# Signal not neriodic if multiplied by decaying exponential?

1. Sep 18, 2010

### SpaceDomain

The signal $$x(t) = e^{jt}$$ is periodic.

The signal $$x(t) = e^{-t}e^{jt}$$ is not periodic.

The decaying exponential makes the complex exponential decay and converge toward zero, but why is it not periodic?

Also, this signal is not considered time limited since it never actually reaches zero. Right?

2. Sep 18, 2010

### klondike

Because you can't find a real T such that x(t)=x(t+nT).

3. Sep 18, 2010