I think almost everything is in the title.
In an exercise, a DTFT is given : $$X(e^{j\Omega}) = \sin(\Omega) + \cos(\Omega/2)$$ The period of this DTFT is $4\pi$. Is that possible? I mean, the definition of the DTFT shows that it is $2\pi$-periodic $$X(e^{j\Omega}) = \sum_{n=-\infty}^\infty x[n]e^{-k\Omega n}.$$
I don't know if a $4\pi$-periodic DTFT has any sense. I'm really confused about this.
Thanks in advance,