# A very basic question about processing high frequency signals

A standard frequency for a modern computer processor is 1-3 GHz. The frequency of a GPS signal is ~1.5 GHz. My question is how is it possible for a computer to do anything at all with a signal that it can only sample once or twice in a period?

So, let's say that your GPS signal is $s(t)=x(t)\cos(2\pi f_c t)$, where $f_c\approx1.5\,\text{GHz}$. The actual information is in the envelope $x(t)$; the purpose of the cosine is simply to shift ("upconvert") $x(t)$ to some appropriate band. In the receiver, the signal $s(t)$ is "downconverted" to some lower (or even zero) frequency $f_I$, but this is done in the analog domain (i.e. by RF electronics), to obtain $s_1(t)=x(t)\cos(2\pi f_I t)$. The signal $s_1(t)$ has a small bandwidth, so it requires a small sampling rate, that can be handled in the digital domain.