$$x(t) = \cos(2 \pi t) \cdot u(t)$$ $$y(t) = x(t) + x(-t)$$Is $y(t)$ periodic. If so, what is the $T$?
$$x(t) = \sin(2 \pi t) \cdot u(t)$$ $$y(t)= x(t) + x(-t)$$ Is $y(t)$ periodic?
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4$\begingroup$ Can I please ask you to edit your question with the progress you have made so far on answering these questions? $\endgroup$– A_AMar 12, 2017 at 7:28
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1$\begingroup$ 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 MüllerMar 12, 2017 at 10:58
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1$\begingroup$ 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 MüllerMar 12, 2017 at 12:13
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$\begingroup$ 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 IngleMar 15, 2017 at 20:08
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1 Answer
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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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1$\begingroup$ You have answered it wrongly. Please edit your answer. $\endgroup$ Mar 16, 2017 at 10:01