(→Part C: Linearity) |
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A system whose output combined with a linear shift is equivalent to the output if the linear shift is on the input of the system. | A system whose output combined with a linear shift is equivalent to the output if the linear shift is on the input of the system. | ||
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| + | An example of a linear system is: | ||
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| + | <math> x(t) = t + 3 </math> | ||
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| + | To prove this: | ||
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| + | <math> Y_1(t) = A*x(t) = Z_1(t) | ||
| + | Y_2(t) = X(At) = Z_2(t) | ||
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| + | Z_1(t) = Z_2(t) </math> | ||
| + | |||
| + | for any number A | ||
Revision as of 09:37, 12 September 2008
Part C: Linearity
My definition of linearity in terms of systems is:
A system whose output combined with a linear shift is equivalent to the output if the linear shift is on the input of the system.
An example of a linear system is:
$ x(t) = t + 3 $
To prove this:
$ Y_1(t) = A*x(t) = Z_1(t) Y_2(t) = X(At) = Z_2(t) Z_1(t) = Z_2(t) $
for any number A
