What is the role of a LPF in oversampling? Lets assume that a signal $x(n)$ is up-sampled by adding 1 zero between two adjacent samples to form a signal $y(n)$. How does a digital LPF give an oversampled version $z(n)$, with more data points? (As show in the image below) I know that the question might seem stupid but the books that I am using don't really explain that part.
@user29568: Your question is very far from stupid. It's a darned good question. To see why time-domain "zero stuffing" generates the additional spectral images, that must be filtered out as described by Fat32, you're welcome to see my explanation of this effect at: http://www.dsprelated.com/showarticle/761.php