Suppose $X(\omega)$ is the discrete Fourier transform (DFT) of a sequence of arbitrary complex numbers $x(n)$. What is the DFT of a new sequence $x(2n)$?
Here is my thinking:
The DFT of $x(2n) = $ $$ \sum_{n=-\infty}^{\infty} x(2n)e^{-j \omega n} $$
But at this point I am stuck. Somehow the answer is $X(\frac{\omega}{2})$