- #1
fishingspree2
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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 eat with C and a complex is a periodic signal. I fail to see how.
Let C = |C| ejα (exponential form of a complex number)
and a = r + jω (rectangular form)
Plugging into x(t) = C eat, and using euler's formula
x(t) = |C| ert * [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 ert 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?
Let C = |C| ejα (exponential form of a complex number)
and a = r + jω (rectangular form)
Plugging into x(t) = C eat, and using euler's formula
x(t) = |C| ert * [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 ert 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?