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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.

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