n]=2X[n]+3 | ||
| + | This system is not linear ,as it violates the additivity property. | ||
Latest revision as of 18:51, 11 September 2008
Linear System: A system is said to be linear if 1) the magnitude of the system output is proportional to the system input,
2)it handles two simultaneous inputs independantly and they do not interact within the system.i.e. if input x produces output X, and input y produces output Y, then an input of x + y will produce an output of X + Y
Eg: Y(t)=t X(t) Proof: Y1(t)=t X1(t)....1
Y2(t)=t X2(t)....2
Let X3(t) be a linear combination of X1(t) and X2(t)
X3(t)=aX1(t)+bX2(t)
Correspondingly the output can also be represented as the linear combination
Y3(t)=aY1(t)+bY2(t)
NONLINEAR SYSTEMS:
Y[n]=2X[n]+3 This system is not linear ,as it violates the additivity property.
