2
$\begingroup$

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?

$\endgroup$
6
$\begingroup$

In digital signal processing, one almost never deals directly with high-frequency signals. The reason is that the frequency band that a signal occupies is completely irrelevant to the information that the signal conveys; the information exists in the envelope of the signal, which usually can be handled either by a generic CPU, a DSP, FPGA, or ASIC.

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.

Note that for quadrature signals the math is very slightly more complicated; see this question and the complex envlope article in wikipedia.

Note also that a similar process exists in the transmitter: the upconversion to RF is done in the analog domain, after the discrete envelope has been converted to an anlog signal.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.