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if I have an example signal in the picture, how canenter image description here i decide its period?

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    $\begingroup$ Sketching a couple of samples should do the work. $\endgroup$ – GKH Dec 30 '19 at 14:46
  • $\begingroup$ You inspect the signal and figure out how often it repeats. @GKH gave you a good way to do that for most of us -- in fact, I encourage you to sketch out the signal for $-8 \le n \le 8$ and post the sketch here. If you you're one of those few who are more comfortable looking at equations than pictures you can probably just figure it out from the summation -- ask yourself what the signal is for m = 0, m = 1, etc., the answer should come to you fairly soon. $\endgroup$ – TimWescott Dec 30 '19 at 15:46
  • $\begingroup$ This question appears to be homework. Complete answers to homework are off-topic, but specific questions about homework are acceptable if they include enough detail. Please edit the question to include more background about what you don't understand. $\endgroup$ – Marcus Müller Dec 30 '19 at 16:17
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It may help you to look at each term separately if you are not used to the math as in:

$$x[n] = 4\sum_{m=-\infty}^{\infty}\delta[n-4m] + 8\sum_{m=-\infty}^{\infty}\delta[n-1-4m]$$

Knowing that $\delta[x]$ is only 1 when x=0, and 0 everywhere else, ask yourself what does n need to be to make those terms go to zero given that m can be any integer? Sketch that out for all n as GKH suggested in his comment.

If this did help you, then I urge you to spend half a day doing multiple variants of this expression so that it becomes second nature (there are no short cuts to that).

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  • $\begingroup$ @Mert Please update your answer once you have the solution to show us what you did $\endgroup$ – Dan Boschen Dec 30 '19 at 20:53

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