# DT/CT Domain Signal Periodicity

An interesting thing about a few unique DT signals is that although they may be periodic in the DT domain, they are aperiodic in the CT domain.

One example of such a signal is: $$x[n]=\cos\left(\frac\pi{10}n^2\right)$$ (whose fundamental period is sought out for in this video, at 10:18: https://www.youtube.com/watch?v=AhoeYb6Qq2c).

What are some other examples of periodic DT signals that are aperiodic in CT?

$\cos(\text{const.} \cdot n^2)$ 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.