There is a continuous time signal


I want to calculate it's period ($T$) however I didn't find any easy way to calculate it. Is there any formula to convert this signal to a periodic signal form? Is it possible to help me?

  • 3
    $\begingroup$ Hint: $\sum\limits_{n=-\infty}^\infty a_n=\sum\limits_{n=-\infty}^\infty a_{n+1}$. $\endgroup$ – metamorphy Oct 11 '19 at 7:22
  • $\begingroup$ so it's period is $\frac{1}{6}$. Is it true? (@metamorphy) $\endgroup$ – Amin Oct 11 '19 at 9:26

Based on the help from @metamorphy, the answer can be calculated.
If we assume that:
$$a_n=e^{-|6t+n|}$$ Then we can say that: $$\sum_{n=-\infty}^{+\infty}{a_n} = \sum_{n=-\infty}^{+\infty}{a_{n+6T}}$$ This is true for each $6T \in Z$. if we replace it in our $y(t)$ then we get:

so period of $y(t)$ is $6T \in Z$ and smallest (main) period is $T_0=\frac{1}{6}$


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