I want to know whether the following is periodic or not periodic I have a question about system properties of the following function whether it is periodic or aperiodic. 
With an insight, I'd determine the function is aperiodic since the unit-step term looks implying that jump discontinuities occur at odd number times but don't have a detailed solution in mathematical terms.
Many thanks in advance for your help.
$$f(t)=\sum_{n=-\infty}^{+\infty}e^{-(2t-n)}u(2t-n)$$

Hint: Let $a\gt0$. Every function $f$ defined as $$f(t)=\sum_{n=-\infty}^\infty g(at-n),$$ is periodic with period $____$.
