I'm taking a signals and systems class and the textbook (Signals and systems by Oppenheim) says the CT complex exponential of the form x(t) = C e(adsbygoogle = window.adsbygoogle || []).push({}); ^{at}with C and a complex is a periodic signal. I fail to see how.

Let C = |C| e^{jα}(exponential form of a complex number)

and a = r + jω (rectangular form)

Plugging into x(t) = C e^{at}, and using euler's formula

x(t) = |C| e^{rt}* [cos(α+ωt) + j sin(α+ωt)]

What's inside the brackets is obviously periodic but the whole function is obviously not because of the e^{rt}term...

A function is periodic if there exists a T such as x(t) = x(t+T) for any t, and obviously there isn't any such T for the CT complex exponential...

Any clarifications?

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# The CT complex exponential is NOT periodic

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