Exam 1
The problem that I found to be the most confusing was problem 2:
Is the following signal periodic?
$ x(t) = \sum_{k = -\infty}^\infty \frac{1}{(t+2k)^{2}+1}\, $
$ x(t+4) = \sum_{k = -\infty}^\infty \frac{1}{(t+4+2k)^{2}+1}\, $
$ x(t+4) = \sum_{k = -\infty}^\infty \frac{1}{(t+2(2+k))^{2}+1}\, $
Simply set w = 2 + k to obtain: $ = \sum_{k = -\infty}^\infty \frac{1}{(t+2w)^{2}+1}\, $
Since this is equivalent to x(t) the signal is periodic.
