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== The following signals are shown to be either an energy signal or a power signal == | == The following signals are shown to be either an energy signal or a power signal == | ||
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| + | <math>\,\!x(t)=e^{-at}u(t)</math> for a > 0 | ||
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| + | solution: | ||
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| + | since <math>Energy(\infty) = \int_{-\infty}^{\infty} \! |x(t)|^2\ dt</math> , | ||
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| + | <math> = \int_{0}^{\infty}\!e^{-2at}dt</math> <math>=\frac{1}{2a} < {\infty}</math> | ||
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| + | therefore x(t) is an energy function because the energy is finite, and not a power function. | ||
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| + | A consequence of this is that P=0. If the energy of the signal was infinite, then the power would be | ||
| + | found to have a finite value. | ||
Latest revision as of 08:24, 5 September 2008
The following signals are shown to be either an energy signal or a power signal
$ \,\!x(t)=e^{-at}u(t) $ for a > 0
solution:
since $ Energy(\infty) = \int_{-\infty}^{\infty} \! |x(t)|^2\ dt $ ,
$ = \int_{0}^{\infty}\!e^{-2at}dt $ $ =\frac{1}{2a} < {\infty} $
therefore x(t) is an energy function because the energy is finite, and not a power function.
A consequence of this is that P=0. If the energy of the signal was infinite, then the power would be found to have a finite value.
