(→Linearity) |
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If a linear system has a response to exp(2jt) of t*exp(-2jt) and a response to exp(-2jt) of t*exp(2jt), then it's response to cos(2t) must be t*cos(-2t). | If a linear system has a response to exp(2jt) of t*exp(-2jt) and a response to exp(-2jt) of t*exp(2jt), then it's response to cos(2t) must be t*cos(-2t). | ||
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| + | Explanation: | ||
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| + | The system seems to have the following characteristics: | ||
| + | x(t) --> SYSTEM --> t*y(-t) | ||
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| + | Therefore, if we put the change the input from x(t) (above) to cos(2t), then it should output the signal t*cos(-2t). | ||
Revision as of 06:55, 15 September 2008
Linearity
If a linear system has a response to exp(2jt) of t*exp(-2jt) and a response to exp(-2jt) of t*exp(2jt), then it's response to cos(2t) must be t*cos(-2t).
Explanation:
The system seems to have the following characteristics: x(t) --> SYSTEM --> t*y(-t)
Therefore, if we put the change the input from x(t) (above) to cos(2t), then it should output the signal t*cos(-2t).
