How does the sample rate work on an SDR?

Question

How can an SDR, which has a sample rate of about 32MHz record signals with a frequency of 1GHz? Shouldn't the sample rate be at least two times as high as the frequency or am i missing something?

Answer 1

There are a few different ways to do this:

1. Frequency shifting via multiplying (frequency mixing): Multiplying a signal by a sine wave of a specific frequency produces a new signal which is shifted downward in frequency. Because your data is encoded in a small frequency range (say, 0.999GHz - 1.001GHz), shifting this down to near DC means that you only need to sample up to 2x the signal's bandwidth to get all the information from it.
   This technique works in both the analog and digital domains and has been used since the earliest days of radio in the superheterodyne reciever.
2. Undersampling/Aliasing: If you filter your signal so that only the frequencies you're interested in are present, you can undersample your signal and figure out what the higher frequency values were via aliasing.

Answer 2

One way to do this is bandpass sampling or undersampling. I've copied the text below from an answer I wrote to a slightly different question.

Here, to avoid aliasing distortion, the signal of interest must be bandpass. That means that the signal's power spectrum is only non-zero between $f_L < |f| < f_H$.

If we sample the signal at a rate $f_s$, then the condition that the subsequent repeated spectra do not overlap means we can avoid aliasing. The repeated spectra happen at every integer multiple of $f_s$.

Mathematically, we can write this condition for avoiding aliasing distortion as

$$\frac{2 f_H}{n} \le f_s \le \frac{2 f_L}{n - 1}$$

where $n$ is an integer that satisfies

$$1 \le n \le \frac{f_H}{f_H - f_L}$$

There are a number of valid frequency ranges you can do this with, as illustrated by the diagram below (taken from the wikipedia link above).

In the above diagram, if the problem lies in the grey areas, then we can avoid aliasing distortion with bandpass sampling --- even though the sampled signal is aliased, we have not distorted the shape of the signal's spectrum.