I want to know whether the following is periodic or not periodic

Question

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.

$$f(t)=\sum_{n=-\infty}^{+\infty}e^{-(2t-n)}u(2t-n)$$

Answer 1

The function is periodic with period $1/2$ since you have $$ f(t+1/2)=\sum_{n=-\infty}^\infty e^{-(2t-n+1)}u(2t-n+1)=f(t), $$ as you can easily see by an index shift in the sum.

Hope this helps...

Answer 2

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