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Hello I just started learning Signals and Systems and I have a question regarding periodic signals.

For instance: $x(t) = \cos(3.2t) + \sin(1.6t) + e ^{j2.8t}$ is periodic because of the HCF of the frequencies.($0.4$ rad/s)

and $x(t) = \cos(4t) + \sin(\pi t)$ isn't because of there is no common factors between $4$ and $\pi$.

But what about this: $x(t) = 6 \sin (12 \pi t) + 4 e ^{ j (8 \pi t + \pi /4)} + 2$

How do I determine whether it is period and its fundamental frequency?

Any help is appreciated!

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  • $\begingroup$ This answer to a related question should also answer your question. $\endgroup$ – Matt L. May 1 '15 at 17:35
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    $\begingroup$ hey, just do the same thing you did before. looks like all of the frequency terms have a $\pi$ factor in there. see what's left when you factor $\pi$ out. $\endgroup$ – robert bristow-johnson May 1 '15 at 18:48
  • $\begingroup$ see MUSIC algorithm and pitch detetcion algorithms $\endgroup$ – Nikos M. May 2 '15 at 7:55
  • $\begingroup$ What got me confused was that the model answer determined the fundamental frequency as HCF of {6, 4 } which is 2. Which in this case is the co-efficient of the signals. Why is this so here? $\endgroup$ – Bolo May 2 '15 at 11:24

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