(→Part C: Linearity) |
(→Part C: Linearity) |
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| Line 11: | Line 11: | ||
To prove this: | To prove this: | ||
| − | <math> Y_1(t) = A*x(t) = Z_1(t) | + | <math> Y_1(t) = A*x(t) = Z_1(t)</math> |
| − | Y_2(t) = X(At) = Z_2(t) | + | <math> |
| − | + | Y_2(t) = X(At) = Z_2(t)</math> | |
| + | <math> | ||
Z_1(t) = Z_2(t) </math> | Z_1(t) = Z_2(t) </math> | ||
for any number A | for any number A | ||
Revision as of 08:38, 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
