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Ex. | Ex. | ||
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The system is y(t)=2x(t+3). | The system is y(t)=2x(t+3). | ||
The output of the signal x1(t)=t is y1(t)=2(t+3)=2t+6. | The output of the signal x1(t)=t is y1(t)=2(t+3)=2t+6. | ||
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The output of the signal x2(t)=t-1 is y2(t)=2(t+3-1)=2t+4. | The output of the signal x2(t)=t-1 is y2(t)=2(t+3-1)=2t+4. | ||
Revision as of 13:57, 12 September 2008
A system is call linear if the system is "distributive".
system(input1+input2)=system(input1)+system(input2)
Ex.
The system is y(t)=2x(t+3).
The output of the signal x1(t)=t is y1(t)=2(t+3)=2t+6.
The output of the signal x2(t)=t-1 is y2(t)=2(t+3-1)=2t+4.
What is the output of the signal x(t)=x1(t)+x2(t)=t+t-1?
y(t)=2(2(t+3)-1)=2(2t+5)=4t+10
This system is linear beacause
y(t)=4t+10
y1(t)+y2(t)=2t+6+2t+4=4t+10
