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  1. $$x(t) = \cos(2 \pi t) \cdot u(t)$$ $$y(t) = x(t) + x(-t)$$Is $y(t)$ periodic. If so, what is the $T$?

  2. $$x(t) = \sin(2 \pi t) \cdot u(t)$$ $$y(t)= x(t) + x(-t)$$ Is $y(t)$ periodic?

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    $\begingroup$ Can I please ask you to edit your question with the progress you have made so far on answering these questions? $\endgroup$ – A_A Mar 12 '17 at 7:28
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    $\begingroup$ Indeed, without showing any attempt, I don't really know how to help you. These are very basic homework problems, and I get the feeling that you should maybe go through your learning material again if you can't answer them by, for example, making a trivial drawing of the two $y(t)$s you describe. $\endgroup$ – Marcus Müller Mar 12 '17 at 10:58
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    $\begingroup$ By the way, hint, whether $y$ are periodic or not depend on the exact definition of $u$. So, if you want a solution, I think you should ask yourself what the value of $u(0)$ is. There's different common definitions of that. $\endgroup$ – Marcus Müller Mar 12 '17 at 12:13
  • $\begingroup$ Hint: Draw a picture of the signal. Another hint: To figure out if a signal is periodic, you should be able to find a constant $T$ such that $y(t-T) = y(t)$ for every $t$. Can you think of such a $T$? $\endgroup$ – Atul Ingle Mar 15 '17 at 20:08
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Yes it is. Y(t), X(t) have the same periodicity periode for the sin signal. The cos signal is not periodic.

That is of course assuming that u(t) is the unit step function with u(0) =1.

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    $\begingroup$ You have answered it wrongly. Please edit your answer. $\endgroup$ – user3161880 Mar 16 '17 at 10:01

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