DT/CT Domain Signal Periodicity
That might happen to any signal that is sampled without respecting Nyquist's sampling theorem.

The effect of that theorem is that


  If your signal has a certain bandwidth, then a real-valued sampling must have at least twice the sampling rate; otherwise, you cannot fully represent your continuous-time signal in discrete-time samples.


\$\cos(\text{const.} \cdot n^2)\$ has infinite bandwidth (simply because the higher you set \$n\$, i.e. the longer you look, the faster the cosine oscillates), and hence, there's no way you can properly represent this continuous signal in discrete time. 

So, your signal class is basically "a lot of signals for which you don't respect Nyquist"; that's not a very useful class.