# Periodicity of signals

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?

• Can I please ask you to edit your question with the progress you have made so far on answering these questions? – A_A Mar 12 '17 at 7:28
• 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. – Marcus Müller Mar 12 '17 at 10:58
• 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. – Marcus Müller Mar 12 '17 at 12:13
• 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 $T$? – Atul Ingle Mar 15 '17 at 20:08