How can I formally determine the period of the following discrete-time function?
$\cos(\frac{\pi}{8}\cdot n^2)$
It's difficult for me to approach this since it is a special property of working in discrete time. I.e. if this function was considered in continuous time then it is not periodic since it's period is constantly changing.
I have noticed that the set of squared numbers are in the pattern {odd, even, odd, even, ... } and I know that $\cos(\pi\times odd) = -1$. Then I get stuck.
I tried using Euler's definition for cos:
$\cos(\theta) = \frac{1}{2}(e^{i\theta}+e^{-i\theta})$
But I haven't gotten anywhere with that. I would really appreciate some help.