When is aliasing a good thing? In Hamming's book, The Art of Doing Science and Engineering, he relates the following story:


  A group at Naval Postgraduate School was modulating a very high
  frequency signal down to where they could afford to sample, according
  to the sampling theorem as they understood it.  But I realized if they
  cleverly sampled the high frequency then the sampling act itself would
  modulate (alias) it down.  After some days of argument, they removed
  the rack of frequency lowering equipment, and the rest of the
  equipment ran better!


Are there any other ways to use aliasing as a primary technique for processing a signal, as opposed to a side-effect to be avoided?
The quoted text in the question is a case of using bandpass sampling or undersampling.

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 $f_L &lt; |f| &lt; f_H$.

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.