Given that $$ x(t) = \sum_{k = -5}^5 w(t - 2k) $$ where $ w(t) $ is a triangular pulse function, why would this be non-periodic?
From my understanding of the equation, $ w(t) $ will either equal $ 1 $, if $ (t - 2k) = 0 $, or $ 0 $, if $ t $ exists outside the bounds of $ -1 $ and $ 1 $.
I hand-drew the graph of $ x(t) $ between $ 0 $ and $ 10 $ and the function would show signs of repetition within the range of $ k $, hence pushing me to the idea that it IS periodic. I am not too sure how to proceed from here as the answer is non-periodic.
Additionally, the following question has a similar function: $$ x(t) = \sum_{k = -\infty}^{\infty} w(t - 3k) $$ where the answer is that it IS periodic. I do not understand the difference between the two functions.